Related calculations use a fact you already know to work out a new calculation quickly.
Look at how each number has changed, then make the same change to the answer.
This is particularly useful when zeros or decimal places have been added or removed.
Common mistake: If both factors in a multiplication are multiplied by 10, the answer is multiplied by 100, not 10. For example, if \(4 \times 3 = 12\), then \(40 \times 30 = 1200\).
Worked example:
Using the fact \(42 \times 15 = 630\), work out \(420 \times 150\).
Step 1
Both factors have been multiplied by 10.
Step 2
So the product is multiplied by 10 × 10, which is 100.
\[630 \times 100 = 63000\]
Answer:
\[420 \times 150 = 63000\]
Worked example:
Using the fact \(432 \times 15 = 6480\), work out \(648 \div 4.32\).
Step 1
Multiply both numbers in the division by 100 to remove the decimal places.
\[648 \div 4.32 = 64800 \div 432\]
Step 2
Since 432 × 15 = 6480, 64800 ÷ 432 = 150.