Distributive Property Examples
Here are some examples to highlight how the distributive property can assist with computation.
Learning multiplication facts
The distributive property makes learning the basic facts for multiplication easy.
For example, if a student knows 6 × 8 then they can work out 7 × 8 (its just 8 more).
Some students struggle to learn the multiples of 9, but these can be determined using the distributive property and the easily learned multiples of 10.
For example, 6 × 9 is the same as 9 × 6 which may be calculated by realising this is one group of 6 (i.e. 6) less than ten groups of 6 (60), or 54.
Try similar examples like:
| 7 × 9 | 9 × 3 | 4 × 9 | 99 × 6 | 7 × 99 |
The 11 times table is easy to work out when students use the distributive property. For example, 4 × 11 is 4 × (10 + 1) which is 4 × 10 + 4 × 1 = 44.
Try similar examples like:
| 8 × 11 | 11 × 6 | 11 × 11 | 11 × 13 | 8 × 12 |
The distributive property with addition
Model to students how to calculate products like 3 × 102, by recognising that 102 is literally 100 and 2 and thus working out 3 × 100 and 3 × 2 and adding the results (300 + 6_ to get 306). Symbolically we are doing
3 × 102 = 3 × (100 + 2) = 3 × 100 + 3 × 2 = 300 + 6 = 306
Try similar examples like:
| 4 × 201 | 3 × 21 | 81 × 5 | 1002 × 7 | 5 × $1.05 | 3 × $6.30 | 6 × 140 |
The distributive property with subtraction
Although the distributive property is traditionally stated as involving a number multiplied by the sum of two numbers, as above, we can also use the distributive property when multiplying by the difference of two numbers (i.e. with subtraction). For example, to work out a product like 4 × 95, we can think of the 95 as (100 - 5) and calculate 4 × 100 and subtract 4 × 5 from that to get to 380. Symbolically we are doing
4 × 95 = 4 × (100 - 5) = 4 × 100 - 4 × 5 = 400 - 20 = 380
Try similar examples like:
| 3 × 99 | 199 × 5 | 3 × 59 | 8 × $9.99 | 7 × $5.95 | 999 × 9 | 6 × 48 |
Final Note
Whenever you do any sort of mental computation in class, it is a good idea to model and explain the strategies that you used in order to expand students' repertoire of techniques.