Multiplication and division can make even the trickiest problems easier. In 11 Plus Maths, they’re essential for tackling sequences, patterns, and logical challenges.
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This is a toughie but you can get through it with trial and error
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To multiply a number by 1,005: first multiply by 1,000, then divide the original number by 2 and move the digits to the left, finally add these two numbers together:
128.2 × 1,005 = (128.2 x 1,000) + ((128.2 ÷ 2) x 10) = 128,200 + (64.1 x 10) = 128,200 + 641 = 128,841 |
To divide a number by 300: first divide by 3, then divide by 100:
14,550 ÷ 300 = (14,550 ÷ 3) ÷ 100 = 4,850 ÷ 100 = 48.5 |
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To multiply a number by 150, first divide by 2, then move the digits 2 places to the left, then multiply the original number by 100, finally add these two answers together:
11,002 × 150 = ((11,002 ÷ 2) x 100) + 11,002 x 100 = (5,501 x 100) + 1,100,200 = 550,100 + 1,100,200 = 1,650,300 |
To divide a number by 9,999, here’s a neat trick - divide by both 10,000 and 100,000,000 and add the two answers together:
350,000 ÷ 9,999 = (350,000 ÷ 10,000) + (350,000 ÷ 100,000,000) = 35 + 0.0035 = 35.0035 |
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To multiply a number by 104, first multiply the number by 100, then add quadruple the original number to it:
1.532 × 104 = (1.532 x 100) + (1.532 x 4) = 153.2 + 6.128 = 159.328 |
To divide a number by 15, first divide by 10, then multiply by 2, and finally divide by 3:
342 ÷ 15 = ((342 ÷ 10) x 2) ÷ 3 = (34.2 x 2) ÷ 3 = 68.4 ÷ 3 = 22.8 |
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To multiply a number by 210, first multiply by 2 and then by 100, next multiply the original number by 10 and add your two answers together:
14.369 × 210 = ((14.369 x 2) x 100) + (14.369 x 10) = (28.738 x 100) + 143.69 = 2,873.8 + 143.69 = 3,017.49 |
To divide a number by 2,000 just divide the number by 2, then by 1,000 – simple!
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27.3 × 98 = (27.3 x 100) - (27.3 x 2) = 2,730 - 54.6 = 2,675.4