2-2 Translating Between Words and Math

Learn to translate between words and math.

2-2 Translating Between Words and Math

In word problems, you may need to identify the action to translate words into math.

Action Operation

Put together or combine

Find how much more or less

Put together groups of equal parts

Separate into equal groups

Add

Subtract

Multiply

Divide

2-2 Translating Between Words and Math

Lake Superior is the largest lake in North America. Let a stand for the area in square miles of Lake Superior. Lake Erie has an area of 9,910 square miles. Write an expression to show how much larger Lake Superior is than Lake Erie.

Additional Example 1A: Social Studies Application

To find how much larger, subtract the area of Lake Erie from the area of Lake Superior.

a – 9,910

Lake Superior is a – 9,910 square miles larger than Lake Erie.

2-2 Translating Between Words and Math

Let p represent the number of colored pencils in a box. If there are 26 boxes on the shelf, write an algebraic expression to represent the total number of pencils on the shelf.

To put together 26 equal groups of p, multiply 26 times p.

26p, or 26 • p

There are 26p pencils on the shelf.

Additional Example 1B

2-2 Translating Between Words and Math

The Nile River is the world’s longest river. Let n stand for the length in miles of the Nile. The Paraná River is 3,030 miles long. Write an expression to show how much longer the Nile is than the Paraná.

Check It Out: Example 1A

To find how much longer, subtract the length of the Paraná from the length of the Nile.

n – 3,030

The Nile River is n – 3,030 miles longer than the Paraná River.

2-2 Translating Between Words and Math

Check It Out: Example 1B

Let p represent the number of paper clips in a box. If there are 125 boxes in a case, write an algebraic expression to represent the total number of paper clips in a case.

To put together 125 equal groups of p, multiply 125 times p.

125p or 125 • p

There are 125p paper clips in a case.

2-2 Translating Between Words and Math

37 + 28

• 28 added to 37

• 37 plus 28

• the sum of 37 and 28

• 28 more than 37

• 28 added to x

• x plus 28

• the sum of x and 28

•28 more than x

x + 28

++Operation

Numerical Expression

Words

Algebraic Expression

Words

There are several different ways to write math expressions with words.

2-2 Translating Between Words and Math

• 12 subtracted from k

• k minus 12

• the difference of k and 12

• take away 12 from k

k — 12

Operation

Numerical Expression

Words

Algebraic Expression

Words

90 — 12

• 12 subtracted from 90• 90 minus 12• the difference of 90 and 12• 12 less than 90• take away 12 from 90

2-2 Translating Between Words and Math

• 8 times w• w multiplied by 8• the product of 8 and w• 8 groups of w

8 w or (8)(w) or 8w

Operation

Numerical Expression

Words

Algebraic Expression

Words

8 48 or 8 48

• 8 times 48• 48 multiplied by 8• the product of 8 and 48

or (8)(48) or

8(48) or (8)48

2-2 Translating Between Words and Math

• n divided by 3

• the quotient of n and 3

n 3 or

Operation

Numerical Expression

Words

Algebraic Expression

Words

327 3 or

• 327 divided by 3• the quotient of 327 and 3

3273

n3

2-2 Translating Between Words and Math

Write each phrase as a numerical or algebraic expression.

Additional Example 2: Translating Words into Math

A. 987 minus 12

987 12

B. x times 45

45 • x or 45x

2-2 Translating Between Words and Math

Write each phrase as a numerical or algebraic expression.

Check It Out: Example 2

A. 42 less than 79

79 42

B. y divided by 22

y 22 or y22

2-2 Translating Between Words and Math

Write two phrases for each expression.

Additional Example 3: Translating Math into Words

A. 16

• 16 divided by b

B. (75)(32)

• 75 times 32

• the quotient of 16 and b

• the product of 75 and 32

b__

2-2 Translating Between Words and Math

Write two phrases for each expression.

Check It Out: Example 3

A. 17 – 14

• 14 subtracted from 17

• 12 divided by c

• 17 minus 14

• the quotient of 12 and c

B. 12c