Translating Algebraic and Translating Algebraic and Verbal ExpressionsVerbal Expressions

Warm UpWarm UpAnswer the following problems1.(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=-93.2a + (b-c) + a2 =4.a+c - (2 x a ÷ 5) + c2 =

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715

5175

WRITING EXPRESSIONS AND WRITING EXPRESSIONS AND EQUATIONSEQUATIONS

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Algebraic ExpressionAlgebraic Expression

• ? represents a number. • That number plus ten equal

14.• How do we represent the

number algebraically?

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What You’ll LearnWhat You’ll Learn

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Build Your VocabularyBuild Your Vocabulary• An algebraic expression contains numbersnumbers and

variablesvariables along with +, -, x, and/or ÷.

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

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

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DIFFERENCEDIFFERENCE is for is for SUBTRACTION.SUBTRACTION.

SUMSUM is for is for ADDITION.ADDITION.

PRODUCTPRODUCT is for is for MULTIPLICATION.MULTIPLICATION.

QUOTIENTQUOTIENT is for is for DIVISION.DIVISION.

Build Your VocabularyBuild Your Vocabulary

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ADDITIONADDITION•plus•the sum of•increased by•more than•added to•The total of

SUBTRACTIONSUBTRACTION•minus•the difference of•decreased by•less than•fewer than•subtracted from

Other TerminologiesOther Terminologies

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DIVISIONDIVISION• divided by• the quotient of• the ratio of• per

MULTIPLICATIONMULTIPLICATION• times• the product of• multiplied by• at• of

Other TerminologiesOther Terminologies

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ExamplesExamplesWrite an algebraic expression for each verbal expression.

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the sum of p and 12

the product of k and q

Your TurnYour TurnWrite an algebraic expression for each verbal expression.

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ExamplesExamplesA python eats 4 pounds of meat each month.

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

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

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The numerical expression is 4 × 54 × 5 or 4(5)4(5).

The algebraic expression is 4 × d4 × d or 4d4d.

ExamplesExamplesWrite a verbal expression for each algebraic expression.

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37 + s37 + s

5 (b – 3)5 (b – 3)

the sum of 37 and s . the sum of 37 and s .

37 increased by s. 37 increased by s.

5 times the difference of b and 3.5 times the difference of b and 3.

5 multiplied by the difference of b and 3.5 multiplied by the difference of b and 3.

Your TurnYour TurnWrite a verbal expression for each algebraic expression.

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x ÷ 7x ÷ 7

4 + (2n)4 + (2n)

x divided by 7x divided by 7

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

What is an Equation?What is an Equation?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.

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Equalityequals

isis equivalent

to

is equal tois the same asis as much as is identical to

ExamplesExamplesWrite an expression for each sentence

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t ÷ 8 = 20t ÷ 8 = 20

3g – 7 = 313g – 7 = 31

The quotient of t and 8 equals 20. The quotient of t and 8 equals 20.

Seven less than three times g is 31.Seven less than three times g is 31.

t/8 = 20t/8 = 20

Your TurnYour TurnWrite an expression for each sentence

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8d – 9 = 238d – 9 = 23

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

The product of 8 and d decreased by 9 equals 23. The product of 8 and d decreased by 9 equals 23.

x + 12 = 27x + 12 = 27

ExamplesExamplesWrite a sentence for each equation

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3z – 12 = 113z – 12 = 11

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4 more than j is equal to 214 more than j is equal to 21j + 4 = 21j + 4 = 21

The product of 3 and z decreased by 12 equals 11

The product of 3 and z decreased by 12 equals 11

Your TurnYour TurnWrite a sentence for each equation

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10 less than r is equal to 510 less than r is equal to 5r – 10 = 5r – 10 = 5

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

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