Today’s subject is… Ratios and Percents Mr. Whalen

Today’s

subject is…

Ratios

and

Percents

Mr. Whalen

Ratio- a comparison of 2 quantities using division.

Key Vocabulary for this lesson

Percent- is a ratio of a number to 100

It means “out of 100.” For example the term “50 per cent” (or 50%) means 50 out of 100”

Key Vocabulary for this lesson

OBJECTIVES FOR THIS LESSON:

1. Describe any ratio using “For every _____,there are _____”

2. Identify, write and compare ratios and rates.

3. Simplify ratios

4. Write equivalent fractions, decimals and percents.

There are many species of woodpeckers in North America. Here are two common species.

Woodpeckers…

Northern Flicker

Red-bellied Woodpecker

The ratio of Red-bellied Woodpeckers to Northern Flickers can be written in 3 ways:

Quick review…

2 to 3 2:3 3

2

Red-bellied Woodpeckers

Northern Flickers

The ratio of Northern Flickers to Red-bellied Woodpeckers is different:

Quick review…

3 to 2 3:2

Red-bellied Woodpeckers

Northern Flickers

2

3

Quick review…

A football (soccer) team has 9 wins in 12 matches played. The team can compare the number of wins to the total number of matches played by using a ratio.

9 to 12 9:12

12

9

Fractions vs. Ratios

oFractions represent “part to whole” relationship.

oRatios can often stand for a part to part relationship.

Helpful website for Ratios.

• http://www.mathsisfun.com/numbers/ratio.html

Dr. Oz’ Green Drink2 apples, cored

1/2 inch gingerroot (or 1 teaspoon)

1 bunch chopped parsley

(approx. 1/2 cup chopped)4 ounces water (handful of ice cubes)

1 stalk celery

1 or 2 cucumbers2 cups spinach1 lime, juice of 1/2 lemon, juice of

Writing Ratios Example 1

The recipe calls for the juice of 1 lime and the juice of half a lemon. To double the recipe, it would be the 2 limes and 1 lemon. The ratio stays the same. Write each ratio in all three forms.

2:1 2 to 11

2

A rate is a ratio that compares two

quantities measured in different units.

In 21 minutes I run 3 miles,

my “rate of travel” is .

Ratios and Rates:“What’s the difference?”

miles3min21

Rates and Unit Rates:If the measure of the second quantity

is one unit, then the rate is a “unit rate.”

To change a rate to a unit rate, divide both numerator and the denominator

by the number in the denominator.

milemilesmiles 1min7

333min21

3min21

Writing Rates and Unit RatesFind the Unit Rates and write them in both fraction and word form.“Leonard hiked 36 miles in 9 hours.”

hrmi936

hrmi

hrmi

14

99936

Rate in fraction form.

Unit rate in fraction form.

Unit rate in word form.“4 miles per hour”

Writing Rates and Unit Rates

A recipe for cookie icing says to mix 8 tablespoons of milk with 4 cups of sugar.

ctbsp48

ctbsp

ctbsp

12

4448

Rate in fraction form.

Unit rate in fraction form.

Unit rate in word form.4 tablespoons of milk per cup of sugar.

To compare the actual cost of two similar items we can use “Unit price.”

To compare which case is a better value, divide the actual price by the number of bottles in the package.

A 24-pack costs $4.99 and a 30-pack costs $5.99. Which one is “cheaper”?

bottles2499.4$

bottles3099.5$

By dividing, we find the 24-pack costs about $0.21 per bottle.The 30-pack costs around $0.20 per bottle.The difference is $0.02 per bottle.

Writing Equivalent RatiosEquivalent ratios are ratios that name the same comparison. You can find an equivalent ratio by multiplying or dividing both terms of a ratio by the same number.

(The procedure is the same as finding equivalent fractions.)

Writing Equivalent Ratios

The ratio of Adelie Penguins to Emperor

Penguins is:

To find an equivalent ratio:

EmperorAdelie

68

34

2628

68

Ratios and Percents

A percent is a ratio of a number to 100.

The symbol % is used to indicate that a

number is a percent. For example, 40%

is the ratio 40 to 100, or .

Percents can be written as fractions or

as decimals.

100

40

Write Percents as FractionsWrite 35% as a fraction in simplest form.

35% =

=

100

35

20

7

Write the percent as a fraction with a denominator of 100.

Simplify.

Writing Percents as Decimals

Write 43% as a decimal.

43% =

= 0.43

100

43 Write the percent as a fraction with a denominator of 100.

Write the fraction as a decimal.

Writing Decimals as Percents

Write each decimal as a percent.

0.07

0.07 =

= 7%

100

7 Write the decimal as a fraction.

Write the fraction as a percent.

Writing Fractions as Percents

Write each fraction as a percent.

=

5

4 Write an equivalent fraction with a denominator of 100.

Write the fraction as a percent.

205

204

x

x

100

80

¿

%80

-Using Division

83

= 3 ÷ 8

= 0.375

= 37.5%

Use division to write the fraction as a decimal.

