1.1. Variables & Expressions

7/28/2019 1.1. Variables & Expressions

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Warm UpAdd or subtract.

1. 6 + 104 2. 12 + 1.9

3. 23 8 4.

Multiply or divide.

5. 324 18 6.

7.13.5(10) 8. 18.2 2

13.9110

15

18

135 9.1

6


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Preparation for 4.0 Students simplifyexpressions before solvinglinear equationsand inequalities in one variable, such as

3(2x 5) + 4(x 2) = 12.

California

Standards


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variable

constant

numerical expression

algebraic expression

evaluate

replacement set

Vocabulary


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A variable is a letter or a symbol used torepresent a value that can change.

A constant is a value that does not change.

A numerical expression contains onlyconstants and/or operations.

An algebraic expression containsvariables, constants, and/or operations.


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You will need to translate between algebraic

expressions and words to be successful in math.The diagram below shows some of the ways towrite mathematical operations with words.

Plus, sum,increased by

Minus, difference,less than

Times, product,equal groups of

Divided by,quotient

+

x


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1-1 Variables and Expressions

These expressions all mean 2 times y:

2y 2(y)

2 y (2)(y)

2 y (2)y

Writing Math


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Give two ways to write each algebraic expressionin words.

A. 9 + r B. q 3

the sum of 9 and r

9 increased by r

the product ofm and 7

m times 7

the difference ofq and 3

3 less than q

the quotient ofjand 6

jdivided by 6

Additional Example 1: Translating from Algebra to

Words

C. 7m D.j 6


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1a. 4 n 1b.

1c.9 + q

1d.3(h)

4 decreased by n

the sum of 9 and q

the quotient oftand 5

the product of 3 and h

Give two ways to write each algebraic expressionin words.

Partner Share! Example 1

n less than 4 tdivided by 5

q added to 9 3 times h


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To translate words into algebraic expressions,read the problem to determine what actions

are taking place.

Put together,combine

Add Subtract

Multiply Divide

Find how muchmore or less

Put togetherequal groups

Separate intoequal groups


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John types 62 words per minute. Write anexpression for the number of words he types inm minutes.

m represents the number of minutes that John types.

62 m or 62m Think: m groups of 62 words

Additional Example 2A: Translating from Words to

Algebra


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Roberto is 4 years older than Emily, who is yyears old. Write an expression for Robertos age.

yrepresents Emilys age.

y+ 4 Think: older than means greater than.

Additional Example 2B: Translating from Words to

Algebra


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Joey earns $5 for each car he washes. Writean expression for the number of cars Joeymust wash to earn ddollars.

drepresents the total amount that Joey will earn.

Think: How many groups of $5 are in d?

Additional Example 2C: Translating from Words to

Algebra


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Miriam is 5 cm taller than Jan. Jan is mcentimeters tall. Write an expression forMiriams height in centimeters.

Partner Share! Example 2

m represents Jans height in centimeters.

m + 5Think: Miriam's height is 5 added to Jans

height.


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To evaluate an expression is to find its value. Toevaluate an algebraic expression, substitutenumbers for the variables in the expression andthen simplify the expression. A replacement set

is a set of numbers that can be substituted for avariable.


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One way to indicate a set is to use braces, { }.The items in a set are called elements.

Writing Math


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Evaluate the expression for the replacement set{6, 7, 2}.

b 1

b 1

Substitute each value in the replacement set for band simplify.

6 1

Additional Example 3A: Evaluating Algebraic

Expressions

b 1

7 1

b 1

2 1

5 6 1


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Evaluate the expression for the replacement set{6, 7, 2}.

3b

3(b)

Substitute each value in the replacement set for band simplify.

3(6)

Additional Example 3B: Evaluating Algebraic

Expressions

18

3(b) 3(b)

3(7) 3(2)

21 6

V i bl d E i


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1-1 Variables and ExpressionsEvaluate the expression for the replacement set

{2, 3, 9} .

Partner Share! Example 3a

n

Substitute each value in the replacement set for n

and simplify.

n

(2)

n n

(3) (9)


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15 n

Evaluate the expression for the replacement set{2, 3, 9} .

Partner Share! Example 3b

Substitute each value in the replacement set for nand simplify.

15 n

152

13

15 n

153

12

15 n

159

6


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Evaluate the expression for the replacement set{2, 3, 9} .

Partner Share! Example 3c

n + 0.15

n + 0.15

Substitute each value in the replacement set for nand simplify.

2 + 0.15

2.15

n + 0.15

3 + 0.15

3.15

n + 0.15

9 + 0.15

9.15

V i bl d E i


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1-1 Variables and ExpressionsAdditional Example 4A: Recycling Application

Approximately eighty-five 20-ounce plastic

bottles must be recycled to produce the fiberfill

for a sleeping bag.

Write an expression for the number ofbottles needed to makes sleeping bags.

The expression 85s models the number of

bottles to make s sleeping bags.

V i bl d E i


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Find the number of bottles needed to make

20, 50, and 325 sleeping bags.

Evaluate 85s for s = 20, 50, and 325.

s 85s

2050

325

85(20) = 170085(50) = 4250

85(325) = 27,625

Additional Example 4B: Recycling Application

Approximately eighty-five 20-ounce plastic

bottles must be recycled to produce the fiberfillfor a sleeping bag.

To make 20 sleeping bags,1700 bottles are needed.

To make 50 sleeping bags,4250 bottles are needed.

To make 325 sleeping bags,27,625 bottles are needed.

V i bl d E i


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Find the number of bottles needed to make

12, 25, and 50 sweaters.

Evaluate 63s for s = 12, 25, and 50.

s 63s

1225

50

63(12) = 75663(25) = 1575

63(50) = 3150

To make 12 sweaters,756 bottles are needed.



Partner Share! Example 4bTo make one sweater, sixty-three 20-ounce

plastic drink bottles must be recycled.

V i bl d E i


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To make one sweater, sixty-three 20-ounce

plastic drink bottles must be recycled.

Write an expression for the number of

bottles needed to makes sweaters.

The expression 63s models the number of

bottles to make s sweaters.

Partner Share! Example 4a

V i bl d E i


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Give two ways to write each algebraicexpression in words.

1.j 3

2. 4p

3. Mark is 5 years older than Juan, who is yyearsold. Write an expression for Marks age.

Assignment No.1

Variables and E pressions


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1-1 Variables and ExpressionsEvaluate each expression for the replacement

set {5, 8, 12}.

4. 5. 6 + d

Shemika practices basketball for 2 hours each

day.

d

2

Assignment No.1

6. Write an expression for the number of hours she

practices in ddays.

7. Find the number of hours she practices in 5, 12,and 20 days.

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1.1. Variables & Expressions