Commutative and Associative Properties of Multiplication

Victor de Velo, in addition to being an accomplished cyclist, is a great lover of fine desserts. His favorite dessert in Paris is Chef Henri's chocolate mousse!

As team captain, he helps motivate his team by promising to treat them to chocolate mousse, after the end of the Tour de France, for every stage that they win.

After winning a stage, Victor prepared to take his team to Le Jardin de la Joie by estimating the cost of nine servings (the number of team members, including himself) of chocolate mousse.

Chef Henri sells his mousse for 15 francs per serving, so Victor must multiply 9 team members times 15 francs per dessert, or he can multiply the cost per dessert times the number of team members.
Either way, he will get the same result.

9 bicyclists x 15 francs = 15 francs x 9 bicyclists

This is called the Commutative Property of Multiplication.

So far, Victor's team has won 3 stages, so Victor owes each of the 9 team members 3 desserts at 15 francs a piece.
9 members × 3 desserts × 15 francs

Using the rules for the Order of Operations, we would multiply 9 × 3 first. However, multiplication is also associative, which means we can do the multiplications in any order.

Therefore, to simplify this problem, Victor can multiply 3 × 15 first, and then multiply by 9.

9 × 3 × 15 = 9 × (3 × 15)
27 × 15 = 9 × 45 = 405

This is called the Associative Property of Multiplication.

As in the case of addition, because multiplication is both commutative and associative, numbers can be multiplied in any order without changing the value of the product.

This can make simplifying expressions with only multiplications easier to do. Use the Commutative and Associative Properties of Multiplication to help Victor with the following problem.

If the team wins a total of 6 stages, what will it cost Victor to treat the team to the promised desserts?

Input the cost of the desserts for all his team members.

NumberTheory Main | DistributiveProperty

Written by: Nikki Siegel

Art by: mC