Mathematics Tricks - Biodun Omosaku

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4. LESSON 23: DIVIDING WITH DECIMALS. LESSON 24: SIMPLE DIVISION USING CIRCLES. ... What will you need to make these tri
MATHEMATICS TRICKS 30 Maths Tricks to stimulate the left side of the brain.

BIODUN OMOSAKU

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Copyright @ 2016 by

Biodun Omosaku Learning Technologies ISBN: 978-908-390 9

All rights reserved. No part of this book may be reproduced or used in any form or by any means, electronics or mechanical, including photocopying, recording, or by an information storage or retrieval system whatsoever (except for brief quotations in a review) without prior written permission of the publisher.

Published by Biodun Omosaku Learning Technologies (BOLT) 21, Abeokuta Street, Anifowoshe,Ikeja, Lagos Tel; 0802-322-6334, 0809-644-3803 All correspondence should be directed to: [email protected]

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CONTENTS

LESSON 1:

ADDING BY ALTERING.

LESSON 2:

ADDING BY ALTERING (2).

LESSON 3:

ADDING OUT OF ORDER.

LESSON 4:

SUBTRACTING BY ADDING.

LESSON 5:

PERCENT ANALYTICS.

LESSON 6:

MULTIPLICATION THE INDIAN WAY.

LESSON 7:

9 MULTIPLICATION TABLE ON YOUR FINGERS.

LESSON 8:

MULTIPLICATION THE JAPANESE WAY.

LESSON 9:

LEARNING YOUR 13-2O TIMES TABLE.

LESSON 10:

MULTIPLYING 2 DIGIT NUMBER UP TO 100.

LESSON 11:

MULTIPLYING BY ZERO.

LESSON 12:

MULTIPLYING BY 5.

LESSON 13:

SQUARE OF A FIGURE THAT ENDS WITH 5.

LESSON 14:

SQUARE OF ANY OTHER NUMBER.

LESSON 15:

SQUARING A NUMBER CLOSE TO 100.

LESSON 16:

SIMPLE TRICKS TO MULTIPLY BY 11.

LESSON 17:

MULTIPLICATION WITH DIFFERENCE.

LESSON 18:

MULTIPLY WITH 9.

LESSON 19:

MULTIPLYING WITH DECIMAL POINT.

LESSON 20:

SQUARING ANY NUMBER ENDING WITH 1 OR 9.

LESSON 21:

MULTIPLYING FROM LEFT TO RIGHT.

LESSON 22:

SIMPLE DIVISION. 3

LESSON 23:

DIVIDING WITH DECIMALS.

LESSON 24:

SIMPLE DIVISION USING CIRCLES.

LESSON 25:

LONG DIVISION BY FACTORS.

LESSON 26:

DIVISION BY NUMBERS ENDING IN 5.

LESSON 27:

FRACTIONS MADE EASY.

LESSON 28:

MULTIPLYING FRACTIONS

LESSON 29:

USING NEGATIVE NUMBERS.

LESSON 30:

MATHS GAME (NUMBER WORK).

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Dedication

To the genius within every child, Crying for expression.

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ACKNOWLEDGEMENTS This book would not have been possible without the help and immense contributions of some very wonderful people. I am most appreciative of the unwavering support of these people in making this book a reality. First, my adorable wife Joke, for her help, support and understanding. I thank two wonderful, distinct and unique personalities, Emmanuel and Tomisin Omosaku. Tosin gave me the reasons to write this book while Emmanuel supported me to give life to the book. I appreciate you guys. My sincere appreciation also goes to my business partner, Mr. Akin Mekuleyi for believing in me. A big thanks to Tosin Sadiku and Fadekemi for their kind assistance in typing out this work. This acknowledgment will not be complete without appreciating some special friends, Mrs. Titi Iwara Eko for her support, Mr. Abiodun Amuda for all his encouragements when I ran into hitches; and my pastor, Pastor Precious Oshideko for his mentorship. To all of you I say a big thank you.

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About The Author

Biodun Omosaku is the Chief trainer at Biodun Omosaku Learning Technologies, an education solution consulting firm based in Lagos Nigeria. He was once a victim of wrong mindset, attitude and strategy to learning and as a result was an underachiever for many years. His academic story however took a sharp turn when he discovered learning strategies that are based on neuro-science, multiple intelligences and quantum learning. Following this discovery, Biodun was among one of the best students from his state – Ogun State within two terms. He has since been sharing these learning strategies with thousands of students across the nations.

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Introduction I am so excited that you are reading this book. You are simply on your way to becoming a Maths wizard. Please ensure that you thank your mum or dad who has gotten this powerful product for you. In this book, you will discover different ways of adding, subtracting, multiplying and dividing faster than you ever thought possible. As a matter of fact, you will be able to work a lot of Maths without pencil and paper because you will be able to work them in your head. Yes! That’s my promise. Do you know the advantage of that?  You will be able to impress your friends and family.  You will begin to fall in love with Maths because these tricks are built to stimulate your area of brain that handles Mathematics. What will you need to make these tricks work for you?  You will need to practice the tricks many times. You are used to the current methods of solving Maths problems because you have used them severally. For these tricks too to become part of you, you will need to practice them very well. They are fun. You won’t have problem doing this.

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 Don’t rush yourself, this book is yours. Enjoy it; don’t try to know everything in one day. You will be confused. Learn one or two tricks per day.  Ensure you follow instructions. To become a Maths genius, all you need is basic understanding of addition, subtraction, multiplication and division. I will also show you tricks on how to solve fractions, decimals and percentages.  If you read anything in this book that you don’t understand, ask your teacher or another grown up person for help.  If you come across some tricks that you don’t like, (or find difficult), don’t use them. You don’t need to know all the tricks in this book; a few tricks could greatly improve your performance. Now it’s time for us to start. Put on your thinking cap and get ready for a journey into the world of numbers unlike you have ever experienced. You may have developed hatred for Maths because you have tried severally to master it but could not. It is not Maths that you hate, but the failure. After reading this book, you will not hate Maths again because you will begin to make remarkable progress in your Maths. The kids that are good at Maths do not have better brains. They only have better methods. In this lesson, you will learn amazing tricks that will enable you to beat others. Every Maths problem is solved by addition, subtraction, multiplication and division. One question may require you 9

to add, subtract, and divide before you arrive at the answer. If you are good at these basics, you will be able to solve any Maths with ease. If you master the tricks, time will never be against you in any Maths exam again because, you will be able to solve Maths problem with great speed.

