# Writing Algebraic Expressions

Algebraic expressions are numerical expressions with variables that show how quantities are related.

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## Algebraic Expressions Using Addition and Subtraction

When writing algebraic expressions, we use variables to represent unknown quantities and symbols to to represent mathematical operations. The answer to an addition problem is called the **sum** and the answer to a subtraction problem is called a **difference.**

## Write algebraic expressions to represent the following phrases.

A. Five less than a number \(n\)

B. A number \(x\) increased by seven

C. The sum of 23 and a number \(p\)

D. The difference of a number \(m\) and 14

Five less than a number \(n\) is \(n-5\) because we are subtracting 5 from \(n.\)A number \(x\) increased by seven is \(x+7\) because we are adding 7 to \(x.\)

The sum of 23 and a number \(p\) is \(23+p\) because the word "sum" indicates addition.

The difference of a number \(m\) and 14 is \(m-14\) because the word "difference" indicates subtraction.

## Algebraic Expressions Using Multiplication and Division

The answer to a multiplication problem is called the **product** and the answer to a division problem is called the **quotient**.

## Write algebraic expressions to represent the following phrases.

A. The product of 34 and a number \(n\)

B. 15 times greater than a number \(x\)

C. The quotient of -10 and a number \(p\)

The product of 34 and a number \(n\) is \(34n\) because the word "product" indicates multiplication.15 times greater than a number \(x\) is \(15x\) because we are multiplying 15 and \(x.\)

The quotient of -10 and a number \(p\) is \(\dfrac{-10}{p}\) because the word "quotient" indicates division.

## Writing Algebraic Expressions from Word Problems

Algebra's power lies in its ability to model real-world situations and represent complex situations in concise ways. In order to accomplish this, we need to express written statements mathematically.

## Stuart belongs to a health club that charges him $100 per month, plus $12 per fitness class that he attends. If he attends \(C\) classes in one month, how much money will he owe the health club?

The base fee for the health club is $100, so Stuart will need to pay $100 whether he takes any classes or not. Since he is paying $12 per class, he will owe a total of \(12C\) for his classes. Therefore, the total amount that he will owe the health club is \(100+12C.\)

**Cite as:**Writing Algebraic Expressions.

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