Times 5 and times 25, the easy way
Regroup the factors.
Roxie’s shortcut
Roxie wants to work out 116 × 5 in her head.
Which is easier in your head?
What this lesson covers
The idea
Multiplying by 5 is the same as multiplying by 10 and dividing by 2, and multiplying by 25 is the same as multiplying by 100 and dividing by 4; factorising and regrouping numbers this way makes multiplication simpler.
Roxie’s shortcut
Roxie wants to work out 116 × 5 in her head.
Which is easier in your head?
- 116 × 5 straight away
- 116 × 10, then half of it
- Both are equally easy
Build the machine
Pick a × step and a ÷ step so the machine gives the same answer as the direct product.
Make it simple
Multiplying by 5 is the same as multiplying by 10 and dividing by 2. Multiplying by 25 is the same as multiplying by 100 and dividing by 4.
116 × 5 = 116 × 10/2 = 58 × 10 = 580 824 × 25 = 824 × 100/4 = 206 × 100 = 20,600
Because 5 = 10/2 and 25 = 100/4. We factorise and regroup the numbers so that the multiplication is simpler.
Notes
× 5 = × 10 ÷ 2 and × 25 = × 100 ÷ 4. Factorising and regrouping numbers this way makes multiplication simpler.
Check yourself
Use ×10 then ÷2: 348 × 5 = ?
Answer: 1740
348 × 10 = 3480; 3480 ÷ 2 = 1740.
Use ×100 then ÷4: 64 × 25 = ?
Answer: 1600
64 × 100 = 6400; 6400 ÷ 4 = 1600.
Which is the same as multiplying by 5?
- Multiply by 10, then divide by 5. 10 ÷ 5 = 2, so that multiplies by 2.
- Multiply by 2, then divide by 10. 2 ÷ 10 is a fifth, so that divides by 5.
- Multiply by 10, then divide by 2 — correct. Yes! 10 ÷ 2 = 5.