CONFIDENTIAL 1

Algebra IAlgebra I

PercentsPercents

CONFIDENTIAL 2

Warm UpWarm Up

1) Parallelogram ABCD parallelogram EFGH. Find the value of x.

A B

D C

E F

H G

2030

18x

2) Trapezoids ABCD trapezoids EFGH. Find the value of x.

A B

CD

E F

H G

8 126 x

1) 12 units

2) 90 units

CONFIDENTIAL 3

Percent

Percent is a ratio that compares a number to 100. For example,

20% = 20100

To find the Fraction equivalent of a percent, write the percent as a ratio with a denominator of 100. Then simplify.

20% = 20 = 1 100 5

To find the decimal equivalent of a percent, divide by 100.20% = 20 = 0.2

100

CONFIDENTIAL 4

Some Common Equivalents

10% 20% 25% 33 1 %3

40% 50% 60% 66 2 %3

75% 80% 100%

1 10

1 5

1 4

1 3

2 5

1 2

3 5

2 3

3 4

4 5

1

0.1 0.2 0.25 0.3 0.4 0.5 0.6 0.6 0.75 0.8 1.0

The greatest percent shown in the table is 100%, or 1. But percents can be greater than 100% or less than 1%.

For example,

130% = 130 = 1.3 and 0.6% = 0.6 = 0.006

100 100

CONFIDENTIAL 5

You can use the proportion part = percent to find unknown whole 100 values.

A) Find 40% of 30.Method 1- Use a proportion:

part = percent Use the percent proportion. whole 100 x = 40 Let x represent the part. 30 100

100x = 1200 Find the cross products.

x = 12 Since x is multiplied by 100, divide both sides by 100 to undo the multiplication.

Check 40% is the same as 2 , and 2 of 30 is 12. 5 5

Finding the Part

CONFIDENTIAL 6

B) Find 110% of 66.

Method 2- Use an equation.

x = 110% of 66 Write an equation. Let x represent the part.

x = 1.1 (66) Write the percent as a decimal and multiply. x = 72.6

Finding the Part

110% of 66 is 72.6.

CONFIDENTIAL 7

1) 50% of 56

Find the Part.

3) 0.5% of 10

2) 25% of 200

4) 120% of 50

1) 28 2) 50

3) 0.05 4) 60

Now you try!

CONFIDENTIAL 8

A) What percent of 60 is 15?.

Method 1 Use a proportion.

part = percent Use the percent proportion. whole 100

15 = x Let x represent the percent. 60 100

60x = 1500 Find the cross products.

x = 25 Since x is multiplied by 60, divide both sides by 60 to undo the multiplication.

Finding the Percent

15 is 25% of 60.

CONFIDENTIAL 9

B) 440 is what percent of 400?

Method 2- Use an equation.

440 = x · 400

440 = 400x

440 = 400x400 400

1.1 = x

110% = x

440 is 110% of 400.

Write an equation. Let x represent the percent.

Since x is multiplied by 400, divide both sides by 400 to undo the multiplication.

The answer is a decimal.

Write the decimal as a percent. This answer is reasonable; 440 is more than 100% of 400.

CONFIDENTIAL 10

1) What percent of 25 is 5?

Find the Percent.

3) 36 is what percent of 9?

2) What percent of 45 is 3?

4) 14 is what percent of 56?

1) 20% 2) 6.67

3) 400% 4) 25%

Now you try!

CONFIDENTIAL 11

A) 30% of what number is 12?Method 1- Use a proportion.

part = percent whole 100

12 = 30 Let x represent the whole. x 100

30x = 1200 Find the cross products.

30x = 1200 Since x is multiplied by 30, 30 30 divide both sides by 30 to undo

the multiplication. x = 40

Finding the Whole

30% of 40 is 12.

CONFIDENTIAL 12

B) 60 is 0.6% of what number?

Finding the Whole

Method 2 Use an equation.

60 = 0.6% of x

60 = 0.006x

Write an equation. Let x represent the whole.

Write the percent as a decimal.

Since x is multiplied by 0.006, divide both sides by 0.006 to undo the multiplication.

60 = 0.006x0.006 0.006

10000 = x

60 is 0.6% of 10000

CONFIDENTIAL 13

Now you try!

1) 160% of what number is 80?

Find the Percent.

3) 45 is 25% of what number?

2) 60% of what number is 90?

4) 70 is 35% of what number?

1) 50 2) 150

3) 180 4) 200

CONFIDENTIAL 14

Use the percent proportion.

Let x represent the percent.

Find the cross products.

Since x is multiplied by 24, divide both sides by 24 to undo the multiplication.

A 14-karat gold ring is approximately 58% gold.