Write the decimal as a percent.

GUIDED PRACTICE

Guided Practice:

There are 12 girls and 15 boys in a class.

Write each ratio three different ways:

1. The ratio of the number of girls to the

number of boys?

2. The number of girls to the total number

of students?

3. The number of boys to the total number

of students?

Guided Practice:

4. Water rushes over Niagara Falls at

the rate of 180 million cubic feet every

30 minutes. How much water goes

over the falls in 1 minute?

Guided Practice:

5. Kay rides her bike 4 miles in 20 minutes. Write her rate as miles per hour.

6. A merchant sells work gloves at $5 for a 3-pack or $15 for a 10-pack. Which is cheaper?

Guided Practice:

7. About of the people in

the United States have the last

name Johnson. What percent of

people in the United States have

this last name?

1251

Guided Practice:

8. A baseball team won 85% of its games. Explain how to write 85% as a fraction in simplest form. Write the equivalent fraction.

Guided Practice:

9. If 23 out of 50 voters students prefers Candidate A in an election, what percentage of voters prefer Candidate A?

10. Write the percentage of people that prefer Candidate A as a decimal.

Guided Practice:

11. .

12. ..

Write the fractions as percents and round to the nearest tenth of a percent if necessary..

4433

9060

GUIDED PRACTICE

Answers

Guided Practice Answers:

There are 12 girls and 15 boys in a class.

Write each ratio three different ways:

1. The ratio of the number of girls to the

number of boys? 12 to 15, 12:15 or

2. The number of girls to the total number

of students? 12 to 27, 12:27 or

3. The number of boys to the total number

of students? 15 to 27, 15:27 or

Guided Practice Answers :

4. Water rushes over Niagara Falls at

the rate of 180 million cubic feet every 30 minutes. How much water goes over the falls in 1 minute?

utemillion

utesmillion

min160

303030180

min30180


5. Kay rides her bike 4 miles in 20 minutes. Write her rate as miles per hour.

hourmilesmiles

xmilesxmiles

112

min6012

3min2034

min204


6. A merchant sells work gloves at $5 for a 3-pack or $15 for a 10-pack. Which is cheaper?

pairpairs 167.1$

3335$

35$

pairpairs 150.1$

10101015$

1015$

Buying a 10-pack is a better value.


7. About of the people in the United States have the last name Johnson. What percent of people in the United States have this last name?

Convert to a decimal, then to a percent.

1251

%8.0008.01251


8. A baseball team won 85% of its games. Explain how to write 85% as a fraction in simplest form. Write the equivalent fraction.

First change to

Then simplify:

10085

2017

5100585

10085


9. If 23 out of 50 voters prefer Candidate A in an election, what percentage of voters prefers Candidate A?

Write as a fraction. Find equivalent ratio with denominator of 100. Then change to a percent.

%4610046

250223

5023

xx


10. Write the percentage of people that prefer Candidate A as a decimal.

That’s easy. Simply move the decimal point over two places to the left. (Divide by 100.)

46% 100= 0.46


11. .

12. ..


%67666.090609060

%7575.044334433

IndependentPRACTICE

Independent Practice: Write each ratio in two other ways.

1. 3:7

2. 2 to 5

3. .5

4

Independent Practice: Write an equivalent ratio for each.

4- James has three pictures on his shelf. The pictures measure 4 in. long by 6 in. wide, 23mm long by 36mm wide, and 6cm long by 7cm wide. Which photos have a length-to-width ratio equivalent to 2:3?

Independent Practice:

Convert from a fraction to a percent.

5-

6-

7-

8-

9-

10-1000

45

100

17

7

3

10

3

9

1

5

4

Independent Practice:

11- If a dog’s heart beats 25 times in 15 seconds, how many times will it beat per minute?

Independent PracticeWrite the percent as a decimal.

12. 5%13. 7.6%

14. 70%15. 85%

16.14%17.48%18. 35%

Write the percent as a fraction in simplest form.

Independent Practice

19. .

20. ..


3415

8629

Conclusion:A ratio is a comparison of two

quantities by division. It can be expressed three different ways.

A rate is a type of ratio that compares quantities of different units. “miles per gallon,” “kilometers per hour” are examples of rates.

Percent is a ratio which compares a number to 100.

Assignments-

1. Short Response:

In Mrs. Whalen’s science class

of the students have a pet.

Explain how to write this fraction as

a percent. What percent of the

students in the class have pets?

2017

Assignments-2- Bottles of water can be sold in various sizes. Write the ratio of price per volume for each size of bottled water. Which is the best value?

$0.29 $0.43 $1.29

12 oz 24.8oz 128oz

Assignments-

3. The Dr. Oz Green Drink recipe makes 5 servings. Rewrite the recipe to make 20 servings. How much of each ingredient would be needed.

Be sure to complete all of the assignments. See you next time.

Documents

Today’s subject is… Ratios and Percents Mr. Whalen