Translate Phrases into an Algebraic Statement

Translate Phrases into an Algebraic Statement

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:

  1. Addition: plus, more than, the sum of, etc.
  2. Subtraction: minus, less than, decreased, etc.
  3. Multiplication: times, product, multiplied, etc.
  4. 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

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

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