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ADDITION

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LESSON 1 ADDING BY ALTERING

This is a powerful trick to add numbers by altering them. Have you noticed that some numbers are easier to add than others? For example, it is easy to add figures that are in friendly whole numbers like 10, 20, 30, 40, 50 60, 70.etc. If you need to add 20 + 30, it is pretty much like adding 2 + 3 and just add back the 0. Now let us use this knowledge for our Maths problems. Suppose you want to add two numbers that are NOT friendly whole numbers, all you need to do is to spot the one that is closer to a friendly whole number like 10, 20, 30 etc. It is easier to add numbers in these friendly whole. Let us see an example:

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Example 1 You are adding some figures, and you get to a point where you need to add 17 + 7 in your head Step 1:

Spot the one that is closer to a friendly whole like 10, 20, 30, etc. In this case both are. Let us use 17

Step 2:

By how much is it lesser than a friendly whole number? In this

case 17 is lesser then 20 by 3 Step 3:

Add 3 to 17

17 + 3 = 20

Step 4:

Remove 3 from 7

7–3=

Your answer is

4 24

That is it 24 Very simple! Let us try another example. Example 2 You are working a Maths question and you get to a point where you need to add 23 + 48. You don‟t need a calculator to do this. You can use your head.

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23 + 48 =? Step 1:

Spot the one that is close to a whole 10, 20, 30, 40, 50, 60, etc. In this case, this is 48.

Step 2:

By how much? 48 is lesser than 50 by 2.

Step 3:

Add the 2 to 48

48 + 2 = 50

Step 4:

Subtract 2 from 23

23 – 2 = 21

Step 5:

Add 50 + 21 (just like adding 5+2)

50 + 21 = 71.

That is it. Your answer is 71. Let us try one more example. Example 3 Add 47 + 34 First ask yourself which one among these two figures is closer to a friendly whole like: 10, 20, 30, 40, 50, etc. and by how much is it lesser than the whole figure. In this case, it is 47 47 is less than 50 by 3

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Add 3 to 47

50

Remove 3 from 34

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Answer is

81

Do you get it? Now it is your turn. Exercise 1. 49 + 25 2. 56 + 39 3. 72 + 19

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(just like adding 5+ 3)

TRICK 2 ADDING BY ALTERING (2) This is a very good trick to add number that ends with 9. It is like the previous method. Whenever you are adding a number that ends with 9 and another number, simply follow these steps: Example 1 29 + 44 =? Step 1;

Add 1 to the number 29

29 + 1= 30

Step 2;

Subtract 1 from the 44

44 - 1 = 43

Step 3;

Add the 43 to 30

30 + 43 = 73 Very Simple!

Now I want you to add this in your head without writing anything down.

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Example 2 Add

59 + 35=?

Step 1:

Add 1 to 59

59 + 1 = 60

Step 2:

Subtract 1 from 35

35 - 1 = 34

Step 3:

Add 34 + 60

60 + 34 = 94

Did you work it off hand? That‟s great! You are becoming a Maths genius already. Let us try one example more. Example 3 Without writing anything down, Add;

19 + 21

Step 1:

Add 1 to 19

1 + 19 = 20

Step 2:

Subtract 1 from 21

21 - 1 = 20

Step 3:

Add 20 + 20

20 + 20 = 40

I tell you, it‟s quite simple. Now do the following exercises.

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Without writing anything down, add the following. EXERCISE: 1. 33 + 44 = 2. 59 + 97 = 3. 89 + 44 =

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LESSON 3 ADDING OUT OF ORDER Like I have pointed out before, it is easier to add numbers in friendly wholes like 10, 20, 30, 40 etc. For example 10 + 20 is easy to add 10 + 20 = 30 (pretty much like saying 1+2 = 3) When you are given a set of numbers to add, Try to quickly spot a combination that can give you a friendly whole 10, 20, 30, etc. Look at this: Example 1 You need to add 6 + 4 + 7 + 3 Step 1:

Look at the 6 and 4

6 + 4 = 10

Step 2:

Look at the 7 and 3

7 + 3 = 10

This is your answer

10 + 10 = 20

Let us look at another example. You are working a Maths question and you got to a point where you need to add 8 + 4 + 2 + 9 + 1.

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This is how to add this in your head. Note; you don‟t have to add this figure in the order they appear above. Step 1:

Look at the 9 and 1

9 + 1 = 10

Step 2:

Look at the 7 and 3

8 + 2 = 10 20

Step 3:

Left with 4, add the 4

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Cool, huh? Example 3 Now you are working a Maths problem and you need to add the following set of numbers 9+2+6+ 7 You should be able to do this addition in your head without writing anything down! Remember that you don‟t have to add them in the order they appear Step 1:

Spot the 9 and 2

Step 2:

Add it to 6

9 + 2 = 11 6 17

Step 3:

Add the 7

7

This is your answer

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Now it is your turn.

Exercise: 1. 9 + 1 + 8 + 6 + 4 2. 2 + 4 + 4 + 6 + 3 3. 7 + 5 + 3 + 9 + 5

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SUBTRACTION

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LESSON 4 SUBTRACTING BY ADDING Subtraction is different from addition. In addition, you can alter the positions of the figures and still get the same answer. E.g. 23 + 19 = 44 and 19 + 23 will still give you 44 In subtraction, if you alter the positions, you will not get the same answer. E.g. 23 – 19 = 4 and 19 – 23 will not give you 4 but – 4. Let me quickly show you a powerful trick to subtract without writing anything down: Example 1 Suppose you need to subtract 54 – 32 Step 1:

Think about what can be added to make 32 become 54. Very easy to know. 32 + 10 = 42

(not up to 54 yet)

42 + 10 = 52

(almost there remaining 2)

52 + 2 = 54 22

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Step 2: Add all you have added to make 32 to 54 as seen by the above arrow that gives you 22. That is your answer. Let us try one more example Example 2 Subtract

72 – 47

Step 1:

Think of what needs to be added to make 47 become 72 47 + 20 = 67 67 + 5 = 72 25

That is your answer

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Now it is your turn. Solve these problems by adding: 62 – 37 50 – 11 84 – 37 41 – 19

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PERCENTAGE

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LESSON 5 PERCENT ANALYTICS Cent means 100. Percent means per 100. Supposed you want to find 15% of 80, how will you do it? The usual (hard) way. That is 15 x 80 100 Then you will start to divide. That is what I call the hard way. To find percentage of a number is very easy. First, there are some facts you need to know. Fact Number I 100% of a number is the same number. Therefore, 100% of 20 is what?

Still 20.

What is 100% of 720?

Still 720.

Do you understand that? Good.

