Q1.
Using the meaning of multiplication and division, can you explain why multiplying by 5 is the same as dividing by 2 and multiplying by 10?
Answer
Because 5 is half of 10.
5 = 10 ÷ 2
So n × 5 = n × (10 ÷ 2) = (n ÷ 2) × 10
Roxie's example: 116 × 5
= 116 ÷ 2 × 10
= 58 × 10
= 580
So n × 5 = n × (10 ÷ 2) = (n ÷ 2) × 10
Roxie's example: 116 × 5
= 116 ÷ 2 × 10
= 58 × 10
= 580
Why it happens: Multiplying by 10 is effortless — just write a zero at the end. Halving is also easy. So instead of the harder “× 5”, do the two easy steps. The same idea powers the other shortcuts in this chapter: × 25 = × 100 ÷ 4 (because 25 = 100 ÷ 4) and × 125 = × 1000 ÷ 8 (because 125 = 1000 ÷ 8).
Check it yourself: Estu's 824 × 25 = 824 ÷ 4 × 100 = 206 × 100 = 20,600 ✓