TRANSLATING ALGEBRAIC AND

VERBAL EXPRESSIONS

Warm - upAnswer the following problems:

7

15

5175

1. (5+2-6) - (1-5+12) + (6-3+11)=

2. 2(5-3)2 + (15÷3x2) - (5+2 x 1-4)=Let a=5 b=7 c=-9

3. 2a + (b-c) + a 2

4. a+c - (2 x a ÷ 5) + c 2

Writing Expressions and Equations

Algebraic Expression

• ? represents a number. • That number plus ten equal 14.• How do we represent the number algebraically?

?

WHAT YOU’LL LEARN

Translate words into algebraic expressions and equations.

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• An algebraic expression contains numbers and variables along with +, -, x, and/or ÷.

• A variable is a symbol used to represent an unknown number.

• A numerical expression contains numbers along with +, -, x, and/or ÷.

BUILD YOUR VOCABULARYCopy

• SUM is for ADDITION.

• DIFFERENCE is for SUBTRACTION.

• PRODUCT is for MULTIPLICATION.

• QUOTIENT is for DIVISION.

BUILD YOUR VOCABULARY Copy

minusthe difference of

decreased byless than

fewer thansubtracted from

plusthe sum of

increased bymore thanadded to

The total of

SubtractionAddition

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Divided byThe quotient of

The ratio ofper

TimesThe product ofMultiplied by

AtOf

DivisionMultiplication

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Write an algebraic expression for each verbal expression.

EXAMPLES

1 the sum of p and 12

2 the product of k and q

p + 12

k � q or kq

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Your Turn Write an algebraic expression for each verbal expressions

a) b decreased by 6

b) the product of 9 and z

b – 6

9 � z or 9z

A python eats 4 pounds of meat each month.

EXAMPLES

3 Write a numerical expression to represent the amount it eats in 5 months.

4 Write an algebraic expression to represent the amount it eats in d months.

The numerical expression is 4 � 5 or 4(5).

The algebraic expression is 4 � d or 4d.

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Write a verbal expression for each algebraic expression.

EXAMPLES

5 37 + s

6 5 (b – 3)

the sum of 37 and s .

5 times the difference of b and 3.

37 increased by s.

5 multiplied by the difference of b and 3.

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Your Turn Write a verbal expression for each algebraic expression

a) x ÷ 7

b) 4 + (2n)

X divided by 7

the sum of 4 and the product of 2 and n.

An equation is a mathematical sentence that contains an equals sign (=). Words are used to indicate the equals sign. An equation may contain numbers, variables, or algebraic expressions.

EqualityEqualityEquals

IsIs equivalent

to

Is equal toIs the same asIs as much as Is identical to

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Write an expression for each sentence.

EXAMPLES

7 The quotient of t and 8 equals 20.

8 Seven less than three times g is 31.

t ÷ 8 = 20 or t/8 = 20

3g - 7 = 31

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Your Turn Write an expression for each sentence.

a) A number x increased by 12 is the same as 27.

b) The product of 8 and d decreased by

X + 12 = 27

8d – 9 = 23

Write a sentence for each equation.

EXAMPLES

9 j + 4 = 21

10 3z – 12 = 11

Four more than j is equal to 21.

The product of 3 and z

decreased by 12 equals 11.

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Your Turn Write a sentence for each equation.

a) r - 10 = 5

b)

Ten less than r is equal to 5.

The quotient of n and 3 increased by 6 equals 30.