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Fact Number II 50% of a number is half of the number Therefore, 50% of 720 is a half of 720

720 divided by 2 = 360

What is 50% (half) of 80? 40! You are correct. Fact Number III 10% of a number can be gotten by just putting a point before the last digit of the number. Do you understand this one? Let me show you what I mean If you want to know 10% of 450, you don‟t need to calculate anything. Just introduce a point before the last digit of the figure. In this case, zero is the last digit of the figure 450. Just put your point before the zero 45.0 There you have your answer

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Now, what is 10% of N20,000 This is the answer 2000.0 (Just introduce a point before the last digit and rewrite your answer) That gives you

N2,000

Fact Number IV 5% of a number is half of its 10% Once you know 10% of a number, you can easily know its 5%

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Let us say you want to find 5% of 500 Step 1;

Get the 10% of 500 which is 50.0 which is same as 50

Step 2;

5% is half of 10% which is 50/2 = 25

Therefore, 5% of 500 is 25. You can perform all of these operations in your head without writing anything down. Now let us use the facts to do some workings. What is 15% of 80 15% is (10% + 5%) Let us add them 10% of 80

8.0

8

5% of 80 (half of its 10%) 8/2

4

Add together

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That is your answer. Very simple! Let us try another example

Example 2 What is 95% of 720? I hope you will not go the usual (hard) way, 28

like this; 95 x720

Hard way

100 Hint:

95% = 100% - 5%

100% of 720 is still

720

Less 5% of 720 (10%/2) which is 72/2 - 36 Add the two

684

That is your answer. Let us try one more example. Example 3 What is 25% of 860. Hint:

25% =

10% of 860 =

86

+10% of 860 =

86

10% + 10% + 5% (just put point before the last digit)

+ 5% of 860 = 43 25% of 860 =

215

Very simple to do this way. It is even long here because; I am trying to explain to you. Most of the operations can be performed in your head without writing anything down. 29

Now I want you to work the following in your head. Exercise 1. What is 55% of 360? 2. What is 85% of 360? 3. What Is 60% of 42? 4. What is 30% of 720? 5. What is 90% of 260?

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MULTIPLICATION

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LESSON 6 MULTIPLICATION THE INDIAN WAY How well do you know your multiplication table? Do you know them up to 15-20 times table? In our schools, we have been taught how to memorize multiplication table. The reason some students are finding Maths difficult is because they have not mastered their time table very well. Multiplication table cannot hold you back again. In this lesson, I want to show you fun, fast and easy ways to master your multiplication. I am not going to show you how to do your times table the usual (Hard) way. Other kids can do that. It won‟t matter again if you forget one of your time tables. You know why it won‟t matter again? Because, if you forget times table, you can work it out. So, are you ready? Ok Let‟s get started.

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How would you add the following numbers? 7+7+7+7+7+7+7+7=? How many 7 are there to count? 8 It means 7 in 8 places. So when you see 7 x 8, it means 7 in 8 places. Do you understand that? Ok. If you have mastered your multiplication table, you don‟t have problem getting the answer. 7 x 8 = 58 If you are not so good in memorizing your time table, let me show you how you can work out your multiplication table. Example 1 What is 7 x 8 =? Step 1:

Draw a circle under each of the numbers 7 x 8

Step 2:

How far away from 10 7 x 8

3

2 33

7 is further away from 10 by 3 8 is further away from 10 by 2 Step 3:

Subtract cross ways 7

x

8 =5

3

2

i.e. 3 from 8 or 2 away from 7(you will always get the same answer either way) Whatever figure you get is the first figure of the answer. 3 away from 8= 5 2 away from 7= 5 Step 4:

For the last part of the answer, multiply the number in the circle. 3 x 2=6

Therefore: 7 x 8 = 56

3

2

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Let us try another one. Example 2 8 x 6= 48 2

4

Did you get 48? Great! Now do you believe me when I told you multiplication table cannot hold you back again? I want you to try out the following exercises in your head without writing anything down. You can do it. Exercise 9 x 9 =? 8 x 8=?

Answers 64

3.

7x7

49

4.

7x9

63

5.

9x6

54

6.

8x9

72

7.

5x9

45

8.

8x7

56

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LESSON 7 9 MULTIPLICATION TABLE ON YOUR FINGERS Figure 9 is an amazing figure in Maths. You may have noticed. In this lesson, I want to teach you, how you can do 9 multiplication on your fingers. Yes! You heard me well. On your fingers! Now let us start. These are your 10 fingers.

Suppose you want to calculate Example 1 9x2

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Step 1: Stretch your two hands forward facing outside and the back of your hands facing you. 9x2 From the left hand, count 2 and fold the second finger

2

Step 2: Take your answer  Before the folded finger, you have 1 finger. 1 is the first digit of your answer.  After the folded finger, you have 8 fingers. 8 is the second digit of your answer  Put them side by side and you will have 1 8 Therefore 9 x 2 = 18. Very simple!

High five for me! Example 2: 9x6=? th

Step 1: from the left hand, count 6 and fold the 6 finger

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6

Step 2: Take your answer  Before the 6th finger, you have 5 fingers. 5 is the first digit of your answer.  After the 6th finger, you have 4 fingers. 4 is the second digit of your answer.  Put them side by side and you will have

54

Therefore, 9 x 6 = 54 Do you want us to try one more example? Example 3 9x8=? Now this time around, use your own fingers. Stretch your 10 fngers out facing outside (back of your fingers facing you) th

Step 1: Count 8 from your left hand and fold the 8 finger.

8

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Step 2: Take your answer  Before the 8th finger, you have 7 fingers. That is the first digit of your answer,  After the 8th finger you have 2 fingers  Place them side by side 7 2 and that is your answer. Now try these; 9 x 5, 9 x 8.

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LESSON 8 MULTIPLICATION THE JAPANESE WAY The Japanese children are known for their exceptional ability to multiply. This is not because they have better brains than other children. It is simply because they have powerful multiplication tricks that they use to stimulate their brains. I want to teach one powerful technique they use. It is quite fun. I am sure you will like it. This is the trick. If you want to multiply any number, you will represent the digit with lines. Let us do our first example. Example 1: Suppose you want to multiply 23 x 22 Step 1: You will represent the twenty three with lines

23

40

Step 2: You will represent the 22 with lines. Note: the lines must be drawn parallel to the one in step one starting from the bottom.

23

22 6

First digit of the answer

4

Second digit of the answer

+

1

0

Step 3: Pick the points at which the lines meet to determine your answer.  First digit of your answer – pick the points at your extreme left 4 points.  Last digit of your answer- pick the points at your extreme right 6 points  For the last digit of your answer – count the rest of the points 10 points  You cannot write 10 in the middle, you will add one to your first digit and write zero in the middle Step 4: Pick your answer – from left to the right Your answer is

506

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Let us try one more example Example 2 32 x 21 = ?

