Ratio, Proportion, Percen

Ratios, Proportions, and Percent

By Amy Dougherty

​Ratios are used to compare two quantities.

Can be written in colon form:

a : b

​Or

In fraction form:

a
b

​Ratios should be simplified just like fractions

Multiple Choice

Select the correct ratio:

A soccer team won 10 games and lost 6 games

• $$\ \frac{6\ losses}{10\ games}$$

• $$\frac{10\ wins}{16\ games}$$

• $$\ \frac{10\ games}{16\ losses}$$

• $$\frac{6\ wins}{10\ losses}$$

Match

Match the ratio to its simplest form

• 8 : 12

• 18 : 6

• 60 : 70

• 3 : 12

• 9 : 24

2 : 3

3 : 1

6 : 7

1 : 4

3 : 8

• 2 : 3

• 3 : 1

• 6 : 7

• 1 : 4

• 3 : 8

​Proportions

​A proportion shows two equal ratios in the form of an equation.

Use cross multiplication to create an equation and solve for "X"

Multiple Choice

Which is the correct proportion to solve this problem?

Ashley read 80 pages of her book in 64 minutes. Later she read for 20 minutes. If she read at that same rate, how many pages did she read?

• $$\frac{80}{64}=\frac{x}{20}$$

• $$\frac{64}{20\ }=\frac{x}{80}$$

• $$\frac{80}{100}=\frac{x}{20}$$

• $$\frac{20}{100}=\frac{64}{x}$$

Fill in the Blanks

Solve the problem:

Ashley read 80 pages of her book in 64 minutes. Later she read for 20 minutes. If she read at that same rate, how many pages did she read?

Drag and Drop

What are the two units being compared for the ratio?

A recipe calls for 2 cups of flour to make a batch of 35 cookies.

It is comparing ​

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cups of flour to cookies

grams of sugar to muffins

liters of water to cakes

tablespoons of butter to brownies

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Solve the problem:

A recipe calls for 2 cups of flour to make a batch of 35 cookies. If Aria plans to make 175 cookies for vacation Bible school, how many cups of flour does she need?

Match

Match what is being compared in each problem

• A lion eats 168 lbs of food in 3 weeks

• A circle with a diameter of 20 units has a circumference of 62.8 units

• There are 2 adults for every 3 children in Sunday School

• A bus used 2 gallons of gas to travel 25 miles.

• She played chess 20 times and won 12 games

• $$\frac{lbs}{weeks}$$

• $$\frac{diameter}{circumference}$$

• $$\frac{adults}{children}$$

• $$\frac{gallons}{miles}$$

• $$\frac{games}{wins}$$

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On a normal week there are 2 adults attending Sunday school for every 3 children. If there were 88 adults in attendance, how many children should there be?

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A school bus went on a field trip and used 2 gallons of gas to travel 25 miles. If they traveled 175 miles, how much gas did the bus use?

Percents

a percent is a part to whole ratio, where the WHOLE is always 100


Percent problems can be found by creating proportions

Drag and Drop

Which proportions could John use to answer this problem?

What is 36% of 150

​

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36 is 30% of what number?

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What percent of 88 is 33?

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What is 125% of 64?

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Of the 300 seventh graders at a school, 246 played sports this year. What percent of the seventh grade class play sports?

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There are 480 juniors and seniors at the local high school. This represents 64% of the entire student body. How many high school students are enrolled?

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A customer brought in a $15 coupon. She purchased $45 worth of items. What percent did she save?

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The bill at a restaurant came to $136.40. The customer decided to leave a 20% tip. What was the total bill including tip?

​Percent of Change

​Describes the change over time either by an increase or a decrease

​%

100

CHANGE

ORIGINAL

​=

Fill in the Blanks

What is the change in cost of a dozen eggs:

In 2020 eggs cost $1.51

Today eggs cost $4.95

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What is the change?

Cost of apples in 2020 $1.17 per pound

In 2025 $1.55 per pound

Fill in the Blanks

What is the percent of change for apples:

Cost of apples in 2020 $1.17 per pound

In 2025 $1.55 per pound

Fill in the Blanks

What is the percent of change for a dozen eggs:

In 2020 eggs cost $1.51

Today eggs cost $4.95

​Percent Error

​Find the absolute error by subtracting the estimated amount by the actual amount

​%

100

​=

​absolute error

actual amount

Fill in the Blanks

Find the percent error:

A party was planned for 30 people but 27 actually attended.

Match

Match the absolute error:

• The weight measured was 56g but the actual weight was 53g

• The temperature recorded was 22°C but the actual temperature was 20°C

• The length measured was 150cm but the actual length was 145cm

• The speed indicated was 80km/h but the actual speed was 75km/h

• The volume measured was 2L but the actual volume was 1.8L

3g

2°C

5cm

5km/h

0.2L

• 3g

• 2°C

• 5cm

• 5km/h

• 0.2L

Fill in the Blanks

Find the percent error:

The object has a mass of 28 grams. Shelly measured it to be 30 grams.

​Simple Interest

​I = interest (money earned)
p= principal (money in the bank)
r = rate (percent)
t= time (in years

Formula to find interest:

I = prt

Match

Identify the numbers for each part of the simple interest formula.

A deposit of $900 for 20 years at a simple interest rate of 4%.

• Interest

• Principal

• Rate

• Time

• Total Value

$720

$900

0.04

20

$1,620

• $720

• $900

• 0.04

• 20

• $1,620

Fill in the Blanks

Solve the interest problems:

A $1645 deposit for 10 years at a 6% interest rate. What was the total amount of interest?

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What is the interest rate?

An $800 deposit for 2 years earned $200 in interest.

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Find the principal:

A deposit earned $90 after 36 months at an interest rate of 5%. What was the deposited amount?