Four is two twos
To multiply a number by 4, double it, and then double the answer. This works because 4 = 2 × 2: multiplying by 2 and then by 2 again is the same as multiplying by 4.
For 15 × 4, double 15 to get 30, then double 30 to get 60. So 15 × 4 = 60. Written as one number sentence, 15 × 4 = 15 × (2 × 2) = (15 × 2) × 2 = 30 × 2 = 60.
One 15 doubles to two 15s, which is 30. Two 15s double to four 15s, which is 60.
Each hop doubles: 15 to 30, then 30 to 60. Two doublings make × 4.
Doubling a two-digit number
To double a two-digit number, double the tens and double the ones, then add. Double 27 is double 20 plus double 7: 40 + 14 = 54.
Numbers that end in 5 double to a number that ends in 0: 25 doubles to 50, 35 to 70 and 45 to 90. So 35 × 4 is 70 doubled, which is 140.
Eight is three twos
8 = 2 × 2 × 2, so to multiply by 8, double three times. For 35 × 8: 35 doubles to 70, 70 doubles to 140, and 140 doubles to 280. So 35 × 8 = 280.
Count the doublings. One doubling multiplies by 2, two multiply by 4, and three multiply by 8. Stopping one doubling early gives half of the right answer, and one doubling too many gives twice the right answer.
Three hops, each one × 2: 35, 70, 140, 280. So 35 × 8 = 280.
35
Double 35 until it is 35 × 8
Each double copies everything there is: 1 strip of 35, then 2, then 4, then 8. Three doubles make × 8.
Worked example: Trays of Eggs Doubled for 4 and for 8
Question A tray holds 27 eggs. (a) How many eggs are in 4 trays? (b) How many eggs are in 8 trays?
1.Multiplying by 4 is doubling twice. Multiplying by 8 is doubling three times. Start with the 27 eggs in one tray.
One tray holds 27 eggs. Each doubling gives twice as many trays. 2.Double 27. Double 20 is 40 and double 7 is 14, so 2 trays hold 40 + 14 = 54 eggs.
Double 27: 40 + 14 = 54 eggs in 2 trays. 3.(a) Double 54. Double 50 is 100 and double 4 is 8, so 4 trays hold 108 eggs.
(a) Double 54: 100 + 8 = 108 eggs in 4 trays. 4.Double once more for 8 trays. Double 100 is 200 and double 8 is 16.
Double 108 for 8 trays: double 100 is 200 and double 8 is 16. 5.(b) 200 + 16 = 216, so 8 trays hold 216 eggs.
(b) 200 + 16 = 216 eggs in 8 trays.
Answer: (a) 108 eggs; (b) 216 eggs
Common mistakes
- Doubling only twice for 8 trays and writing 108. Two doublings multiply by 4. A third doubling is needed to multiply by 8.
- Doubling only the tens, for example writing double 27 as 47. Both parts are doubled: double 20 is 40 and double 7 is 14.
More multiplying and dividing in your head problems, worked step by step →