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The Properties of multiplication exercise appears under the 3rd grade (U.S.) Math Mission. This exercise explores some of the common properties of multiplication including the associative, commutative and distributive properties.

## Types of Problems

There are three types of problems in this exercise:

1. Demonstrate the associative property: This problem has blanks in two related multiplication problems. The user is asked to fill in the blanks with the correct numbers.
2. Utilize the distributive property: This problem has several boxes that are used to split up a multiplication problem. The user is asked to fill in the slots with the correct numbers.
3. Establish the commutative property: This problem has several blanks in a step-by-step calculation manipulating a product. Users are asked to put the correct numbers in the correct spaces.

## Strategies

Knowing the associative, commutative and distributive properties before beginning this problem provides motivation for it's purpose.

1. The associative property of multiplication establishes that the grouping symbols do not affect the result of an arithmetic problem involving multiplication. That is, ${a(bc)=(ab)c}$.
2. The commutative property of multiplication states that the order that multiplication is performed in does not affect the result. That is, ${ab=ba}$.
3. The distributive property allows many avenues to increase general mental arithmetic proficiency and efficiency. The distributive property for multiplication through addition is ${a(b+c)=ab+ab}$.

## Real-life Applications

1. Multiplication is needed and used by mechanics for repairing cars by multiplying when they overhaul the engine, measure the pistons or just to put in a new gearbox or engine.
2. By learning multiplication and memorizing the times tables, users provide themselves with essential building blocks to do higher learning math, like division, fractions and even algebra.
3. Multiplication is necessary for a career in the stock market.