1. 1.5 Translating Words into Mathematical Symbols
Algebra 1
1.5 Translating Words into Mathematical Symbols

2. Translate Addition Phrases
TRANSLATION
The sum of 6 and a number
6 + x
8 more than a number
x + 8
A number plus 5
x + 5
A number increased by 7
x + 7

3. Translate Subtraction Phrases
TRANSLATION
The difference between 5 and a number
5 – y
7 minus a number
7 – y
A number decreased by 9
y – 9
4 less than a number
y - 4

4. Write the phrase as a variable expression. Let n represent the number
The sum of a number and 11
32 decreased by a number
The difference of a number and 12
20 more than a number
15 increased by a number
25 less than a number

5. IMPORTANT NOTE
Order does not matter for addition and multiplication. “The sum of 6 and a number” can be written either as 6 + x or x Order is important for subtraction and division. “The quotient of a number and 4” means n/4, not 4/n.

6. Translate Multiplication and Division Phrases
Translation
The product of 9 and a number 9n
10 times a number
10n
A number multiplied by 3 3n
One fourth of a number
(1/4)n
The quotient of a number and 6
n/6
7 divided by a number
7/n

7. Write the phrase as a variable expression. Let x represent the number.
The product of 17 and a number
One half of a number
The quotient of 15 and a number
24 times a number
A number multiplied by 7
A number divided by 8

8. Translate Sentences
Sentence
Translation
The sum of a number x and 12 is 6.
x + 12 = 16
The quotient of 15 and a number x is less than 3.
(15/x) < 3
The word is by itself means “=“ You can also use is with inequality symbols

9. Write the sentence as an equation or inequality
8 times a number x is 56.
24 less than a number x is greater than 5.
10 times a number x is less than or equal to 50.

10. Write and Solve an Equation
Translate into mathematical symbols: “A number divided by 4 is 7.” Let y represent the number.
Use mental math to solve the equation.
Check your solution.

11. You make a long distance telephone call. The rate is $
You make a long distance telephone call. The rate is $.20 for each minute. The total cost of the call is $ How long was the call?

12. You drive 275 miles in 5 hours. What is your average speed?

13. Write a sentence that could be translated to x - 11 = 5