Guided Practice

If two ratios are equal, then they form a proportion. When two ratios are equal, you can multiply the numerator and denominator of one ratio by the same number to get the other ratio.

This means that you can divide the numerators and then divide the denominators. If you get the same quotient each time, then the ratios form a proportion.

For this example, 5 ÷ 1 = 5 and 10 ÷ 2 = 5.Another way to determine if two ratios are equal and form a proportion is to cross multiply.

When two ratios form a proportion, their cross products are equal.

For this example, 1 × 10 = 10 and 2 × 5 = 10.Enter the height to shadow length ratio for each student. Write each ratio as a decimal by dividing each numerator by the denominator. Round to the nearest hundredth. If the ratios are equal, then they form a proportion.

Corinne's ratio:

Ryan's ratio:

The ratios (do / do not) form a proportion.

Enter the shadow length to height ratio for each student. Write each ratio as a decimal (in the form 0.X) by dividing each numerator by the denominator. Round to the nearest tenth. If the ratios are equal, then they form a proportion.

Corinne's ratio:

Ryan's ratio:

The ratios (do / do not) form a proportion.

Complete each statement. Round to the nearest tenth.

Ryan's and Corinne's shadow lengths are each times their height.

Ryan's and Corinne's heights are each times their shadow length.

The ratios for Billy and the flagpole must be equal.

Enter the ratios for Billy. Write each ratio as a decimal. Round to the nearest hundredth.

Height to shadow length:

Shadow length to height:

Use your previous work to determine the flagpole's height to the nearest whole number.

The height of the flagpole is feet.

Determine if the ratios 12 : 3 and 4 : 1 form a proportion.

The ratios 12 : 3 and 4 : 1 (do / do not) form a proportion.

Determine if the ratios 6 : 1 and 18 : 6 form a proportion.

The ratios 6 : 1 and 18 : 6 (do / do not) form a proportion.

Determine if the ratios 5 : 10 and 6 : 12 form a proportion.

The ratios 5 : 10 and 6 : 12 (do / do not) form a proportion.

Determine if the ratios 1.25/10and 125/100form a proportion.

The ratios 1.25/10and 125/100(do / do not) form a proportion.

Determine if the ratios 58/2and 7.25/0.25 form a proportion.

The ratios 58/2and 7.25/0.25(do / do not) form a proportion.

Divide across to determine if the ratios form a proportion. Write your answers as decimals or whole numbers.

45 ÷ 3 =

75 ÷ 5 =

The ratios (do / do not) form a proportion.

Divide across to determine if the ratios form a proportion. Write your answers as decimals or whole numbers.

32 ÷ 16 =

5 ÷ 2 =

The ratios (do / do not) form a proportion.

Divide across to determine if the ratios form a proportion. Write your answers as decimals or whole numbers.

8.2 ÷ 2 =

15 ÷ 30 =

The ratios (do / do not) form a proportion.

68.9 ÷ 13.78 =

40.6 ÷ 8.12 =

The ratios (do / do not) form a proportion.

Cross multiply to determine if the ratios form a proportion. Write your answers as decimals or whole numbers.

3 × 12 =

8 × 6 =

The ratios (do / do not) form a proportion.

Cross multiply to determine if the ratios form a proportion. Write your answers as decimals or whole numbers.

95 : 6 = 19 : 1.2

95 × 1.2 =

6 × 19 =

The ratios (do / do not) form a proportion.

Cross multiply to determine if the ratios form a proportion. Write your answers as decimals or whole numbers.

1/4= 25/100

1 × 100 =

4 × 25 =

The ratios (do / do not) form a proportion.

Kay worked part-time at the store for 6 hours and earned $9. Jill worked for 4 hours and earned $6. Is their pay proportional?

The ratios $9 : 6 h and $6 : 4 h are equal, so they form a proportion. The points (6, 9) and (4, 6) represent Kay's and Jill's pay ratios. Since the ratios form a proportion, the points can be connected by a straight line that runs through the origin at (0, 0).

Trinh made $12 working 8 hours, and Trudy made $6 working 4 hours. Is their pay proportional?

Plot the ordered pairs on the coordinate plane. If the points can be connected by a line running through the origin, then the students' pay ratios are proportional.

If their pay is proportional, enter the constant of proportionality. If not, enter "none".

Kim made $12 working 6 hours, and Sal made $10 working 4 hours. Is their pay proportional?

Plot the ordered pairs on the coordinate plane. If the points can be connected by a line running through the origin, then the students' pay ratios are proportional.

If their pay is proportional, enter the constant of proportionality. If not, enter "none".

At one store, you paid $1 for 2 pounds of bananas. At another store, you got 6 pounds of bananas and paid $3. Are these cost ratios proportional?

Plot the ordered pairs on the coordinate plane. If the points can be connected by a line running through the origin, then the cost ratios are proportional.

If the cost ratios are proportional, enter the constant of proportionality as a decimal. If not, enter "none".

A cyclist traveled 20 miles in 3 hours. After 5 hours, the cyclist had traveled 30 miles. Did the cyclist travel a constant speed?

Plot the ordered pairs on the coordinate plane. If the points can be connected by a line running through the origin, then the two distance-time ratios are proportional, which would mean that the cyclist's speed was constant.

If the two distance-time ratios are proportional, enter the constant of proportionality. If not, enter "none".

Are the triangle dimensions proportional?

Plot the ordered pairs on the coordinate plane. If the points can be connected by a line running through the origin, then the triangle dimensions are proportional.

If the two ratios are proportional, enter the constant of proportionality. If not, enter "none".Suppose we reverse the quantities on the coordinate plane. Do the ratios still form a proportion?

Kay's ratio: h to $

Jill's ratio: h to $

Kay's and Jill's pay ratios are proportional. In this case, that means that they both make the same per hour. This common pay ratio is called the constant of proportionality.

What is the constant of proportionality for Jill and Kay?

Jill and Kay each make $ per hour.

So, the constant of proportionality is .

Constant of proportionality:

Constant of proportionality:

Constant of proportionality:

Constant of proportionality:

Constant of proportionality:

When two angle measures add up to 90 degrees, the two angles are called complementary angles.

The two angles shown together make up a right angle, so the sum of their measures is 90 degrees. You can determine what x is by solving the equation x + 30 = 90.

So, x = 60 degrees.

When two angle measures add up to 180 degrees, the two angles are called supplementary angles.

The two angles shown together make up a straight line, so the sum of their measures is 180 degrees. You can determine what x is by solving the equation x + 20 = 180.

So, x = 160 degrees.

The two angles shown are complementary angles. Determine the value of p.

p = °

The two angles shown are complementary angles. Determine the value of h.

h = °

The two angles shown are complementary angles. Determine the value of s.

s = °

The two angles shown are supplementary angles. Determine the value of g.

g = °

The two angles shown are supplementary angles. Determine the value of w.

w = °

The two angles shown are supplementary angles. Determine the value of z.

z = °

Write a ratio equal to the given ratio to form a proportion.

10 : 60 = :