# ISEE Lower Level Math : How to find the distributive property

## Example Questions

### Example Question #61 : Numbers And Operations

Sam purchased  gummy bears and wants to make gift bags to give to his friends at school. How many different ways can Sam make gift bags with an even number of gummy bears in each bag?

Explanation:

We will solve this problem by finding factor pairs. Factor pairs are composed of two numbers that are multiplied together to equal a product. List all the factor pairs of Sam’s gummy bears.

Do not forget to list their reciprocals.

Sam can make  different gift bag combinations with an even amount of gummy bears in each bag.

### Example Question #62 : Numbers And Operations

Simplify the following expression:

Explanation:

Simplify the following expression:

When we are multiplying something in parentheses, we need to use the distributive property and multiply each term within the parentheses. With that in mind we can rewrite the given expression

Next, we need to do the multiplication. Recall that when multiplying variables, we add the exponents together and multiply the coefficients:

### Example Question #63 : Numbers And Operations

Simply the following expression:

Explanation:

To distribute a value into parantheses, you must multiply all the separate values by the value on the outside.

So

and

.

### Example Question #64 : Numbers And Operations

What is the value of the expression ?

Explanation:

Using the distributive property, you would distribute what is outside of the brackets or the parentheses to whatever is inside the parentheses.

Now take the difference of the two values found above.

### Example Question #65 : Numbers And Operations

Simplify the following using the distributive property.

Explanation:

To solve using the distributive property, we take the number on the outside and multiply it by each term on the inside of the parentheses.

So in the problem,

we will multiply or distribute the 5 through.

We will multiply the 5 by the first term.  We get

Now, we multiply the 5 by the second term.  We get

Now, we combine the two answers.  We get

or

### Example Question #66 : Numbers And Operations

Which of the following expressions is equal to ?

Explanation:

With the distributive property if there is a common factor in the terms of an expression, you can take it out of all of them a place it outside of parenthesis around the expression.

Since  and  have a common factor of , you can divide both by

.

### Example Question #67 : Numbers And Operations

Solve for .

Explanation:

With the distributive property, you want to multiply both numbers inside the parentheses by 4.

Therefore, you are left with

.

Then we have,

.

### Example Question #68 : Numbers And Operations

Solve for .

Explanation:

With the distributive property you must multiply each number in the parentheses by the number outside of the parentheses.

So to start the problem, we have

Then we simplify this to

.

So,

.

### Example Question #69 : Numbers And Operations

Solve for .

Explanation:

To start the problem, first multiply what is inside the parentheses by what is outside the parentheses.

So, we first have

.

Then,

.

Then we must get  alone, so we subtract 8 from both sides of the equation and are left with

.

To get  alone, we need to divide both sides by 2, so we are left with

### Example Question #70 : Numbers And Operations

Simplify

Explanation:

To use the distributive property, you multiply the outside value by each one in the parentheses.

and