1. Understanding Algebra Word Problems
*Represent a given situation using algebraic expressions or equations in one variable.
*Simplify and evaluate algebraic expressions.

2. The biggest challenge to solving word problems is figuring out whether to add, subtract, multiply or divide.
Words Meaning Addition
and
increased
more
more than
plus
sum
total
Words Meaning Subtraction
decreased
difference
less
less than
left
lower than
minus
Words Meaning Multiplication
double
half (× ½)
product
times
triple
twice
Words Meaning Division
divide into
half (÷ 2)
divide by
divide among quotient

3. To solve a word problem, you must first interpret the action you need to perform and then choose the correct operation for that action.
Action
Operation
Possible Question Clues
Combine
Add
How many all together?
Combine equal groups
Multiply
How many all together?
Separate
Subtract
How many more? How many less?
Separate into equal groups
Divide
How many equal groups?

4.   + – Word Phrases Expression a number plus 5 add 5 to a number
sum of a number and 5
5 more than a number
a number increased by 5
a number minus 11
subtract 11 from a number
difference of a number and 11
x  11
11 less than a number
a number decreased by 11
3 times a number
3 multiplied by a number 3m
product of 3 and a number
a number divided by 7
or a  7 a 7
7 divided into a number
quotient of a number and 7

5. TEST YOUR SKILL!! Match the phrase with the correct algebraic expression.

6. 1) 2 more than y
y - 2 2y
y + 2
y/2

7. 2) 16 divided into m
16 - m
16m
m + 16
m/16

8. 3) 2 less than s
s - 2 2s
s + 2
s/2

9. 4) Triple John’s age j
3 + j
j - 3 3j
j ÷ 3

10. 5) Twice the sum of y and 15
2y + 15
2 + y + 15
2 (y + 15)
2(15) + y

11. 6) n feet lower than than 10
10 - n
n - 10
n + 10
10 + n

12. 7) The quotient t and 4 4 goes into t t goes into 4 Multiply 4 by t
Add 4 and t

13. 8) 18 divided by a number, g
18 - g
18 ÷ g
g + 18
18 × g

14. ABC 2.4 Setting Up Algebra Word Problems

15. To set up algebra word problems:
To complete an algebra problem, an equal sign must be added.
The words is or are as well as equals tell you that you should add an equal sign.
Double Jake’s age, x, minus 4 is 22.
2x - 4 = 22

16. Translate the word problem into an equation
Translate the word problem into an equation. DO NOT find the solution yet.
Triple the original number, n, is 2,700.
The product of a number, y, and 5 is equal to 15.
Four times the difference of a number, x, and 2 is 20.
The total, t, divided into 5 groups is 45.
3n = 2700
5y = 15
4(x – 2) = 20
t ÷ 5 = 45

17. Translate the word problem into an equation
Translate the word problem into an equation. DO NOT find the solution yet.
The number of pants in the store, p, minus 54 pants sold today is 320.
One-half an amount, x, added to $50 is $262.
One hundred plants, divided by 5 rows, equals n number of plants per row.
A number, y, less than 50 is 82.
p – 54 = 320
x/ = 262
100 ÷ 5 = n
y - 50 = 82

18. Translate the word problem into an equation
Translate the word problem into an equation. DO NOT find the solution yet.
Seventeen more than half a number, h, is 35.
The quotient of a number, w, and 4 is 32.
Six less a number, d, is 12.
Four times the sum of a number, y, and 10 is 48.
h/ = 35
w ÷ 4 = 32
d – 6 = 12
4(y + 10) = 48