Algebra I Pre-AP – Class Notes --Translating Words into Symbols
To solve problems using algebra, you must often translate phrases about numbers into
expressions containing variables.
Table of Common Translations:
Operation Phrase Translation
The sum of 8 and a number
A number increased by 7
5 more than a number
The difference between a number and 4
A number decreased by 8
5 less than a number*
6 minus a number
The product of 4 and a number
Seven times a number
One-third of a number
The quotient of a number and 8
A number divided by 10
4 times the sum of 6 and a number
Translate each phrase into a variable expression or equation. Use x for a variable.
1) The product of three and a number. ________________________________________
2) Five more than a number. ________________________________________
3) One-fourth of a number ________________________________________
4) Eight less than a number ________________________________________
5) Nine more than twice a number. ________________________________________
6) Three times the sum of six and a number. ________________________________________
7) Three-fourths of a number is 192. ________________________________________
8) Four less than twice a number is nine. ________________________________________
9) Eleven less than twice a number is seven more than the number. _______________________
10) Three times the quantity two less than a number is 8. _____________________________
Complete each statement with a variable expression:
11) Leann is 3 cm taller than Fred. If Fred’s height is f cm, then Leann’s height is _________ cm.
12) Dale has twice as much money as Leo. If Dale has d dollars, then Leo has ________ dollars.
13) There are 12 fewer boys than girls. A) If there are g girls, then there are _________ boys.
B) If there are b boys, then there are _________ girls.
Work the following problems on notebook paper.
A. Translate each phrase or sentence below into an algebraic expression or equation. Use n for a
1) Seven decreased by three times a number.
2) Twice the sum of a number and three.
3) Five times the sum of a number and two.
4) The difference between three times a number and one.
5) Six times the difference of a number and five.
6) Five less than six times a number.
7) Two increased by five times a number.
8) Eleven more than one-third of a number.
9) Seven less than three times a number.
10) Three less than twice a number is eight.
11) Four times the quantity eight plus a number is fifteen.
12) Two less than three times a number is six less than the number.
13) The product of ten and number is eight more than the number.
14) Eleven less than twice a number is seven more than the number.
15) One-third of the sum of ten and a number is fourteen.
B. Complete each statement with a variable expression.
16) Maria has $10 more than Lindsay. If Lindsay has L dollars, then Maria has _____ dollars.
17) The sum of two numbers is 17. If one number is x, then the second number is ________.
18) Adam is 4 inches shorter than Jeff. If Jeff’s height is j inches, then Adam’s height is ____ in.
19) Ruth weights 5 pounds less than Erin.
a) If Erin’s weight is e lbs., then Ruth’s weight is ______ lbs.
b) If Ruth’s weight is r lbs., then Erin’s weight is ______ lbs.
20) Two numbers differ by 12.
a) If the smaller number is s, then the larger number is _________.
b) If the larger number is l, then the smaller number is __________.
C. Define two variables as we did in class and indicate the dependent variable and the
21) Pencils sell for $0.20 each.
22) The faster you ride your bicycle, the greater distance it takes for you to stop.