32

21 2

First digit of the answer

Second digit of the answer

6

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Step I: Represent the 32 with lines – that is the red lines Step 2: Represent the 21 with lines – that is the green lines Step 3: Pick the points the lines meet to determine your answer.  First digit of the answer – count the points where the lines meet at your extreme left side. 6 points.  Last digit of the answer – count the points where the lines meet at your extreme right side. 2 points  For the middle figure – count the remaining points where the lines meet. 7 points Step 4: Pick your answer from left to right

672

Your answer is

672 42

LESSON 9 LEARNING YOUR 13 -20 TIMES TABLE I want to show you a powerful trick to multiply any number between 13 – 20 times tables. Are you ready? Ok Example 1: 19 x 14 = ? You don‟t need to memorize anything to get the answer. As a matter of fact, you can work it out from your head. 19 X 14 = ? Step 1: pick the 19 in the front and add the last digit of the second figure. 19 x 14 = 19 + 4 =

23

Step 2: put zero behind whatever figure you got in step 1 = 230 Step 3: multiply the two last digits (9 x 4) and add to what you got in step 2 19 x 14 - ? = 36 + 230 = 266 That is your answer 266 Let us try another example Example 2: 14 x 15 - ? 43

Solution 14 x 15 = (14 +5) = 19 Put zero = 190

call that (A)

14 x 15 = (4 x 5)= 20

call this (B)

Add A + B = 190 + 20 = 210 Answer is 210 One more example Example 3: 17 x 16 = ? Solution 17 x 16 = 17 + 6 = 23

Add

Put zero

= 230

call that A

17 x 16

= 42

call that B

A+B

272

That is your answer. Very simple! With this trick, you don‟t have problem multiplying from 13 to 20. Please do the following in your head without writing anything down. Exercises 15 x 20, 13 x 12, 15 x 12, 19 x 17, 18 x 16

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LESSON 10 MULTIPLYING 2 DIGIT NUMBERS UP TO 100 If you are to multiply 21 x 31 I am sure you have been taught to do it this way:

x

1

3

4

5

6

5

5

2

5

8

5

In this lesson, I want to teach you an easier method you can use to multiply any 2 digit numbers up to 100. Are you ready for it? Ok Example 1 Multiply

13 x 45

45

Step 1

Step 2

Step 3

1

1

Step 1: multiply the first digits of the numbers you are multiplying. In this case, it is 1 x 4 = 4 Step 2: cross multiply the two numbers and add their values together. 4 x 3 = 12 5x1= 5 17 You can‟t write 17 in the middle therefore take 1 to the first column and write 7 Step 3: Multiply the last digit of the two numbers and that gives me 15. You cant write 15 as the last digit of the answer, therefore take one to the second column and write 5 Finally, take your answer Colum 1: (4 + 1) = 5 Column 2: (7+1)=8 Column 3; you have 5 Your answer is 585. 46

EXERCISES: 1. 17 X 12 = 2. 16 X 19 = 3. 15 X 15

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LESSON 11 MULTIPLYING BY ZERO I suppose you should know this trick but if you don‟t, here is how to multiply number that are in friendly wholes, 10, 20, 200, 300 etc. Assuming you are solving a Maths problem and you get to a point where you need to multiply 20 x 50. How will you do it? The usual (hard) way? i.e.

2

0

x5

0

0

0

1 0

0

1 0

0

0

You don‟t have to go through this long process of multiplying two figures ending with zero. As a matter of fact you should be able to do this in your head. Now let us do this the easier way.

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Example I 300 x 500 Step 1:

Remove the zero (note how many they are) 3 00 x 5 00 Four zeros

Step 2: multiply what you have left. i.e. after removing zeros, you will be left with 3 x 5 3 x 5 = 15 Step 3: put back the four zeros 3 x 5 = 150000 There you have the answer 150,000 Example 2 Multiply 300 x 400 Step 1:

Remove the zeros (four)

Step 2:

multiply the remaining 3 x 4=12

Step 3:

Add back the zeros (the four zeros) 300 x 400 = 120000

That is your answer = 120,000

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Exercises; 1. 320 X 400 = 2. 400 X 200 = 3. 100 X 100 =

50

LESSON 12 MULTIPLY BY 5 Five multiplication table is simple to memorize. If however, you have to multiply any figure by 5, and you are not so good at 5 multiplication table, here is the trick to do it. The easiest way to multiply a number by 5 is to first divide the number into 2, then multiply by 10. Example 1 14 x 5=? Step 1: cut the 14 in half 14 ÷ 2 = 7 Step 2:

multiply what you have got by 10 I.e.

7 x 10 = 70 there you have your answer. Example 2 15 x 5 Step I:

15 ÷ 2 = 7.5

Step 2:

multiply what you got by 10 7.5 x 10

When you multiply 7.5 x 10 it will remove the point in-between the 7.5. You will be left with a whole number = 75 51

Therefore 15 x 5 = 75 Very simple Exercise; 1. 2. 3. 4.

17 X 5 12 X 5 15 X 5 19 X 5

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LESSON 13 SQUARE OF A FIGURE THAT ENDS WITH 5 If you are given a question to find a square of a number that ends with 5, you can use this easy method I am about to show you. Example 1 252 =? Don‟t go the usual (hard) way. 2

5

x 2

5

1 2

5

5 0 6 2 5 The above process is too long. Here is a shorter way to multiply 252 Step 1:

Add 1 to the first digit of the figure. i.e. 2+1=3

Step 2: Multiply the first digit with the new figure you got in step 1 i.e. 2 x 3 = 6

53

There you got the first figure of your answer Step 3: 52 is 25. Just put the 25 behind what you got in step 2 and that is your answer. Therefore, answer to 252 = 625 Let us try another example 352 Step 1:

3+1=4

Step 2:

3 x 4 = 12

Step 3:

Put 25 behind what you have got in step 2 i.e. 1225

That is the answer Example 3 952 Step 1:

add 1 to 9 =10

Step 2:

9 x 10 = 90

Put 25 behind = 9025 Example 4 752 Step 1:

add 1 to 7 7 + 1 = 8

Step 2:

7 x 8 = 56 54

Step 3:

put 25 behind what you got in step 2 = 5625

Exercises Calculate 1. 2. 3. 4. 5. 6.

152 452 252 652 852 752

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LESSON 14 SQUARE OF ANY OTHER NUMBER Now if you need to square any other number aside numbers that end with 5, you can use this trick. Example 1 What is 242 ? I hope you will not go the conventional way. This is what you need to do.

28 24 4 20

560 16 576

Step 1:

24 is more than friendly number 20 by 4

Step 2:

Add the 4 to 24, that gives me 28

Step 3: answer.

Multiply 28 by 20 i.e. 2 x 28 and add back the zero in your That gives you 560

Step 4

Add the square of the 4 which is 16 to what you got in step 3.

