2
Regrouping factors
Discover Mathematics P3: Term 2, Lessons 61–70
GoalGroup three factors in the easiest way and break a factor into tens and ones.
New words
factor · a number that is multipliedproduct · the answer to a multiplicationgrouping · choosing which two factors to multiply first
Explanation
When we multiply three numbers, we can multiply any two of them first. Brackets show which two. For 2 × 4 × 8 we can find (2 × 4) × 8 = 8 × 8 = 64, or 2 × (4 × 8) = 2 × 32 = 64. The product is the same, so choose the grouping that is easier. A good choice makes a ten or uses a fact you know well. We can also break one factor into tens and ones. To find 12 × 7, think of 12 as 10 + 2: (10 × 7) + (2 × 7) = 70 + 14 = 84.
| Grouping | First step | Product |
|---|---|---|
| (2 × 4) × 8 | 2 × 4 = 8 | 8 × 8 = 64 |
| 2 × (4 × 8) | 4 × 8 = 32 | 2 × 32 = 64 |
Worked examples
Find 3 × 2 × 5. Group 2 × 5 first, because it makes a ten: 2 × 5 = 10. Then 3 × 10 = 30.
| Grouping | Steps |
|---|---|
| (5 × 2) × 7 | 10 × 7 = 70 |
| 5 × (7 × 2) | 5 × 14 = 70 |
Find 12 × 7 by breaking 12 into 10 and 2. 10 × 7 = 70 and 2 × 7 = 14, so 12 × 7 = 70 + 14 = 84.
Class activity
Dice grouping. Roll a die three times and write the three numbers, for example 4, 5 and 2. Find the product with two different groupings and check that both agree. Do this five times. Which grouping was easier each time?
Practice
1
Find 2 × 5 × 6 by grouping 2 × 5 first.
2 × 5 = 10, and 10 × 6 = 60.
2
Find 4 × 3 × 2 with two different groupings.
(4 × 3) × 2 = 12 × 2 = 24 and 4 × (3 × 2) = 4 × 6 = 24.
3
Break 13 × 6 into tens and ones and find the product.
(10 × 6) + (3 × 6) = 60 + 18 = 78.
4
Habiba packs 3 boxes. Each box has 2 rows of 8 dates. How many dates are there?
2 × 8 = 16 dates in a box, and 3 × 16 = 48 dates. Or group 3 × 2 = 6 rows, and 6 × 8 = 48.
5
Break 14 × 5 into tens and ones and find the product.
(10 × 5) + (4 × 5) = 50 + 20 = 70.