What Words Tell Us to Add Subtract Multiply and Divide?

AddDecreased By

DepositDifferenceDiminishDivideHalf

Increased ByLess Than (switch order)

MinusMore Than

MultiplyOf

PlusProductQuotientSubtract

Subtracted From (From comes First)Sum

TimesTwice

Withdraw

Name_______________________________________________

Packet 16: Algebraic Expressions & One-Step Equations

Mathematical Operations

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

Verbal Expressions

x + 4 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

AdditionSubtraction

MultiplicationDivision

To check the equation, replace the variable with the solution

Solve each equation and check to see if your answer makes sense

1) 2) 3)

4) 5) 6)

7) 8) 9)

10) 11) 12)

Show all work in the box, check your solutions!

1) 2) 3)

4) 5) 6)

7) 8) 9)

10) 11) 12)

13) 14) 15)

16) 17) 18)

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 EquationsWrite 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

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)

Solve each equation for the given variable.

6) 7)

8)

Word Problems: Show all work to receive credit.

To solve equations-Do ‘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.

9) 4 less than a number is 18. Find the number.

10) 30 is 15 more than a number. Find the number.