56

560 + 16 = 576 Therefore, 242

= 576

Punch your calculator, you will get 576 That is your answer! Let us try one more Example Example 2: 982 = ? This is the way to do it:

96 98 22 100

9600 4 9604

Step 1:

98 is less than 100 by 2

Step 2:

less 2 from 98 that gives me 96

Step 3:

multiply 96 by 100, that gives me 9600

Step 4:

add the square of 2 which is 4

Step 5:

add your answer in steps 3 and 4 = 9600 + 4 = 9604

Check your calculator. What did you get?

57

9604

LESSON 15 SQUARING A NUMBER CLOSE TO 100 This is a good trick to square numbers slightly above 100. Example 1 Now, what is 1032 ? To calculate 1032 is quite simple. Just follow the following steps Step 1: Ask yourself, with how many numbers is the number you want to square greater than 100? In this case it is (103 – 100) 3. Just add the 3 to the original number (103 + 3) = 106. That is the first part of the answer. Step 2: subtract 100 from the number being squared. (103 – 100) = 3. Square the 3 = that is 9 that gives us the last part of the answer. Because 9 is not a 2 digit number, we shall introduce 0 and call it 09. So, your answer is 10609

58

Example 2 1082 = ? Step 1: 108 is more than 100 by 8, therefore, add 108 + 8 = 116. That is the first part of the answer Step 2: remove 100 from 108 that gives us 8. Square of 8 is the reamiaing part of the answer 16 Therefore, the answer is 11616. You want me to try one more? Ok. Example 3: 1122 = ? 100 -112 = 12, therefore add 112 + 12 = 124. That is the first part of the answer. What is 122 =

144

144 is 3 digits. You can‟t write 3 digit behind 124 we got before. Just add 1 in 144 to the 4 in 124 to give you 125 Then, put the remaining 44 behind the 125 That is your answer there. Exercises Try the following: 1022, 1052, 1102, 1062, 1072

59

12544

LESSON 16 SIMPLE TRICKS TO MULTIPLY BY 11 Suppose you are solving a Maths problem, and you need to multiply a figure by 11. I don‟t advise that you do it the usual (hard) way. Use this easier trick Example I; 22 x 11=? I don‟t expect you to go to the usual way i.e. 2

2

x 1

1

2

2

2 2 2 4

2

There is a faster and easier way 22 x 11 Step 1:

Add the two digits of the figure, multiply 11 i.e. 2 + 2 = 4. 60

Step 2: Put whatever you got in the middle of the figure multiplying 11 i.e. 242. There you have the answer

242

Example 2 25 x 11 Step 1:

Add 2 + 5 = 7

Step 2:

put it in the middle of 25 = 275

There, 25 x 11 = 275 Let us consider one more example 74 x 11 =? Step 1:

Add 7 + 4 = 11

Step 2:

put the 11 in between 7 and 4 (you need to be careful here) 714 = 814

We have used this method before. You remember? Exercises 1. 21 x 11 2. 62 x 11 3. 92 x 11

61

LESSON 17 MULTIPLICATION WITH DIFFERENCE If you are asked to multiply 6 times 17, I wouldn‟t expect you to use “circle under” method as I think it is not the easiest way to solve this particular problem. All you could do is to simply multiply 6 times 10 and add 6 times 7. 6 x 10 = 60 6 x 7 = 42 60 + 42 = 102 So our answer is 102 Example 2: How about 6 times 27? 6 x 20 = 120. It can also be gotten 6 x 2 x 10 = 120 6 times 7 is 42. Then, you will add

120 + 42 = 162.

There you have your answer This is much easier than working with positive and negative numbers. It is easy to multiply a two-digit number by a one=digit number. 62

For these types of problems, you have the option of using 60, 70 and 80 as reference numbers. This means that there is no gap in the numbers up to 100 that are easy to multiply. Let‟s try a few more for practice: 7 x 63 = You could use two reference number for this, so we will try both methods. Firstly, let‟s use direct multiplication. 7 x 60 = 420 i.e 7 x 6 x 10 = 420 7 x 3 = 21 420 + 21 = 441 Simple enough Example 3: You need to multiply 8 x 93 Step 1:

8 x 90 = 720 i.e 8 x 9 x 10 = 720

Step 2:

8 x 3 = 24

Step 3:

Add 720 + 24 = 744

63

LESSON18 MULTIPLIYING WITH 9 Anytime you need to multiply any number with 9, this trick will help you to do that easily and faster. Example 1 Suppose you are put on the spot and you are asked;

23 x 9 =?

To solve this problem in your head, all you need to do is to multiply the 23 x 10 and subtract 23 from whatever figure you get. Let us do this. Step 1:

multiply 23 by 10

23 x 10 = 230

Step 2:

subtract 23 from whatever you get

=

This is your answer

23 207

Very simple you said. Let us try one more example 47 x 9 = ? Step 1:

multiply

47 x 10 = 470

Step 2:

subtract 47 from what you got

-47 423

This one is very simple.

64

Example 2: You need to multiply 27 x 9 Step 1: Multiply

27 x 10 = 270

Step 2: Subtract 27 from what you got in step 1 Your answer is

Now try to do the following in your head. 1. 2. 3. 4. 5.

21 x 9 43 x 9 400 x 9 420 x 9 27 x 9

65

- 27 243

LESSON 19 MULTIPLYING WITH DECIMAL POINT The trick here is to ignore the decimal point at the beginning of problem, then put it back (if necessary) at the end of the problem. Let‟s apply this method to our tricking problem. Example1 2.5 x 3 Step 1:

Rewrite the problem without the decimal point. 25 x 3

Multiply

25 x 3 = 75

Step 2:

Put the decimal back in 75 Answer:

7.5

7.5

Example 2 Now let us try a problem with decimal point and zeroes; 200 x 3.3 Step 1:

Rewrite the problem without the decimal and zeroes 2 x 33

Step 2:

multiply

2 x 33 = 66 66

Step 3:

put back the two zeroes

Step 4:

put back the decimal point

The answer is

6,600 660.0

660

Example 3 Multiply

2.3 x 23.2

Step 1: Multiply without the decimal

23 x 232

(2 places of decimal removed) = 5336 Step 2: Add back the decimal (remember 2 places of decimal was removed before) =53.36 That is your answer! Now, it is your turn. 1. 2. 3. 4.

1.2 1.4 2.2 3.5

x x x x

3 3 4 2

67

LESSON 20 SQUARING ANY NUMBER ENDING WITH 1 OR 9 Here is the trick You can use this trick to square any number that ends with 1, like 31, 61, 41 or 21. You can also use it to square any number that ends with 9, like 29, 99, 49. The trick is to multiply together the whole number on either side of the number you are squaring, and then add 1. Let see how it works on our volley ball example. Example 1 21 x 21 (or 212) Step 1:

multiply the two whole numbers on either side of 21.

