Translating English Phrases to Mathematical Phrases & vice-versa
Objectives:
At the end of this section, you should be able to:
● translates English phrases to mathematical phrases and English
sentences to mathematics sentences, and vice versa
Try This!
Write an expression for each of the following. No one is done for you!
1. add 4 and 8, then multiply by 3
(4 + 8) (3) or 3 (4+8)
2.
3.
4.
5.
6.
7.
subtract 9 from 14, then multiply by 2 = (14 – 9) (2)
subtract 7 from 24, then divide by 6 = (24 – 7) / 6
the quotient of a number and 4 = n / 4
the product of 23 and twice a number = 23 x 2n
times the sum of 9 and a number y = 9
15 less than 7 times a number = n (15 – 7)
Think Ahead!
Read each scenario. Answer what is being asked.
1.
The cafeteria bought lots of frozen pizzas to serve. If you know the total amount
of money they spent and how many pizzas they bought, how could you figure out
the cost of 1 pizza? Why do you believe that? What is the action of this
operation?
2.
Pete bought some candy and gave some of the pieces to his best friend, Hal.
How could you figure out how many pieces Pete has left? Why do you believe
this? What is the action of the operation?
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Bob and Tyler do not have enough money to buy a box of donuts, but they have
the exact amount needed if they combine their money. How would you find the
cost of a box of donuts? What is the action of this operation?
4. Macy wants to buy each of her classmates a Coke. How would you figure out the
cost? What is the action of this operation?
3.
Read and Ponder!
Translate English Phrases to Mathematical Expressions
Many words and phrases suggest mathematical operations . The following common
words and phrases indicate addition, subtraction, multiplication, and division.
Verbal phrases can be translated into variable expressions. Some examples are below.
Whenever possible, select a single variable to represent an unknown quantity. Then
express related quantities in terms of the first variable selected.
Examples
For each relationship, select a variable to represent one quantity and state what that
variable represents. Then express the second quantity in terms of the variable selected.
a) The Kings scored 7 more points than the Rangers.
Let r = number of points scored by the Rangers
Let r + 7 = number of points scored by the Kings
b) Bob and Marc share $65.
Let a = how much Bob receives.
Let 65 - a = amount Marc receives.
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Practice
Write each statement as an algebraic expression.
1) Kim has 7 more than 5 times the amount Sylvia has. =
Let s = The amount Sylvia has.
Let 5s + 7 = The amount Kim has.
2) The length of a rectangle is 3 feet less than 4 times its width.
Let w = Width of the rectangle
Let 4w – 3 = Length of the rectangle
3) One train travels 3 miles more than twice the distance another train travels. The total
distance traveled by both trains is 800 miles.
Translate Mathematical Expressions to English Phrases
Mathematical phrases can be written as verbal sentences
Example:
The product of two and three.
Word „product” indicates,that there should be multiplication of these numbers
(“product” is a result of multiplication).
If there is a word: number, variable or constant, you should write a letter (use
letters from the end of the alphabet for “number” and “variable”, letters from the
beginning of the alphabet for “constant”).
Example:
The sum of a number and seven
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The Proper Terminology
When you translate algebraic expressions into phrases, you should use proper
terminology. Some operations may be described in different ways especially when
there is subtraction.
Mathematical phrases (for
examples)
Examples:
addition
The sum of two and a number
or
The total of two and a number
or
Two increased by a number
subtraction
The difference of twelve and five
or
Twelve decreased by five
or
Twelve less five
or
Five less than twelve
The product of three and seven
or
Three times seven
multiplication
*Twice a number
division
The quotient of a
number and fifteen
fraction of a
number
One-fourth of a number
Additive inverse
Opposite of a number
The fourth power of ten
*The square of three
exponentiation
*The cube of a number
radical expression
The square root of four
multiplicative
inverse
The multiplicative inverse of a
number
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or
The reciprocal of a number
See if you can do this!
Translate each verbal phrase into a math expression.
1.
2.
3.
4.
Three times a number, increased by 1 = 3n + 1
3 more than 5 times a number = (3 + 5) (n)
Five times the difference of d and 3.2 = (d – 3.2) (5)
One-third of the quantity 6.5 and p = 1/3
Write an English sentence for each expression but do not use add, subtract,
multiply, divide, sum product or quotient.
5. x + 18 = The sum of a number and 18.
6. 5n = The product of 5 and a number.
Write a math expression for each situation.
7. Jim is 2 years older than 3 times the age of his little brother, Tommy.
8. Sally spent one-half of her money and then lost 8 dollars.
9. Sam went fishing. His first fish weighed a certain number of pounds. He then
caught 5 fish that each weighed 7 pounds.
10. Mary has 4 more fish than twice the amount of fish that George has.
Congratulations for a job well done!
______________________ __________ END ___________________________
REFERENCES
http://www.brainfuse.com/jsp/alc/resource.jsp?s=compass&c=42654&cc=120446
http://www.mathquickeasy.com/mathematical_phrases.html
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WMSU-ISMP-GU-001.00
Effective Date: 7-DEC-2016
Page 109 of 6
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