Q:

How do you use distributive property to solve word problems?

A:

The distributive property states that a*(x+y)=a*x+a*y. The distributive property can be applied when the same operation is being done to multiple terms in an expression. Distributing out the coefficients in a word problem can make it easier to manipulate and isolate the variables in word problems.

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1. Find numbers, operations and relationships

Read the word problem. Look for any numbers and how they relate to each other. Find comparative phrases, such as "3 more than" or "15% less than," to determine the operation that creates the relationship. Write these relationships as equations. For example, a word problem might say that a father purchased five ice cream cones for a total of \$32, four of which were served with a second scoop that cost \$3 more than the regular price he paid for the fifth. The number 32 is the total and is made up of a combination of one cone at regular price and four cones at a price \$3 higher. Where c is a regular cone and d is a double, c+3=d and 4d+c=32.

2. Use substitution to make all of the variables the same

In the example above, because c+3=d, c can be substituted for d:

4d+c=

4(c+3)+c=32.

3. Use distribution and isolate the variable

In the example above, the coefficient 4 can be distributed:

4(c+3)+c=

4(c)+4(3)+c=

4c+12+c=

5c+12

To isolate the variable, subtract constants, then divide out the coefficients:

5c+12=32

5c+12-12=32-12

5c=20

5c/5=20/5

c=4

Sources:

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