Applications and Problem Solving

1-4Translating Words into Symbols

Overview

Math vocabulary maps to operations: ‘sum’ → +, ‘difference’ → −, ‘product’ → ×, ‘quotient’ → ÷.

Key ideas

  • ‘More than’ and ‘increased by’ mean addition.
  • ‘Less than’ reverses order: ‘5 less than n’ is n − 5.
  • ‘Twice,’ ‘doubled,’ and ‘of’ often signal multiplication.

Worked examples

Example 1

Problem. Translate: ‘8 less than 3 times a number x.’

Solution. 3x − 8

Example 2

Problem. Translate: ‘the quotient of n and 4.’

Solution. n / 4

Practice

Try each one. Click Show answer when ready.

  1. 1.

    Translate: ‘the sum of x and 10.’

  2. 2.

    Translate: ‘5 more than twice y.’

  3. 3.

    Translate: ‘7 decreased by a number n.’

Challenge problems

A little tougher — great for test prep. Click Show answer when ready.

  1. 1.

    Write an expression for: The product of 5 and the sum of a number and 3.

  2. 2.

    Write an expression for: 4 less than the quotient of a number and 2.