ICSE-VIII-Mathematics
05: Playing with Number Class 8 Maths
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- #Section : A
- Qstn #1Write quotient when the sum of 73 and 37 is divided byAns : Sum of 73 and 37 b is to be divided by
- #1-i11Ans : 11
- #1-ii10Ans : 10
Let ab = 73
and ba = 37
∴ a = 7
and b = 3
(i) The quotient of ab + bc i.e (73 + 37) when divided by 11 is a + b = 7 + 3 = 10
(ii) The quotient of ab + ba i.e. (73 + 37) when divided by 10 (i.e. a + b ) is 11
- Qstn #2Write the quotient when the sum of 94 and 49 is divide byAns : Sum of 84 and 49 is to be divide by
- #2-i11Ans : 11
- #2-ii13Ans : 13
Let ab = 94
and ba = 49
∴ a = 9 and b = 4
(i) The quotient of 94 + 49 (i.e 9 + 4 = 13
(ii) The quotient of 94 + 49 (i.e. ab + ba)
When divided by 13 i.e. (a + b) is 11
- #3-i9Ans : 9
- #3-ii4Ans : 4
Let ab = 73 and ba = 37
∴ a = 7 and b = 3
(i) The quotient of 73 - 37 (i.e. ab - bc) when divided by 7 is a - b i.e. 7 - 3 = 4
(ii) The quotient of 73 - 37 (i.e. ab - ba) when divided by 4 i.e. (a - b) is 9
- #4-i9Ans : 9
- #4-ii5Ans : 5
Let ab = 94 and ba = 49
∴ a = 9 and b = 4
(i) The quotient of 94 - 49 i.e. (ab - ba) when divided by 9 is (a - b) i.e. 9 - 4 = 5
(ii) The quotient of 94 - 49 i.e. (ab - ba) when divide by 5 i.e.(a - b) is 9
- Qstn #5Show that 527 + 752 + 275 is exactly divisible by 14.Ans : Property:
abc = 100a + 106 + c ...(i)
bca = 1006 + 10c + a ...(ii)
and cab = 100c + 10a + b ...(iii)
Adding, (i), (ii) and (iii), we get
abc + bca + cab = 111a + 111b + 111c = 111(a + b + c) = 3 × 37 (a + b + c)
Now, let us try this method on
527 + 752 + 275 to check is it exactly divisible by 14
Here, a = 5, 6 = 2, c = 7
527 + 752 + 275 = 3 × 37(5 + 2 + 7) = 3 × 37 × 14
Hence, it shows that 527 + 752 + 275 is exactly divisible by 14.