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The Distributive property exercise appears under the 6th grade (U.S.) Math Mission, Pre-algebra Math Mission, Mathematics I Math Mission, Algebra I Math Mission and Mathematics II Math Mission. This exercise works with the distributive property, specifically for multiplication through addition.

## Types of Problems

There are two types of problems in this exercise:

1. Factor out a GCF: This problem provides a standard addition problem and asks users to factor out the greatest common factor to write it as the product of a number and a sum.
2. Distribute number in: This problem provides a numerical expression with an integer multiplied by a sum. The user is asked to expand this expression into the sum of two numbers by distributing.

## Strategies

This exercise is easy to get accuracy badges because the numbers involved are small (primarily two digits). The speed badges are also easy with knowledge of the distributive property because the problems are clearly distinct upon observation of the problem.

1. The distributive property states that ${a(b+c)=ab+ac}$.
2. The Distribute number in is the form of the distributive property that most users will recognize the fastest. It is common to call the Factor out a GCF problem a factoring application although it is based on the distributive property.

## Real-life Applications

1. One of the most common ways that teenagers start to make money is by selling candy. If one buys a case of candy, it can cost them about 26 dollars for a box of 30 pieces of big candy bars, which means that if they sell each candy bar for \$1, they can get a \$4 profit. If them and their friend are selling candy, they can represent this relationship by using and proving the distributive property.