Practice Arithmetic laws
Arithmetic laws describe when numbers can be reordered, regrouped or distributed without changing a result.
They help you choose simpler ways to calculate.
Exercises with solutions
Arithmetic laws let you simplify calculations cleverly. The commutative law allows you to change the order: 4 + 7 = 7 + 4. The associative law allows you to move brackets: (3 + 7) + 9 = 3 + (7 + 9). The distributive law lets you multiply a sum term by term.
Exercise 1
Calculate cleverly: 7 + 18 + 3.
Show solution and working
28
Reorder to 7 + 3 + 18 = 10 + 18 = 28. That way you build a round ten first.
Exercise 2
Calculate cleverly: 4 · 9 · 25.
Show solution and working
900
Reorder to 4 · 25 · 9 = 100 · 9 = 900.
Exercise 3
Calculate cleverly: (8 + 12) + 7.
Show solution and working
27
Deal with the bracket first: 8 + 12 = 20, then 20 + 7 = 27.
Exercise 4
Use the distributive law: 6 · 12.
Show solution and working
72
Split 12 into 10 + 2: 6 · 10 + 6 · 2 = 60 + 12 = 72.
Common mistake
Applying the commutative law to subtraction. 10 − 4 is not the same as 4 − 10. With minus you may not swap the order; with plus and times you may.
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