The two whole number on either sides of 21 are 20 21 22 20 x 22 = 440 Step 2:

Add 1 to 440

440 + 1 = 441

Answer is

441

Let us look at one more example 68

Example 2: Step 1:

19 x 19 (or 192) multiply the two whole numbers on either side of 19

The two whole numbers on the either sides of 19 are 18 19 20 18 x 20 = Step 2:

add 1 to 360

361

There you have your answer

361

Now it is your turn to try the following exercises out: 1. 2. 3. 4. 5.

11 41 31 39 29

x x x x x

360

11 41 31 39 29

69

LESSON 21 MULTIPLYING FROM LEFT TO RIGHT The trick is to split the two digit number into two parts, multiply each part separately, then add the two products together. Since multiples of 10 are easy to multiply, start by splitting out a multiple of 10. Example 1 Let‟s now multiply 13 by 8 Problem: 13 x 8 Step 1:

Split 13 into 2 parts

10 + 3

Step 2:

Multiply the 10 by 8

10 x 8 = 80

Step 3:

multiply the 3 by 8

3 x 8 = 24

Step 4:

Add the 80 and 24

80 + 24 =104

Your answer is

will give 13

104.

Let us try another example Example 2 24 x 7 Step 1:

Split the 24 in two part

20 + 4

Step 2:

Multiply the 20 by 7

20 x 7 = 140 70

Step 3:

Multiply the 4 by 7

4 x 7 = 28

Step 4:

Add the 140 and the 28

140 + 28 = 168 Answer: 168

Now it is your turn 1. 2. 3. 4. 5. 6.

12 15 26 37 18 23

x x x x x x

9 8 6 3 7 8

71

DIVISION

72

LESSON 22 SIMPLE DIVISION Dividing Smaller Numbers. If you have to divide 10 oranges among 5 people, they would receive 2 oranges each. It is just a matter of dividing 10 by 5 = 2 Do you get? This is simple to do because 5 can divide 10 without any remainder. If you have to divide 33 tin of milk among 4 people, they would each receive 8 tin of milk and there would be 1tin of milk left over. It is a matter of dividing 33 by 4 = 8 remainder 1 Thirty three cannot be evenly divided by 4. We call the 1 tin left over the remainder. We would write the calculation like this: 8r1 4 33 Or like this: 4 33 8r1

73

Dividing Larger Numbers: Here is how we would divide a large number. To divide 3,721 by 4, we would set up the problem like this: 9 4 3,721 We begin from the left hand side of the number we are dividing, 3 is the first digit on the left. We begin by asking, what do you multiply by 4 to get an answer of 3? Three is less than 4, so we can‟t evenly divide 3 by 4. So we join the 3 to the next digit, 7, to make 37. What do we multiply by 4 to get an answer of 37? There is no whole number that gives you 37 when you multiply it by 4, we now ask, what will give an answer just below 37? The answer is 9, because 9 x 4 =36. That is as close to 37 as we can get without going above. So, the answer is (9 x 4=36), with 1 left over to make 37. One is our remainder. We would write „‟9‟‟ above the 7 in 37. (Or below, depending on how you set up the problem). The 1 left over is carried to the next digit and put in front of it. The 1 carried changes the next number from 2 to 12. The calculation now looks like this: 9 4 3,721 Or like this: 4 37121 9 74

We now divide 4 into 12. What number multiplied by 4 gives an answer of 12? The answer is 3 as in (3 x 4=12) write 3 above (or below) the 2. There is no remainder as 3 times 4 is exactly 12. The last digit is less than 4 so it can‟t be divided. Four divides into 1 zero times with 1 remainder. The finished problem should look like this: 930 R 1 4 371 21 The 1 remainder can be expressed as a fraction, ¼. The ¼ comes from the 1 remainder over the divisor 4. The answer would be 930 ¼ or 930.25. This is a simple method and should be carried out on one line. It is easy to calculate these problems mentally this way.

75

LESSON 23 DIVIDING WITH DECIMALS. How would you divide 567.8 by 3? We set up the problem in the usual way. 3

567.8

The calculation begins as usual. Step 1: Three divides 5 only once remainder 2. We carry the 2 remainder to the next digit, making 26. Step 2: We write the answer, 1, below (or above) the 5 we divided. The calculation looks like this: 1 3 52 67.8 Step 3: We now divide 26 by 3. 3 divides 26 only 8 times. As in 3 x 8 = 24 with 2 remainder. So the next digit of the answer is 8, with 2 remainder. We carry the 2 to the 7. 18 3

52 62 7.8

Three divides 27 exactly 9 times (9 x 3 = 27), so the next digit of the answer is 9.

76

189 3 52 62 7.8 Note: Because the decimal point follows the 7 in the number we are dividing, it will follow the digit in the answers above the 7. Step 4: 3 divides 8 two times with 2 remainder. Two is the next digit of the answer. We carry the remainder, 2, to the next digit. 189.2 3

52 62 7.8

Because there is no next digit, we must supply a digit ourselves. We can write a whole string of zero‟s after the last digit following a decimal point without changing the number. We are calculating in two decimal places, so we make another division to see how we round off our answer. We will write two more zeros to make three digits after the decimal. 189.26 3

52 62 7.

82 00

Three divides 20 into 6 times (6 x 3=18) with 2 remaining. The remainder is carried to the next digit, making 20 again. Because we will keep ending up with 2 remainder. This will go on forever. 189.266 3

52 62 7.82020

Therefore we round off upward, if the next digit is below 5 we round down. The third digit is 6, so we round the second digit off to 7. Our answer is 189.27. 77

LESSON 24 SIMPLE DIVISION USING CIRCLES Let‟s try a simple example 56 divided 8 7 2

8

3

56

Here is how it works. We are dividing 56 by 8. We set up the problem as above, or, if you prefer, you can set up the problem as below. Stick to the way you have been taught.

8 56 2

7

3

First: We draw a circle below the 8 (the number we are dividing by – the divisor) and then ask, how many do we need to make 10? The answer is 2. So we write 2 in a circle below the 8. We add the 2 to the tens digits number we are dividing 5 is the tens digit of 5T 6U) and get an answer of 7. Write 7 above the 6 in 56. Draw a circle above our answer (7). Again, how many more do we need to make 10? The answer is 3. 78

So we write 3 in the circle above the 7. Now multiply the numbers in the circles 2x3=6 Subtract 6 from the units‟ digit of 56 to get the remainder 6–6=0 There is 0 remainder. The answer is 7 with 0 remainder. Example 2: Here is another example: 75 ÷ 9

2

8 r3 9

75

1

How many away from 10 is the divisor? 1 Add one to the Tens figure (7T 5U). In this case it is 7 (7+1) = 8 That is the first figure of your answer How many away is 8 from 10 = 2 Multiply the figures in the circles i.e 2 x 1= 2 Subtract the 3 from the Unit of your figure, in this case, it is 5 (5-3) = 2 That is your reminder.

