To solve some algebra problems, sometimes you need to translate phrases into algebraic statements then solve the problem

## Step by step guide to translating phrases into an algebraic Statement

Translating key words and phrases into algebraic expressions:

**Addition:**plus, more than, the sum of, etc.**Subtraction:**minus, less than, decreased, etc.**Multiplication:**times, product, multiplied, etc.**Division:**quotient, divided, ratio, etc.

### Example 1:

Write an algebraic expression for this phrase “\(12\) times the sum of \(5\) and \(x\)”.

**Solution:**

Sum of \(5\) and \(x: 5 \ + \ x\). Times means multiplication. Then: \(12 \ × \ (5 \ + \ x)\)

### Example 2:

Write an algebraic expression for this phrase. “Nine more than a number is \(18\)”

**Solution:**

More than mean plus, a number \(=x\)

Then: \(9 \ + \ x=18\)

### Example 3:

Write an algebraic expression for this phrase. “Eight more than a number is \(20\)”

**Solution:**

More than mean plus, a number \(=x\)

Then: \(8+x=20\)

### Example 4:

Write an algebraic expression for this phrase. “\(5\) times the sum of \(8\) and \(x\)”

**Solution:**

Sum of \(8 \) and \(x: 8+x\). Times means multiplication. Then: \(5×(8 +x)\)

## Exercises

### Write an algebraic expression for each phrase.

- A number increased by forty–two.
- The sum of fifteen and a number
- The difference between fifty–six and a number.
- The quotient of thirty and a number.
- Twice a number decreased by \(25\).
- Four times the sum of a number and \(– 12\).

### Download Translate Phrases into an Algebraic Statement Worksheet

## Answers

- \(\color{blue}{x + 42}\)
- \(\color{blue}{15 + x}\)
- \(\color{blue}{56 – x}\)
- \(\color{blue}{30/x}\)
- \(\color{blue}{2x – 25}\)
- \(\color{blue}{4(x + (–12))}\)