This document discusses translating between English phrases and mathematical symbols in algebra. It provides examples of common words used in English phrases that translate to addition, subtraction, multiplication, division and other operations. Tables show translations between verbal phrases and algebraic expressions. The document also discusses writing mathematical expressions in English and provides practice problems for translating between the two representations.

1. TRANSLATING
ENGLISH PHRASES
TO MATHEMATICAL
SYMBOLS AND VICE
VERSA

2. OBJECTIVES:
• familiarize the terms used in translating
algebraic expressions.
• translate English or verbal phrases to
mathematical phrases or symbols and vice
versa.

3. NAME THE FOLLOWING LOGOS

5. MATHEMATICS SYMBOLS

6. ACTIVITY:
• Match each verbal phrase under Column A to its mathematical phrase
under Column B. Each number corresponds to a letter which will reveal
a quotation if answered correctly. A letter may be used more than once.
• Column A Column B
1. The sum of a number and three A. x + 3
2. Four times a certain number decreased by one B. 3 + 4x
3. One subtracted from four times a number E. 4 + X
4. A certain number decreased by two I. x + 4
5. Four increased by a certain number L. 4x – 1

7. 6.A certain number decreased by three M. x –
2
7.Three more than a number N. x – 3
8.Twice a number decreased by three P. 3 –
x
9.A number added to four Q. 2 – x
10.The sum of four and a number R. 2x –
3
11.The difference of two and a number U. 4x +
3
12.The sum of four times a number and three

8. ANSWER THE FOLLOWING QUESTIONS:
• Based on the activity , what word is formed?
• Which phrase is easy to translate ?
• Did you get the quote?
• What is the difference between verbal phrase to mathematical phrase?
• What must be considered in translating verbal phrase to mathematical phrase.?
• How do you write a verbal phrase to mathematical phrase?

9. ENGLISH PHRASES KEY WORDS
ADDITION SUBTRACTION MULTIPLICATION DIVISION
the sum of the difference of the product of the quotient of
added to diminished by multiplied by divided by
increased by decreased by of all over
plus minus times ratio
more than subtracted from twice split into
greater than less than thrice
exceeds by take away

10. ENGLISH PHRASES KEY WORDS
ADDITION SUBTRACTION MULTIPLICATION DIVISION
more less
EXPONENTS
square cube
ADDITION SUBTRACTION
5 more x 5 + x 5 less x 5 - x
5 more than x x + 5 5 less than x x – 5
5 added to x x + 5 5 subtracted from x x – 5
5 greater than x x + 5

11. MULTIPLICATION/ DIVISION
• In expressions , there are many different ways to write
multiplication:
1. ab
2. a . b
3. a ( b ) or ( a ) b
4. (a ) ( b )
Division , on the other hand , is written as
1.
𝑎
𝑏
2. a÷ b

12. LET US ANSWER THE FIRST ACTIVITY:
English Phrases Key Words Algebraic Translation
The sum of a number and three Sum x + 3
Four times a certain number decreased by
one
times , decreased 4x - 1
One subtracted from four times a number subtracted , times 4x - 1
A certain number decreased by two decreased x - 2
Four increased by a certain number increased 4 + x
A certain number decreased by three decreased x - 3
Three more than a number more than x + 3
Twice a number decreased by three twice , decreased 2x - 3
A number added to four added 4 + x
The sum of four and a number sum 4 + x
The difference of two and a number difference 2 - x
The sum of four times a number and three sum ,times 4x + 3
A number increased by three increased x + 3
The difference of four times a number and
one
difference , times 4x - 1

13. TRANSLATING MATHEMATICAL SYMBOLS TO
ENGLISH PHRASES
• 2x + 5 The sum of twice a number and 5
sum Two times x increased by 5
• x – 3y The difference of x and thrice y
subtraction A number x diminished by three times
y
• 3 ( x + 9 ) Thrice the sum of x and nine.
multiplication Three times the sum of x and nine
Expressions are usually named by the last operation to be performed in the
expression.

14. APPLICATION:
• Translate each into mathematical symbol . Let x represent a certain
number.
1. The sum of twice the number and 7.
2. The quotient of thrice a number and 15.
3. Twenty more than 4 times a number.
• Translate mathematical symbols to English Phrases.
4.
5𝑎
4
5.
𝑎+𝑏
𝑎 −𝑏

15. ASSESSMENT
• Write your answer in your lecture notebook:
1. The area ( A ) of a rectangle is the product of length (L ) and ( W )
2. The verbal translation of the formula for area of a square : A = 𝑠2

16. ASSIGNMENT:
• Translate the mathematical expression 2 ( x – 3 ) in verbal phrases at least in two
ways.