playing with numbers class 8

covers all the concepts

1. MATHS PORTFOLIO

2. PLAYING WITH NUMBERS TOPIC :

3. INTRODUCTION We have studied different types of numbers such as natural numbers, whole numbers, integers and rational numbers. We have also studied interesting properties about them.

4. The general form of numbers helps us in solving puzzles or number games. A two digit number ab can be written in general form as ab = 10a + b. NUMBERS IN GENRAL FORM Let us take the number 52 and write it as  52 = 50 + 2 = 10 × 5 + 2 In general, any two digit number ab made of digits a and b can be written as ab = 10 × a + b = 10a + b  ba = 10 × b + a = 10b + a Let us now take number 351. This is a three digit number. It can also be written as 351 = 300 + 50 + 1 = 100 × 3 + 10 × 5 + 1 × 1 Similarly , In general, a 3-digit number abc made up of digits a, b and c is written as abc = 100 × a + 10 × b + 1 × c  = 100a + 10b + c In the same way,                                                    cab = 100c + 10a + b bca = 100b + 10c + a and so on.

5. GAMES WITH NUMBERS Think of a number. Multiply it by 3. Add 6. Divide this number by 3. Subtract the number from Step 1 from the answer in Step 4 . AND THE ANSWER WILL BE 2 LET’S CHECK Let’s take the number 24 So, 24 x 3 = 72 72 + 6 = 78 78 / 3 = 26 26 – 24 = 2 AND THE ANSWER IS 2

6. GAMES WITH NUMBERS Think of any three-digit number in which each of the digits is the same. Add up the digits. Divide  the three-digit number by the answer in Step 2. The answer is 37. LET’S CHECK LET’S TAKE 222 2+2+2= 6 222 / 6 = 37 AND THE ANSWER IS 37

7. GAMES WITH NUMBERS Take any three-digit number and write it twice to make a six-digit number. Examples include 371371 or 552552. Divide the number by 7. Divide it by 11. Divide it by 13. The answer is the three digit number Lets take 242 so it turns 242242 242242 / 7 = 34606 34606 / 11 = 3146 3146 / 13 = 242 The answer is 242 Six Digits Become Three

8. Here, we have puzzles in which letters are used in place of digits in an arithmetic ‘sum’, and the problem is to find out the digit represented by the letter used. We shall confine here to the problems of addition and multiplication. The following rules are followed while solving such puzzles. Rules Each letter must stand for just one digit. Each digit must be represented by just one letter. The first digit of a number cannot be zero. LETTERS INSTEAD OF NUMBER

9. SOLVE THESE

10. A number is divisible by 2  if the last digit is 0, 2, 4, 6 or 8 . 168 is divisible by 2 since the last digit is 8 TEST OF DIVISBILITY BY 2

11. A number is divisible by 3  if the sum of the digits is divisible by 3 . 168 is divisible by 3 since the sum of the digits is 15 (1+6+8=15), and 15 is divisible by 3. TEST OF DIVISIBLITY BY 3

12.   A number is divisible by 4  if the number formed by the last two digits is divisible by 4 . 316 is divisible by 4 since 16 is divisible by 4. TEST OF DIVISIBLITY BY 4

13. A number is divisible by 5  if the last digit is either 0 or 5 . 195 is divisible by 5 since the last digit is 5. TEST OF DIVISIBLITY BY 5

14. A number is divisible by 6  if it is divisible by 2  AND  it is divisible by 3 . 168 is divisible by 6 since it is divisible by 2  AND  it is divisible by 3. TEST OF DIVISIBLITY BY 6

15. Double the last digit and subtract it from a number made by the other digits. The result must be divisible by 7.  672 (Double 2 is 4, 67−4=63, and 63÷7=9)  Yes TEST OF DIVISIBLITY BY 7

16. A number is divisible by 8  if the number formed by the last three digits is divisible by 8 7,120 is divisible by 8 since 120 is divisible by 8 7,120 is divisible by 8 since 120 is divisible by 8 TEST OF DIVISIBLITY BY 8

17. A number is divisible by 9  if the sum of the digits is divisible by 9. 549 is divisible by 9 since the sum of the digits is 18 (5+4+9=18), and 18 is divisible by 9. TEST OF DIVISIBLITY BY 9

18. TEST OF DIVISIBLITY BY 10 A number is divisible by 10 if the last digit is 0. 1,470 is divisible by 10 since the last digit is 0.

19. MATHS TRICKS

20. If you multiply 6 by an even number, the answer will end with the same digit. The number in the ten's place will be half of the number in the one's place. Example: 6 x 4 = 24. Multiplying by 6

21. This is a quick way to multiply two-digit numbers by 11 in your head. Separate the two digits in your mind. Add the two digits together. Place the number from Step 2 between the two digits. If the number from Step 2 is greater than 9, put the one's digit in the space and carry the ten's digit. Examples: 72 x 11 = 792. 57 x 11 = 5 _ 7, but 5 + 7 = 12, so put 2 in the space and add the 1 to the 5 to get 627 The 11 Rule

22. To remember the first seven digits of , count the number of letters in each word of the sentence: "How I wish I could calculate pi." This becomes 3.141592.   Memorizing  

23. To easily multiply two double-digit numbers, use their distance from 100 to simplify the math: Subtract  each number from 100. Add these values together. 100 minus this number is the first part of the answer. Multiply the digits from Step 1 to get the second part of the answer. Multiply Large Numbers in Your Head

24. Japanese Multiplication Trick

25. Solve The Magic Square Complete the magic square given below so that the sum of the numbers in each row or in each column or along each diagonal is 15 .

26. THANK YOU SO MUCH HOPE YOU GOT TO LEARN SOMETHING