Practice Distributive law
The distributive law lets you multiply a sum by multiplying each term separately: a(b + c) = ab + ac.
It helps with mental arithmetic and simplifying expressions.
Exercises with solutions
The distributive law says you may multiply a sum term by term: 4 · 12 = 4 · 10 + 4 · 2. The other way round you may factor out a common factor: 4 · 10 + 4 · 2 = 4 · (10 + 2). This helps with clever calculation and later with expanding brackets.
Exercise 1
Use the distributive law: 3 · 14.
Show solution and working
42
Split 14 into 10 + 4: 3 · 10 + 3 · 4 = 30 + 12 = 42.
Exercise 2
Use the distributive law: 6 · 25.
Show solution and working
150
Split 25 into 20 + 5: 6 · 20 + 6 · 5 = 120 + 30 = 150.
Exercise 3
Factor out the common factor: 7 · 8 + 7 · 2.
Show solution and working
7 · (8 + 2) = 70
The common factor is 7. Factoring out gives 7 · 10 = 70.
Exercise 4
Calculate cleverly: 12 · 9 + 12 · 1.
Show solution and working
120
Factor out: 12 · (9 + 1) = 12 · 10 = 120.
Common mistake
Multiplying only the first term by the number. 4 · 12 is not 4 · 10 + 2 but 4 · 10 + 4 · 2. Every term inside the bracket must be multiplied.
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