Multiplication and division help us understand patterns and change. In 11 Plus Maths, they are essential for solving problems that involve growth, sharing, and scaling.
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1?5 × 23 = 23 ÷ 5 = 4 remainder 3 = 43?5. In general, multiplying by 1 over a number is the same as dividing by that number: in this case, 5
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Multiplying by 1?4 is the same as dividing by 4 ? 17 ÷ 4 = 4 remainder 1 = 41?4. In general, multiplying by 1 over a number is the same as dividing by that number: in this case, 4
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To divide by a fraction, invert (turn upside down) the fraction and multiply. LEARN this technique. So, 14 ÷ 3?8 = 14 × 8?3 = (14 × 8) ÷ 3 = 112 ÷ 3 = 37 remainder 1 = 371?3
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To divide by a fraction, invert (turn upside down) the fraction and multiply. LEARN this technique. So, 11 ÷ 2?3 = 11 × 3?2 = (11 × 3) ÷ 2 = 33 ÷ 2 = 16 remainder 1 = 161?2
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21 × 17 = (20 × 17) + 17 = 357. Decrease 21 by 1 and do the multiplication THEN add 17. Be on the LOOKOUT for products that can be simplified: this will enable you to do the calculation in your head
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Remember that dividing by 1 over a number is the same as multiplying by that number: in this case, 2:
24 x 2 = 48
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27 ÷ 5 = 5 remainder 2. As we are dealing with fifths, the remainder becomes 2?5
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To make this easier, first convert 13?4 into quarters:
37 ÷ 13?4 = 37 ÷ 7?4 Next, invert (turn upside down) the fraction and multiply: 37 ÷ 7?4 = 37 × 4?7 = (37 × 4) ÷ 7 = 148 ÷ 7 = 21 remainder 1 = 211?7 |
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Remember that multiplying by 1 over a number is the same as dividing that number: in this case, 20:
3.4 ÷ 20 = (3.4 ÷ 2) ÷ 10 = 1.7 ÷ 10 = 0.17 |
33 x 2 = 66 and 33 x 20 = 660 so 33 x 22 = 66 + 660 = 726. Look for shortcuts like this which allow you to work out the answer in your head
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