So, your answer is 8 R 2 79

Example 2 Here is another example that will explain what we do when the result is too high. 3 7 8

52

2

Eight is 2 below 10, so we write 2 in the circle. Two plus 5 equals 7.we write 7 above the unit digit. We now draw another circle above the 7. How many to make 10? = 3. So we write 3 in the circle. To get the remainder we multiply the two numbers in the circles and take the answer from the units‟ digit. Our work should look like this.

7 8

3

52

2

2 x 3 = 6.

Though that we can‟t take 6 from the units digits, 2. Our answer is too high. To rectify this, we drop the answer by 1 to 6, and write a small 1 in front of the units digit, 2, making it 12. Six is 4 below 10, so we write 4 in the circle.

80

6R4 8

51 2

2

4

We multiply the two circled numbers, 2 x 4 = 8. We take 8 from the units‟ digits, now 12; 12 – 8 = 4. Four is the remainder. The answer is 6 R 4. Test yourself: a) 76 ÷ 9 b) 76 ÷ 8 c) 71 ÷ 8 The answers are: a) 8 R 4 b) 9 R 4 c) 8 R 7

81

LESSON 25 LONG DIVISION BY FACTORS. What are factors? We have already made use of factors when the need 20 as a reference number with our multiplication. To multiply by 20, we multiply by 2 and then by 10. Two times 10 equals 20. We are using factors, because 2 and 10 are factors of 20.Four and 5 are also factors of 20, because 4 times 5 equal 20. Let‟s try long division by 36. What can we use as factors? Four times 9 is 36, and so is 6 times 6. We could also use 3 times 12. Let‟s try out an example using 6 times 6. We will use the following division as an example: 2, 340 ÷ 36 = We can set up the problem like this: 6 6 2,340

82

Or like this: 6

2,340

6

Use the layout you are comfortable with. Now, to get started we divide 2,340 by 6. We use the method we learned in the previous chapter. We begin by dividing the digit on the left. The digit on the left is 2, so we divide 6 into 2. Two is less than 6, so we can‟t divide 2 by 6, so we join 2 to the next digit, 3, to make 23. What number do we multiply by 6 to get an answer of 23? There is no whole number that gives you 23 when you multiply it by 6. We now ask, what will give an answer just below 23? Three times 6 is 18. Four times six is 24, which is too high, So our answer is 3. Write 3 above the 3 of 23. Subtract 18(3 x 6) from 23 to get an answer of 5 for our remainder. We carry the 5 remainder to the next digit, 4, making it 54. Our work so far looks like this: 6

3

6

2,3540

We now divide 6 into 54. What do we multiply by 6 to get an answer of 54? The answer is 9. Nine times 6 is exactly 54, so we write 9 and carry no remainder. 83

Now we have one digit left to divide. Zero divided by 6 is 0, so we write 0 as the final digit of the first answer. Our calculation looks like this: 6

390

6

2,3540

Now we divide our answer, 390, by the second 6. Six divides into 39 six times with 3 remainder (6 x 6 = 36). Write 6 above the 9 and carry the 3 remainder to make 30. 6 6

393 0

6

2,3540

Six divides into 30 exactly 5 times, so the next digit of the answer is 5. Our answer is 65 with no remainder. Depending on which layout you use, your final calculation would look like one of these! 6

3930

6

2,3540

6

2,3540 3930 65

84

LESSON 26 DIVISION BY NUMBERS ENDING IN 5 To divide by a two-digit number ending in 5, double both numbers and use factors. As long as you double both numbers, the answer doesn‟t change. Think of 4 divided by 2. The answer is 2. Now double both numbers. It becomes 8 divided by 4, the answer remains the same. (This is why you can cancel fractions without changing the answer.) Let‟s have a try: Example 1 1,120 ÷ 35 = Double both numbers... Two times 11 is 22, and two times 20 is 40; so 1,120 doubled is 2,240. Thirty-five doubled is 70. The problem is now. 2,240/70 = To divide by 70, we divide by 10, then by 7. We are using factors. 2,240 ÷ 10 = 224 224 ÷ 7 = 32. 85

This is an easy calculation. Seven divides into 22 three times (3 x 7 = 21) with 1 remainder, and put 1 in front 4, it becomes 14.7 divides 14 two times. This is a useful shortcut for division by 15, 25, 35 and 45. You can also use it for 55. This method also applies to division by 1.5, 2.5, 3.5, 4.5, and 5.5. Let‟s try another: Example 2 512 ÷ 35 = Five hundred doubled is 1,000. Twelve doubled is 24. Therefore 512 doubled is 1,024. 35 doubled is 70. The problem is now: 1,024 ÷ 70 Divide 1,024 by 10, then by 7. 1024 ÷ 10 = 102.4 102.4 ÷ 7 = Seven divides ten once; 1 is the first digit of the answer. Carry the 3 remainder to the 2, giving 32. 32 ÷ 7 = 4.4 We now have 2 answers which are 1 and 4 with a remainder 4. We carry the 4 to the next digit, 4 to get 44. Don‟t forget to put your point. 44 ÷ 7 = 6 R 2 Our answer is 14.6 R 2. 86

We have to be careful with the remainder. The 2 remainder we obtained is not the remainder for the original problem. We will now look at obtaining a valid remainder when we divide using factors. Test yourself: Try these for yourself, calculating the remainder. a). 2,345 ÷ 36 = b). 2, 713 ÷ 25 = The answers are: a). 65 R 5. b). 108 R 13.

87

FRACTIONS

88

LESSON 27 FRACTIONS MADE EASY When I was in primary school, I noticed that many of my teachers had problems when they had to explain fractions. But fractions are easy. Working With Fractions. Now we are going to learn how to work with fractions by; a). Adding fractions. If we are adding quarters, the calculation is easy. One quarter plus onequarter makes two quarters, or a half. If you add another quarter you have three-quarters. If the denominators are the same, you simply add the numerators. For instance, if you wanted to add one-eighth plus two-eighth, you would have an answer of three-eighths. Three-eighths plus eighth gives an answer of six-eights. How would you add one-quarter plus one=eight? 1/4 + 1/8 = If you change the quarter to 2/8; then you have an easy calculation of 2/8 + 1/8.

89

It is not difficult to add 1/3 and 1/6. If you can see that 1/3 is the same as 2/6, then you just add the sixths together. So 2/6 plus 1/6 equals 3/6. You just add the numerators. This can be easily seen if you are dividing slices of a cake. If the cake is divided into 4 slices, and you eat 1 piece (1/4) and your friend has 2 pieces (2/4), you have eaten 3/4 of the cake.

Example 2: 1÷3 + 2÷5 = 1

+

3

2 5

=

5 + 6

=

15

11 15

1 x 5 = 5. 3 x 2 = 6. 5 + 6 = 11. 90

Step 1:

Eleven is the top number (the numerator) of the answer.

