MAT 070-Algebra I-Word Problems - Mass

MAT 070-Algebra I-Word Problems

Read and translate

Comparisons

Fixed rate and variable rate

Objectives

a

Read and translate word problems.

b

Solve problems involving comparisons.

c

Solve fixed rate + variable rate word problems.

a Reading and translating word problems

Students taking Algebra frequently complain that the course would be easier if it

were only in English. Yet the minute they encounter a word problem, they

complain that it would be easier if they had an equation to solve. Reading Math is

not like reading a Science Fiction novel. It is more like learning a foreign

language.

There are certain ¡°key¡± words that are used for mathematical meanings.

Addition ( )

English Words

English Phrases

sum

The sum of a

number and 4

4 more than a

number

A number

increased by 4

4 greater than a

number

more than

increased

greater than

Algebraic

Translation

x

4

x

4

x

4

x

4

plus

A number plus 4

x

4

added to

A number added

to 4

x

4

1

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MAT 070-Word Problems: Read/Translate; Comparisons; Fixed Rate & Variable Rate

Subtraction ( )

English Words

difference

less than

decreased

fewer than

Multiplication

( or )

Division ( )

The difference

between a number

and 4

4 less than a

number

A number

decreased by 4

4 fewer than a

number

x

4

x

4

x

4

x

4

A number minus 4

x

4

subtracted

4 subtracted from

a number

x

4

less

A number less 4

x

4

English Words

English Phrases

Algebraic

Translation

product

The product of a

number and 4

4x

times

4 times a number

4x

of

4 of a number

4x

English Words

English Phrases

Algebraic

Translation

x

4

x

4

quotient

)

Algebraic

Translation

minus

divided by

Equals (

English Phrases

A number divided

by 4

The quotient of a

number and 4

English Words

English Phrases

is (or was, will be)

A number plus 4

is 6.

A number plus 9

equals 15

equals

Algebraic

Translation

x

x

4

6

9

15

Objective a: Reading and translating word problems

3

There are a couple of special words that you also need to remember. Double or

twice a number means 2x, and triple or thrice a number means 3x.

Example 1: Use the tables above to translate the following English phrases into

algebraic expressions. Let x the unknown number.

A) 5 more than a number.

Solution: ?

5 more

than

number

??

??

??

??

?? a????

??

??

??

x

5

??

So the algebraic expression is: 5 x (or x 5 ).

B) half of the number.

Solution: half

number

? of

? the

????

??????

1

?? 2

x

So the algebraic expression is:

1

x

x (or ).

2

2

C) 8 more than a number.

than

number

Solution: 8?more

??

????

??

?? a??

??

????

??

8

x

??

So the algebraic expression is: 8 x (or x 8 ).

Practice Problem 1: Use the tables above to translate the following English

phrases into algebraic expressions. Again let x the unknown number.

A) a number increased by 7.

B) one-third of a number.

C) a number times 9.

The solution to this Practice Problem may be found starting on page 24.

Addition and multiplication are commutative. This means that the order in which

the terms are written doesn¡¯t matter. For example, 2 3 is the same as 3 2 .

Likewise, 2 x is the same as x 2 .

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MAT 070-Word Problems: Read/Translate; Comparisons; Fixed Rate & Variable Rate

However, subtraction and division are NOT commutative. So the order in which

the terms are written does matter. For example, 5 3 is not the same as 3 5 .

Likewise, this also means that 2 x is not the same as x 2 . It is because of this

that subtraction and division pose a particular problem for beginning Algebra

students. Consider the examples below.

Example 2: Use the tables above to translate the following English phrases into

algebraic expressions. Let x the unknown number.

A) a number subtract 10.

Solution:

x 10

a ??

number

10

??

????

?? subtract

??

??

???

??? ?

10

?? x

So, the algebraic expression is:

B) 10 subtracted from a number.

Solution: 10 subtracted from a number.

We need to be careful of the order in which the terms are subtracted, since

10 is being subtracted from the number.

So, the algebraic expression is: x 10

C) 10 less than a number

Solution: 10 less than a number.

We need to be careful of the order in which the terms are subtracted since

we have 10 less than a number.

So, the algebraic expression is: x 10

D) a number divided by 6.

Solution: In algebra, a fraction bar is usually used to indicate division. So

we can view the word expression as:

x

????

?? ??

??

a number

divided by

6

??

So the algebraic expression is:

x

6

Objective a: Reading and translating word problems

5

E) 6 divided by a number.

Solution: In Algebra, a fraction bar is usually used to indicate division. So

we can view the word expression as:

6

divided by

a????

number

??

??

??

x

??

6

So the algebraic expression is:

x

Practice Problem 2: Use the tables above to translate the following English

phrases into algebraic expressions.

A) A number subtract 15

B) A number subtracted from 15

C) 15 less than a number

D) 15 divided by a number

The solution to this Practice Problem may be found starting on page 24.

The examples above use English to describe a single algebraic operation. It is

possible to use English to describe more than one algebraic operation. Consider

the examples below.

Example 3: Use the tables above to translate the following English phrases into

algebraic expressions.

A) Triple a number plus 5.

Solution: triple a number plus

5

??????

???????

? ? ?

3 x

5

??

So, the algebraic expression is: 3x

5

B) A number divided by 4 plus 3.

number divided by 4 plus

3

Solution: a??

????

???

???????

? ??

??? ? ?

x

4

??

x

So the algebraic expression is:

4

3

3

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