• proportional

• proportion

• cross product

• Solve proportions.

Identify Proportional Relationships

MATH Before dinner, Mohammed solved 8 math problems in 12 minutes. After dinner, he solved 2 problems in 3 minutes. Is the number of problems he solved proportional to the time?

Method 1 Compare unit rates (We did this before).

Since the unit rates are equal, the number of math equations is proportional to the time in minutes.

Identify Proportional Relationships

Method 2 Compare ratios by comparing cross products.

Answer: Since the cross products are equal, the number of math equations is proportional to the time in minutes.

24 = 24Multiply.

?

8 × 3 = 12 × 2 Find the cross products.?

1. A

2. B

A. yes

B. no

Determine if the quantities $30 for 12 gallons of gasoline and $10 for 4 gallons of gasoline are proportional.

Solve a Proportion

5x = 8 ● 18Find the cross

products.

5x = 144Multiply.

Answer: x = 28.8

Write the proportion.

Divide each side by 5.

x= 28.8

1. A

2. B

3. C

4. D

A. k = 9.4

B. k = 12

C. k = 10.8

D. k = 18.6

Solve a Proportion

3.5 ● n = 14 ● 6Find the cross

products.

3.5n = 84Multiply.

Answer: The solution is 24.

Write the proportion.

Divide each side by 3.5.

n = 24Simplify.

1. A

2. B

3. C

4. D

A. w = 5.25

B. w = 5.5

C. w = 5.75

D. w = 6.25

FLAGS According to specifications, the ratio of the length of the U.S. flag to its width must be 1.9 to 1. How long must a U.S. flag be if it is designed to have a width of 2.5 feet?

Answer: The length of a U.S. flag having a width of 2.5 feet must be 4.75 feet.

length Write a proportion.width

Find the cross products.

Multiply.

1. A

2. B

3. C

4. D

A. 72 girls

B. 108 girls

C. 120 girls

D. 148 girls

SCHOOL The ratio of boys to girls at Blue Hills Middle School is 4 to 5. How many girls attend the school if there are 96 boys?

End of the Lesson