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# Multiplication and Division Phrases as Expressions

## Use keywords to write verbal phrases as expressions.

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Multiplication and Division Phrases as Expressions

The Cashway Sluggers have just won the city’s Little League Baseball championship game, and Mr. Amos has volunteered to take his son’s team to dinner. Mr. Amos tells the 16 team members that he is going to split 125 evenly between the team members. How can he use the information he has to figure out how much each member of the baseball team will be allotted for lunch? In this concept, you will learn to write multiplication and division phrases as single variable expressions. ### Writing Multiplication and Division Phrases as Expressions Here are some key words that mean multiplication and division. Multiplication: • product • times • groups Division: • split up • quotient • divided These key words will indicate what operation is involved in the expression. When deciphering phrases, identify any numbers first. Next, identify the operation involved. Then, identify the variable. Once you have identified all the elements, you can write the expression. Here is an example. The product of eight and a number To write this as an expression, first, identify any numbers. The number in this phrase is eight. 8 Next, identify the operation. The word “product” means multiply. ×\begin{align*}\times\end{align*} Then, identify the variable. “A number” means use a variable. Let y\begin{align*}y\end{align*} represent the variable. y\begin{align*}y\end{align*} The answer is 8y\begin{align*}8y\end{align*}. Remember that a number next to a variable means multiply. You could have also used parentheses to show multiplication. 8(y)\begin{align*}8(y)\end{align*} Now let’s look at writing an expression for phrase with division. Twenty-four divided by a number First, identify any numbers. 24 Next, identify the operation. Divided by means division (÷)\begin{align*}(\div)\end{align*} Then, identify the variable. “A number” means use a variable. y\begin{align*}y\end{align*} The answer is 24÷y\begin{align*}24 \div y\end{align*}. You can also use a fraction bar to show division. 24 ___ (this means divided by) y\begin{align*}y\end{align*} ### Examples #### Example 1 Earlier, you were given a problem about the championship dinner. Before the Cashway Sluggers divide the125 Mr. Amos is giving the team for dinner, they must decide whether to eat at a local burger restaurant or a sub shop. Hamburger combo lunches are $6 at the burger restaurant, and sub sandwich combos are$8 each. Mr. Amos is going to split 125 between the 16 team members. What variable expression can the team use to decide which restaurant to eat at? First, identify the numbers involved. 16 – Number of team members 125 – Amount the team has to be split Next, identify the operation involved. “Split” mean division. ÷\begin{align*}\div\end{align*} Then, identify the unknown number which will be the variable y\begin{align*}y\end{align*}. How much each team member will have to spend is the unknown number or variable. y\begin{align*}y\end{align*} Finally, write the expression and solve. yy==125÷167.81\begin{align*}\begin{array}{rcl} y &=&125 \div 16 \\ y &=&7.81 \end{array}\end{align*} The answer is:7.81

Each member of the team will have \$7.81 to spend, so the team should eat at the burger restaurant.

#### Example 2

Write the phrase as an expression: the quantity six times an unknown number divided by 2.

There are two operations in this problem. Let’s break it down.

First, the quantity six times an unknown number becomes 6x\begin{align*}6x\end{align*}.

6x\begin{align*}6x\end{align*}

Next, identify the second part of the phrase as divided by two. You can use a fraction bar for division.

2¯\begin{align*}\bar{2}\end{align*}

Then, because it is divided by the quantity, put the 6x\begin{align*}6x\end{align*} on top of the fraction bar.

6x2\begin{align*}\frac{6x}{2}\end{align*}

The answer is 6x2\begin{align*}\frac{6x}{2}\end{align*}

Again, this could be written as 6x÷2\begin{align*} 6x \div 2\end{align*}.

#### Example 3

Write the phrase as an expression: six times an unknown number.

First, identify any numbers.

6

Next, identify the operation.

Times means multiplication (x)\begin{align*}(x)\end{align*}

x\begin{align*}x\end{align*}

Then, identify the variable.

“An unknown number” means use a variable.

y\begin{align*}y\end{align*}

The answer is 6(y)\begin{align*}6(y)\end{align*} or 6y\begin{align*}6y\end{align*}.

#### Example 4

Write the phrase as an expression: an unknown number divided by two.

First, identify any numbers.

2

Next, identify the operation.

Divided by means division.

(÷)\begin{align*}(\div)\end{align*}

Then, identify the variable.

“An unknown number” means use a variable.

x\begin{align*}x\end{align*}

The answer is x÷2\begin{align*}x \div 2\end{align*}.

This can also be written as a fraction.

x2\begin{align*}\frac{x}{2}\end{align*}

#### Example 5

Write the phrase as an expression: the product of seven and a number.

First, identify any numbers.

7

Next, identify the operation. Product means multiplication.

(x)\begin{align*}(x)\end{align*}

Then, identify the variable.

“And a number” means use a variable.

y\begin{align*}y\end{align*}

The answer is 7(y)\begin{align*}7(y)\end{align*} or 7y\begin{align*}7y\end{align*}.

### Review

Write single-variable expressions from the following multiplication and division phrases.

1. The product of six and a number
2. A number divided by two
3. Fifteen divided by an unknown number
4. A number times seven
5. The product of ten and a number
6. Eighteen divided by a number
7. Twenty times a number
8. A number divided by three
9. An unknown number divided by twelve
10. An unknown number times sixteen
11. The product of five and an unknown quantity
12. The quantity six times an unknown number divided by three
13. The quantity four times an unknown number divided by seven
14. The quantity six times an unknown number divided by ten
15. The product of three and an unknown times four

To see the Review answers, open this PDF file and look for section 12.2.

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### Vocabulary Language: English

Variable

A variable is a symbol used to represent an unknown or changing quantity. The most common variables are a, b, x, y, m, and n.

Variable Expression

A variable expression is a mathematical phrase that contains at least one variable or unknown quantity.