algebra 12 lessons 78 through 80

8/9/2019 Algebra 12 Lessons 78 Through 80

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Algebra ½

Lesson 78Opposites



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What are Opposites?

To get the opposite of a number, change the sign

Opposites are equidistant from 0 on the number line

Opposites have the same absolute value, but have different signs

The sum of opposites equal 0

When two numbers are opposites, they are a pair of opposites



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The negative sign (-)

-n is equal to the opposite of nA negative sign changes the sign of n

If n = 2, then – n = -2. -2 is the opposite of 2.If n = -13,then – n = -(-13) = 13. 13 is the opposite of -13.

Every negative sign, changes the sign of the number

- - - - 7 = 7-(-{-[-(-7)]}) = -7

An even number of negative signs indicates a positive number.An odd number of negative signs indicates a negative number.



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Practice Problems

Simplify:

a) -[-(-3)]

b) -{-[-(-7)]}

c) -(-81)

d) -(+{-[-(+5)]})



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Algebra ½

Lesson 79Simplifying More Difficult

Notations



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Using Opposites in ExpressionsWhen opposites are in mathematicalexpressions, enclose all numbers and addalgebraically.

-(-4) + (-2) + [-(-6)]Practice Problems:

a. -(-3) _ (-4)b. +(-5) + [-(-6)]

c. -(+6) – (-8) + 7 – (-3) + (-5)

d. -(-3) – [-(-4)] + [-(-6)]



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Algebra ½

Lesson 80Increases in Percent



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Review of Lesson 77Percents Greater than 100

A percent equal to 100 means the whole. 100% of 125 = 125

A percent less than 100 means less than the whole.75% of 125 = 93.75

A percent greater than 100 means more than the whole.260% of 125 = 325

The percent of a number is another number

The formula for percentages is p of x = y is p * x = y , where p is the decimal equivalent of the percent x is the whole y is the percentage of the wholeSolve for the missing number!



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Formula for Percent

p * x = yThe formula for p of x = y is p * x = y , where

p is the decimal equivalent of the percent x is the whole y is the percentage of the whole

Percent Decimal Fraction

100% 1.0 100/100

15% 0.15 15/100

115% 1.15 115/100

or you can use the methods shown in Lesson 77



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Percent Increase is Given

Find the New Amount“The price of gallon of gas is expected to increase 10% by July 4”

If a gallon of gas costs $2.79 today, what is the estimated cost by July 1?

There are two ways to figure this out:

1. A 10% increase means 110% of the current cost. Since 110% = 1.10, theformula is 1.10 * 2.79 = $3.07 rounded

2. 10% of 2.79 = .10 * 2.79 = 0.28 rounded. 2.79 + .28 = $3.07



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Find the Percent Increase20 years ago, burgers were smaller and had about 333 calories. Today’s burgers haveabout 590 calories. What percent increase is this?

1. Calculate the difference => 590 – 333 = 2572. Calculate the percent of 333 that 257 is => p * 333 = 2573. p = .77 = 77%4. So the size of burgers increased 77% from 20 years ago.



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Practice ProblemsExample 1: To their dismay, the townspeople found that the rodent population hadincreased 140%. If the rodent population had been 400 before, what is the rodentpopulation now?

Example 2: The number of cheering fans increased from 60 to 240. What percentincrease was this?

Practice:

a) The number of acorns on the ground increased 240 percent during the storm. If 5400 acorns were on the ground before the storm, how many were on the groundafter the storm?

b) The number increased from 40 to 280. What percent increase was this?

algebra 12 lessons 78 through 80

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