What Words Tell Us to Add Subtract Multiply and Divide?
Mathematical
Operations
Add
Decreased By
Deposit
Difference
Diminish
Divide
Half
Increased By
Less Than (switch order)
Minus
More Than
Multiply
Of
Plus
Product
Quotient
Subtract
Subtracted From (From comes First)
Sum
Times
Twice
Withdraw
Name_______________________________________________
Packet 16: Algebraic Expressions & One-Step Equations
What Words Tell Us to Add Subtract Multiply and Divide?
Mathematical
Operations
Matching Practice
_____1) A number x multiplied by fourteen
A. 14 - x
_____2) The quotient of fourteen and a number x
B. 2 ( x + 7)
_____3) Fourteen less than a number x
C. 14 ÷ (7 – x)
_____4) Seven increased by a number x
D. 7 + 14x
_____5) A number x subtracted from fourteen
E. 14 ÷ x
_____6) Fourteen more than a number x
F. 7 ( 14 + x)
_____7) Seven more than the product of fourteen and x
G. x - 14
_____8) Twice the sum of a number x and seven
H. 7 + x
_____9) The product of seven and the sum of fourteen and x
I. 14x
_____10) Fourteen divided by the difference between seven and x
J. x + 14
Algebraic Expressions
Study each algebraic expression. Then shade in all of the boxes next to it which contain a
phrase that matches the algebraic expression.
Algebraic
Expression
x + 4
Verbal Expressions
4 more than x
4 increased by x
sum of x and 4
t – 3
product of t and 3
3 less than t
t increased by 3
x - 7
7 less than x
x decreased by 7
difference
between x and 7
m + 9
9 less than m
m decreased by 9
quotient of m and
9
6 + y
6 plus y
y added to 6
6 more than y
8 – b
8 subtracted from b
sum of 8 and b
b increased by 8
h + 5
difference between
h and 5
h decreased by 5
sum of 5 and h
d – 2
d decreased by 2
d diminished by 2
2 subtracted
from d
1 - z
1 subtracted from z
z increased by 1
z subtracted
from 1
Rule: Solve each equation by using the inverse operation
Operation
Inverse Operation
Addition
Subtraction
Multiplication
Division
To check the equation, replace the variable with the solution
Solve each equation and check to see if your answer makes sense
1) 26y  910
2) k  18.3  29.1
4) r  64  157
5) 7.2m  43.2
7) r  30  214
8) 52.16  16y
3)
c
 11
23
6)
x
 42
33
9) x  78  38
10) 120  x  59
11) 37  b  61
12) 31m  527
Show all work in the box, check your solutions!
1) 2.5  k  0.5
2) 12.2  x  4.2
4) 5  6  x
5) 2  k  9
7) 5x  30
8) 21.6  x  5.6
10) x  4  17
11)
d
 5
9
13) m  4.6  7.7
14) 832  26y
16) 475  19b
17) x  41  5
3) b  3  15
6)
m
8
3
9) 72  3b
12) a  12.4  9.2
15)
m
 26
47
18) 4.3x  17.2
One-Step Equation Word Problems
Name__________________________
* To write an equation from a word problem:
1. Translate the statement into an expression.
2. Set the expression equal to the given value.
3. Solve the equation using the inverse operation.
4. Check your work.
Hint: The word “is” means equal
Examples:
a) The difference of a number and 15 is 27. What is the number?
b) 45 is 62 more than a number. What is the number?
c) The sum of 12 and a number is 68. What is the number?
d) The product of 6.35 and a number is 88.9. What is the number?
Writing and Solving One-Step Equations
Write and solve an equation for each set of clues below. Check your work!
1. Two less than a number is 10
2. The product of three times a number equals the
answer to problem 1.
3. The sum of 10 and a number equals the answer of
problem 2.
4. The sum of a number and - 7 equals the answer to
problem 3.
5. The sum of a number and the opposite of 2 equal
the answer to problem 4.
6. – 12 is equal to a number subtracted from the answer
to problem 5.
7. The sum of a number and – 9 is equal to the answer
of problem 6.
8. – 3 times a number equals the answer to problem 7.
9. A number divided by – 6 equals the answer to
problem 8.
10. 96 is the same as the answer to problem 9
multiplied by a number.
11. If the answer to problem 10 is decreased by this
number, the result is – 39.
12. The quotient of the answer to problem 11 and a
number equals 1.
13. To determine your score, double your answer to problem 12 and add 18.
IMPORTANT WORDS TO MEMORIZE!
ADDITION
SUBTRACTION MULTIPLICATION
DIVISION
plus
minus
multiplied by
divided by
increased by
decreased by
product
quotient
more than
subtracted
from
times
less than
twice, doubled,
tripled, etc.
To solve word problems LOOK FOR KEY MATH
WORDS
 WRITE A LET
STATEMENT
To solve equationsDo ‘opposite’ operations to get the letter alone!
If they add, you subtract.
If they subtract, you add.
If they multiply, you divide.
If they divide, you multiply.
 SOLVE BY DOING
‘OPPOSITE’
OPERATIONS TO GET
THE LETTER ALONE
 CHECK THAT YOUR
ANSWER MAKES
SENSE
WATCH OUT FOR
SUBTRACTED FROM
AND LESS THAN!
Matching
1) __________ 6 less than twice a number is 14
A) 6 – 2x = 14
2) __________ twice a number less than 6 is 14
B) x – 6 = 14
3) __________ a number decreased by 6 is 14
C) 2x – 6 = 14
4) __________ 10 divided by a number is 2
D) 2x = 10
5) __________ the product of 2 and a number is 10
E)
10
2
x
Solve each equation for the given variable.
6) x  2.8  5.3
7)
x
 122
9
8) 8  x  15
Word Problems: Show all work to receive credit.
9) 4 less than a number is 18. Find the
number.
10) 30 is 15 more than a number. Find the
number.