Grade 7 Algebraic Expressions

What Are Algebraic Expressions?

Algebraic expressions are mathematical phrases that contain variables, numbers, and operations. They help us represent real-world situations using mathematical language.

An algebraic expression can include:

  • Variables - Letters like x, y, z that represent unknown values
  • Coefficients - Numbers that multiply variables (like the 3 in 3x)
  • Constants - Regular numbers without variables (like the 5 in x + 5)
  • Operations - Addition (+), subtraction (−), multiplication (×), division (÷), etc.

Examples of Algebraic Expressions:

5x + 3

2y − 7

3a + 4b − 2

x² + 2x + 1

Translating Words to Algebraic Expressions

One of the most important skills in algebra is being able to convert word problems into algebraic expressions. Here's how to translate common phrases:

Word Phrase Mathematical Operation Algebraic Expression
(if x = unknown number)
Sum of a number and 5 Addition x + 5
7 less than a number Subtraction x - 7
A number decreased by 3 Subtraction x - 3
6 more than twice a number Multiplication, Addition 2x + 6
Product of 4 and a number Multiplication 4x
Half of a number Division x ÷ 2 or x/2
A number divided by 8 Division x ÷ 8 or x/8
Square of a number Exponent x²

Key Words for Operations

Look for these key words to identify which operation to use:

  • Addition (+): sum, plus, increased by, more than, total, added to
  • Subtraction (-): difference, minus, decreased by, less than, reduced by, subtracted from
  • Multiplication (×): product, times, multiplied by, twice, double, triple
  • Division (÷): quotient, divided by, ratio, half, third, quarter

Translating Examples:

Word phrase: Three more than twice a number

Translation: 2x + 3


Word phrase: Five less than half of a number

Translation: x/2 - 5

Translating Algebraic Expressions to Words

You also need to know how to convert algebraic expressions back into words. There are often multiple correct ways to state the same expression:

3x + 4 could be stated as:

  • Three times a number plus four
  • Four more than three times a number
  • The sum of three times a number and four

2x - 7 could be stated as:

  • Seven less than twice a number
  • Twice a number minus seven
  • The difference between twice a number and seven

Real-World Applications

Algebraic expressions help us solve many real-world problems:

Example Problem:

Mia babysits and charges $12 per hour plus a $5 transportation fee. Write an algebraic expression that represents her earnings for h hours of babysitting.

Solution: 12h + 5

This means: $12 multiplied by the number of hours, plus $5

Practice Problems:

  1. Write an algebraic expression for "ten more than three times a number."
  2. Write an algebraic expression for "a number divided by 4, then decreased by 6."
  3. Express "the product of a number and 7, increased by the number" algebraically.
  4. Translate the expression 5y - 12 into words.
  5. James is x years old. His father is 28 years older. Write an expression for his father's age.

Tips for Success

  • Identify what variable to use (what's unknown)
  • Look for key words that indicate operations
  • Pay attention to the order of operations
  • Draw pictures or diagrams if it helps
  • Practice, practice, practice!

Remember: Translating between words and algebra is a skill that gets better with practice. The more problems you solve, the better you'll become!

Try it yourself!

Translate these word phrases into algebraic expressions:

1. Four times a number, increased by 9

2. The difference between a number and 15

3. A number divided by 3, then doubled