Now we multiply the bottom numbers (the denominators) to find the denominator of our answer. 3 x 5 = 15. The answer is 11÷15. Example 3: Here is another example: Multiply crossways. 3/8 + 1/7 = 3 8

+

1

=

7

21 + 8

=

56

29 56

3 x 7 = 21 8x1= 8 21 + 8 = 29 We add the totals for the numerator, which gives us 29. Then we multiply the denominators! 8 x 7 = 56. This is the denominator of the answer. Our answer is. 29/56

91

LESSON 28 MULTIPLYING FRACTIONS Here is how to do it. We simply multiply the numerators to get the numerator of the answer, and we multiply the denominators to get the denominator of the answer. Easy! Let‟s try it to find; ½ of 12 = 1

x

2

12

= 12

1

2

= 6

Any whole number can be expressed as that number over (divided by) one. So, 12 is the same as 12/1. Let‟s try another: Example 3 2

x

3 2 3

4

=

5 x

4 =8 5 = 15

92

To calcuate the answer, we multiply 2 x 4 to get 8. That is the top number of the answer. To get the bottom number of our answer, we multiply the bottom numbers of the fractions. 3 x 5 = 15 The answer is 8 ÷ 15. It is as easy as that. What is half of 17? 17

x

1

1

=

2

Multiply the numerators. 17 x 1 = 17 Seventeen is the numerator of the answer. Multiply the denominators 1x2=2 Two is the denominator of the answer. So, the answer is 17 divided by 2, which is 8 with 1 remainder. The remainder goes to the top (numerator) and the 2 at the bottom remains where it is for the answer. Our answer is 81/2. Dividing Fractions. In the previous section we multiplied 17 by ½ to find half of 12. How would you divide 17 by 1/2? Let‟s assume we have 17 orange in half (divide by ½), we would have enough for everyone, plus some left over. 93

If we cut an orange in half, we get 2 pieces for each orange, so we have 17 oranges but 34 orange halves, dividing the orange makes the number bigger. So, to divide by one-half we can actually multiply by 2, because we get 2 halves for each orange. So 17/1 ÷ 1/2 is the same as 17/1 x 2/1. To divide by a fraction, we turn the fraction we are dividing by upside down and mke it a multiplication. That‟s not too hard! Who said fractions are difficult?

Test yourself. Try these problems in your head: a) b) c) d)

1/2 1/3 2/5 1/4

÷ 1/2 = ÷ 1/2 = ÷ 1/4 = ÷ 1/4 =

Here are the answers. How did you do? a) b) c) d)

1. 2 / 3. 8 / 5 or 13/5. 1.

94

LESSON 29 USING NEGATIVE NUMBERS I debated with myself whether this section should be included in the book. If you find it difficult, don‟t worry about it. Try it anyway. But you may find this quite easy. It involves using positive and negative numbers to solve problem in direct multiplication. If you are multiplying a number 79, it may be easier to use 80 -1 as your multipier. Multiplying by 79 means you are multiplying by two high numbers and you are likely to have high subtotals. Let‟s try it. 68 x 79 = We set it up as! 6 8 8–1 We begin by multiplying the unit digits. Eight times minus 1 is minus 8. We don‟t write -8. We borrow 10 from the tens column and write 2, which is left over when the minus the 8. We carry -1 (ten), which we borrowed, to the tens column.

95

The work looks like this: 6 8 8 -1 -1

2

Now we multiply crossways. Eight times 8 is 64 and 6 times -1 is -6 = 64 – 6 = 58. We substract the 1 that was carried (because it was -1) to get 57, we write the 7 and the 5.

5

6

8

8

-1

7

-1

2

For the final step we multiply the tens digits 6 x 8 = 48 48 + 5 = 53 We add the 5 that was carried. Answer = 5,372.

96

LESSON 30 MATHS GAME NUMBER WORDS Let us round off on a lighter mood. I discovered that Maths is a magic just that it doesn‟t involve other lies of magic. If you assign figures to the 24 English alphabets, some important words adds up to 100. I really do not think this is just a coincidence. Let us examine and explore. Step 1 Assign numbers to each alphabet; A = 1; B = 2; C=3 etc A=1 J=10 S=19

B=2 C=3 D=4 E=5 F=6 G=7 H=8 I=9 K=11 L=12 M=13 N=14 O=15 P=16 Q=17 R=18 T=20 U=21 V=22 W=23 X=24 Y=25 Z=26

Step 2 Convert the alphabets in a word to numbers and find the word‟s total.

97

Let us try it for my name; BIODUN B=2 I= 9 0 = 15 D=4 U = 21 N = 14 Total

65

Wow! My name is not up to 100% Let us try Mathematics; Pick the corresponding figure for each alphabet that forms the word Mathematics and you will have:

Challenge for you: Use the table below to find a word that will total 100 A=1,

B=2,

C=3,

D=4,

E=5,

F=6,

L=12,

M=13, N=14,

U=21,

V=22,

O=15,

P=16,

Q=17, R=18,

W=23, X=24,

Y=25,

Z=26,

98

G=7,

H=8,

I=9

S=19,

T=20,

J=10

K=11,

Solution: TELESCOPE = 20 + 5 + 12 + 5 + 19 + 3 + 15 + 16 + 5 = 100 SQUARES

= 19 + 17 + 21 + 1 + 18 + 5 + 19 = 1 + 5 + 17 + 18 + 2x19 + 21 = 100

AN EXCELLENT ANWSER IS EXCELLENT A=1,

B=2,

C=3,

D=4,

E=5,

F=6,

L=12,

M=13, N=14,

U=21,

V=22,

G=7,

O=15,

P=16,

Q=17, R=18,

W=23, X=24,

Y=25,

Z=26,

H=8,

I=9

S=19,

T=20,

E-X-C-E-L-L-E-N-T 5 + 24 + 3 + 5 + 12 + 12 + 5 + 14 + 20 = 100 See the following words in their other of importance to success in academic and life in general: H-A-R-D-W-O-R-K 8+1+18+4+23+15+18+11

=

98%

=

96%

=

100%

K-N-O-W-L-E-D-G-E 11+14+15+23+12+5+4+7+5 A-T-T-I-T-U-D-E 1+20+20+9+20+21+4+5

99

J=10

K=11,

On this note I want to sign out. ATTITUDE IS EVERYTHING. Your attitude will determine your altitude in life. Practice these tricks as many times as you can until they become part of you. The aim for this trick is to stimulate your brain, when you are going through it again, make sure you do them off hand. Hope you have enjoyed the journey so far. I wish you the very best. To your success, Mr. Biodun Omosaku www.biodunomosaku.com 0802-322-6334

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