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.
Translate: ‘the sum of x and 10.’
- 2.
Translate: ‘5 more than twice y.’
- 3.
Translate: ‘7 decreased by a number n.’
Challenge problems
A little tougher — great for test prep. Click Show answer when ready.
- 1.
Write an expression for: The product of 5 and the sum of a number and 3.
- 2.
Write an expression for: 4 less than the quotient of a number and 2.