Using x-ax-b-x2-a-b x-a b- findi 103 - 104 ii 5-1 - 5-2 iii 103 - 98 iv 9-7 - 9-8

(i) 103 times; 104 = (100 + 3) (100 + 4) = (100)2 + (3 + 4) (100) + (3) (4) = 10000 + 700 + 12 = 10712 (ii) 5.1 times; 5.2 = (5 + 0.1) (5 + 0.2) = (5) ...

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Standard VI

Mathematics

Addition and Subtraction of Decimals

Using x+ax+b=...

Question

Using (x + a) (x + b) = x² + (a + b) x + ab, find

(i) 103 × 104 (ii) 5.1 × 5.2 (iii) 103 × 98 (iv) 9.7 × 9.8

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Solution

(i) 103 × 104 = (100 + 3) (100 + 4)

= (100)² + (3 + 4) (100) + (3) (4)

= 10000 + 700 + 12 = 10712

(ii) 5.1 × 5.2 = (5 + 0.1) (5 + 0.2)

= (5)² + (0.1 + 0.2) (5) + (0.1) (0.2)

= 25 + 1.5 + 0.02 = 26.52

(iii) 103 × 98 = (100 + 3) (100 − 2)

= (100)² + [3 + (− 2)] (100) + (3) (− 2)

= 10000 + 100 − 6

= 10094

(iv) 9.7 × 9.8 = (10 − 0.3) (10 − 0.2)

= (10)² + [(− 0.3) + (− 0.2)] (10) + (− 0.3) (− 0.2)

= 100 + (− 0.5)10 + 0.06 = 100.06 − 5 = 95.06

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Using (x + a) (x + b) = x2 + (a + b) x + ab, find (i) 103 × 104 (ii) 5.1 × 5.2 (iii) 103 × 98 (iv) 9.7 × 9.8

Using (x + a) (x + b) = x² + (a + b) x + ab, find

(i) 103 × 104 (ii) 5.1 × 5.2 (iii) 103 × 98 (iv) 9.7 × 9.8