Writing & Solving Proportions Lesson

Writing & Solving Proportions Using Proportional Reasoning

TAKE NOTES AS YOU COMPLETE THIS LESSON​

​A proportion is 2 equivalent ratios.

​We can use proportional reasoning to solve problems.

​She has 24 quarts of Blazing Blue paint. How many quarts of Ruby Red does she need?

​She has 24 quarts of Blazing Blue paint. How many quarts of Ruby Red does she need?

​The ratios of the paint needs to be proportional, so we can set up a proportion.

​She has 24 quarts of Blazing Blue paint. How many quarts of Ruby Red does she need?

​x = 16

16 quarts of Ruby Red paint​

In an animal shelter, the ratio of dogs to cats is 5 to 7. There are 25 dogs. Write a proportion and use proportional reasoning to find the total number of animals.

Let's write the proportion in words first.

Dogs

Cats

The ratio of dogs to cats is 5 to 7. There are 25 dogs. Write and solve a proportion to find the total number of animals

Now let's fill in the numbers.

Dogs = 5

Cats 7

the ratio of dogs to cats is 5 to 7. There are 25 dogs. Write and solve a proportion to find the total number of animals

Now we need to set up a proportion​

the ratio of dogs to cats is 5 to 7. There are 25 dogs. Write and solve a proportion to find the total number of animals

​

​We ask ourself: "How did I get from 5 to 25?"

MULTIPLY BY 5​

​If you multiply the numerators by 5, you have to multiply the denominator by 5

BUT.........​

​

​THE QUESTION ASKS:

​

​WHAT IS THE TOTAL NUMBER OF ANIMALS?????

​25 DOGS + 35 CATS = 60 ANIMALS

In an exercise class, the ratio of men to women is 3:4. If there are 21 men, how many women are in the exercise class?

Set up a proportion of men over women.​

In an exercise class, the ratio of men to women is 3:4. If there are 21 men, how many women are in the exercise class?

In an exercise class, the ratio of men to women is 3:4. If there are 21 men, how many women are in the exercise class?

​3 x 7 = 21

4 x 7 = 28​

​There are 28 women in the class.

The ratio of boys to girls is 3 to 2. If there are 12 boys, how many girls are there?

Multiple Choice

The ratio of boys to girls is 3 to 2. If there are 12 boys, how many girls are there?

• 8

• 4

• 16

• 11

Multiple Choice

The ratio of boys to girls is 3 to 2. If there are 12 boys, how many total students are there?

• 20

• 8

• 16

• 14

Multiple Choice

• 4

• 12

• 3

• 2

Multiple Choice

Solve for x 

• x = 1/10
• x = 10
• x = 4
• x = 5

Multiple Choice

The ratio of boys to girls in the club is 2:3. There are 10 boys in a club.Use a proportion to find the total number of people in the club.

• 35

• 15

• 25

• 90

Multiple Choice

In a certain apartment building, the ratio of people to cars is 3:5. If there are 30 people, how many cars are there?

• 35
• 60
• 18
• 50