Ratios, Unit Rate, and Proportions

Proportional if...

100

How do you find the constant of proportionality (k)?

k = y/x

200

An equation is proportional if...

The equation only uses multiplication or division (no addition or subtraction).

300

A graph is proportional if...

The shape of the graph is a straight, diagonal line and the graph line passes through (0,0).

400

A table is proportional if...

When x=0, then y=0, and x is multiplied or divided by the same constant number to equal y.

500

A proportional relationship is...

A multiplicative relationship between 2 amounts that changes at a steady rate.

Unit Rate

100

If Mimi drives 50 miles in 2 hours, what is her rate (speed per hour)?

What is 25 miles per hour

200

If James types 120 words per 3 minutes, what is his rate of typing?

What is 40 words per minute

300

If 10 bags of Hot Cheetos cost $3.50, then how much does 1 cost?

What is $0.35

400

Which is the better deal:

$65 for 5 t-shirts or $100 for 8 t-shirts?

What is $100 for 8 t-shirts (rate of $12.50 per shirt)

500

How do you find the unit rate?

Divide y/x to find out the rate at which y changes per 1 unit change in x.

Proportional or Not?

100

2/3 and 4/6

Yes, proportional, 2 x 6 = 12, 3 x 4 = 12

200

Are 1/6 and 2/7 proportional?

Not Proportional, 1 x 7 = 7 and 2 x 6 = 12

300

Are 18/21 and 36/49 proportional?

No. 18/21 can be simplified to 6/7, which would be proportional to 36/42.

400

Are 51/100 and 101/200 proportional?

No. 51/100 is proportional to 102/200.

500

Are 6.1/18.3 and 8/24 proportional?

Yes. Both are equivalent to 1/3.

Solving Proportions

100

Solve for x.

x/6 = 6/12

What is 3?

200

Solve for x.

x/2 = 9/6

What is 3?

300

Solve for x.

x/3 = 2.5/7.5

What is 1?

400

Solve for x.

7/9 = 42/x

What is 54?

500

Solve for x.

1.2/0.8 = 10.8/x

What is 7.2?

Word Problems

100

Anna earns $12 in 3 hours. How much does she make in 5 hours?

What is $20?

200

Ramon gets 10 points in 4 games. How many does he get in 6 games?

What is 15 points?

300

Henry reads 8 pages in 6 minutes. How long does it take him to read 4 more pages?

What is 3 minutes?

400

Morris drives to the boba shop. He drives at 25 miles per hour. It takes him 30 minutes to get there.

How long would the drive take if he drove 50 miles per hours?

What is 15 minutes?

500

Beth goes to the amusement park. It costs $12 to get in, and $2 per ride. She goes on the roller coaster twice and on the bumper cars four times. How much does she spend?

What is $24?