MAT 070-Algebra I-Word Problems
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 sum
more than increased greater than
plus added to
English Phrases
The sum of a number and 4 4 more than a
number A number increased by 4 4 greater than a number
A number plus 4
A number added to 4
Algebraic Translation
x4
x4
x4
x4
x4 x4
1
2
MAT 070-Word Problems: Read/Translate; Comparisons; Fixed Rate & Variable Rate
Subtraction ( )
English Words
difference less than decreased fewer than
minus subtracted
less
English Phrases
The difference between a number
and 4 4 less than a
number A number decreased by 4 4 fewer than a number
A number minus 4
4 subtracted from a number
A number less 4
Algebraic Translation
x4
x4 x4 x4 x4 x4 x4
Multiplication ( or )
English Words English Phrases
product times
of
The product of a number and 4
4 times a number
4 of a number
Division ( ) Equals ( )
English Words divided by quotient
English Phrases
A number divided by 4
The quotient of a number and 4
English Words English Phrases
is (or was, will be) equals
A number plus 4 is 6.
A number plus 9 equals 15
Algebraic Translation
4x
4x
4x
Algebraic Translation
x 4 x 4
Algebraic Translation
x4 6
x 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 anum ber
5
x
So the algebraic expression is: 5 x (or x 5).
B) half of the number.
Solution: half of the number
1
x
2
So
the
algebraic
expression
is:
1 2
x
(or
x 2
).
C) 8 more than a number.
Solution: 8more than anum ber
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 .
4
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: a num b er s ub tract 10
x
10
x 10
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
divided by So the algebraic expression is: x
6
a number 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:
divided by
6
anum be r
x
So the algebraic expression is: 6
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: triplean umb er plus 5
3 x
5
So, the algebraic expression is: 3x 5
B) A number divided by 4 plus 3.
Solution: anumber divided by4 plus 3
x
4
3
So the algebraic expression is: x 3
4
................
................
In order to avoid copyright disputes, this page is only a partial summary.
To fulfill the demand for quickly locating and searching documents.
It is intelligent file search solution for home and business.
Related download
- antimicrobial effectiveness testing
- grade 4 mathematics support document for teachers
- sample amc 8 mock test ivy league education center
- note warm up
- translating words into algebra leeward community college
- translating english words into algebraic expressions
- grade 5 mathematics vocabulary word wall cards table of
- translating key words and phrases into algebraic expressions
- mat 070 algebra i word problems
- national health statistics reports
Related searches
- algebra word problems worksheets and answers
- algebra word problems pdf
- algebra word problems and answers
- algebra word problems worksheets pdf
- pre algebra word problems pdf
- pre algebra word problems worksheet
- algebra 1 word problems pdf
- algebra equations word problems worksheets
- algebra one word problems worksheet
- algebra age word problems pdf
- algebra 1 word problems worksheets
- algebra 2 word problems worksheet