A) Jewelers use the karat system to determine the amount of pure gold in jewelry. Pure gold is 24 karat, meaning the item is 100% gold. A 14-karat gold ring contains 14 parts gold and 10 parts other metal. What percent of the ring is gold? Round

your answer to the nearest percent.

part = percent whole 100

14 = x

24 100

24x = 1400

24x = 1400

24 24

x = 58.3

CONFIDENTIAL 15

B) A man gives 40% of his money to his children and 20% of the remaining to a trust. If he is still left with

$9600, what did he originally have?

Let the original amount of money with him be $100.

Since 40% of original money is given to children.

Therefore, remaining money =$(100 - 40) = $60.

Money given to trust = 20% of the remaining = 20 of $60 = $12 100

SOLUTION:

Next page

CONFIDENTIAL 16

It is given that remaining money =$9600.

When the remaining amount is $48, original amount = $100.

When the remaining amount is $9600,

Original amount = $ 100 ×9600 = $20,000 48

Therefore, remaining money =$(60 - 12) = $48.

The man originally had $20,000.

CONFIDENTIAL 17

Now you try!

1) A certain granola bar has 2 grams of fiber. This is 8% of the recommended daily value. How many grams of fiber are recommended daily?

1) 25 grams

2) After deducting 10% from a sum and then 20% from the remainder, $3600 are left. Find the original amount?

2) $5000

CONFIDENTIAL 18

Assessment

1) Find 75% of 60.

2) Find 115% of 80.

3) What percent of 40 is 25?

4) What percent of 225 is 135?

5) 56 is what percent of 20?

1) 45

2) 92

3) 62.5%

4) 60%

5) 280%

CONFIDENTIAL 19

6) 1 is what percent of 16?

7) 48 is 32% of what number?

8) 16 is 20% of what number?

9) 8% of what number is 7?

10) 105% of what number is 37.8?

6) 6.25%

7) 150

8) 80

9) 87.5

10) 36

CONFIDENTIAL 20

11) A certain can of iced tea contains 4% of the recommended daily allowance of sodium. The recommended daily allowance is 2500 milligrams. How many milligrams of sodium are in the can of iced tea?.

12) On average, sloths spend 16.5 hours per day sleeping. What percent of the day do sloths spend sleeping? Round your answer to the nearest percent.

11) 100 milligrams

12) 68.75

CONFIDENTIAL 21

Let’s review

Percent

Percent is a ratio that compares a number to 100. For example,

20% = 20100

To find the Fraction equivalent of a percent, write the percent as a ratio with a denominator of 100. Then simplify.

20% = 20 = 1 100 5

To find the decimal equivalent of a percent, divide by 100.20% = 20 = 0.2

100

CONFIDENTIAL 22

Some Common Equivalents

10% 20% 25% 33 1 %3

40% 50% 60% 66 2 %3

75% 80% 100%

1 10

1 5

1 4

1 3

2 5

1 2

3 5

2 3

3 4

4 5

1

0.1 0.2 0.25 0.3 0.4 0.5 0.6 0.6 0.75 0.8 1.0

The greatest percent shown in the table is 100%, or 1. But percents can be greater than 100% or less than 1%.

For example,

130% = 130 = 1.3 and 0.6% = 0.6 = 0.006

100 100

review

CONFIDENTIAL 23

review

A) What percent of 60 is 15?.

Method 1 Use a proportion.

part = percent Use the percent proportion. whole 100

15 = x Let x represent the percent. 60 100

60x = 1500 Find the cross products.

x = 25 Since x is multiplied by 60, divide both sides by 60 to undo the multiplication.

Finding the Percent

15 is 25% of 60.

CONFIDENTIAL 24

review

B) 60 is 0.6% of what number?

Finding the Whole

Method 2 Use an equation.

60 = 0.6% of x

60 = 0.006x

Write an equation. Let x represent the whole.

Write the percent as a decimal.

Since x is multiplied by 0.006, divide both sides by 0.006 to undo the multiplication.

60 = 0.006x0.006 0.006

10000 = x

60 is 0.6% of 10000

CONFIDENTIAL 25

review

Use the percent proportion.

Let x represent the percent.

Find the cross products.

Since x is multiplied by 24, divide both sides by 24 to undo the multiplication.

A 14-karat gold ring is approximately 58% gold.

A) Jewelers use the karat system to determine the amount of pure gold in jewelry. Pure gold is 24 karat, meaning the item is 100% gold. A 14-karat gold ring contains 14 parts gold and 10 parts other metal. What percent of the ring is gold? Round

your answer to the nearest percent.

part = percent whole 100

14 = x

24 100

24x = 1400

24x = 1400

24 24

x = 58.3

CONFIDENTIAL 26

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