Academic Worksheet 6.1
Tell whether the ratio is in simplest form. If not, write it in simplest form. Then, write the ratio in two other
ways.
39
13
1.
4:6
5.
Order the ratios from least to greatest.
2.
3.
17 to 44
4.
63 to 18
12
4
, 7 to 10, 8 : 12, 9 to 15, .
16
18
Find the unit rate.
6.
72 people
3 buses
7.
288 mi
12 gallons
8.
1125 calories
4.5 hours
Tell whether the ratios are equivalent.
9.
12
24
and
9
18
10.
14 : 4 and 21 : 8
12.
12 km
?m

1h
1 min
Write the equivalent rate.
11.
8 calls ? calls

1 hour
1 day
13. One box of cereal is 20 ounces and costs $3. A smaller box of the same type of cereal is 12 ounces and
costs $2. Which box of cereal is the better buy? Explain.
14. There are 60 students presenting experiments at a science fair. Each student must present their
experiment to a panel of judges. The time allotted for all the presentations is 5 hours. How many
minutes does each student have to present their experiments?
15. Find the ratio of the area of the shaded square region to the area of the unshaded square region.
Academic Worksheet 6.2
Use equivalent ratios to solve the proportion.
1.
x
154

20 280
2.
25 375

28
x
3.
34
x

9 162
5.
x 12

36 16
6.
x 11

14 35
Use algebra to solve the proportion.
4.
15
x

65 13
In Exercises 7 – 9, write and solve a proportion to solve the problem.
7. Four notebooks cost $4.40. How many notebooks can you buy for $6.60?
8. Two roses cost $3.50. How many roses can you buy for $17.50?
9. Carl works 8 hours and earns $52. How many hours would he have to work to earn $130?
10. Store A sells 10 CD jewel cases for $9. Store B sells 15 CD jewel cases for $12. How much money will
you save if you buy 30 CD jewel cases at the store with the lower unit price?
Academic Worksheet 6.3
Tell whether the ratios form a proportion.
1.
70 20
,
28 8
2.
115 161
,
85 136
Solve the proportion using cross products.
3.
9
12

102
x
4.
14.6
x

23 11.5
5.
12 0.4

x
9
7.
x  4 14

42
84
8.
18 3 x

50 175
Find the value of 𝑥.
6.
51
15

x  11 5
9. In a batch of 120 manufactured machine parts, 3 are found to be defective. At this rate, how many
machine parts would be defective in a batch of 12,000?
10. You travel 24 miles in 2 hours while biking.
a. At this rate, how far can you bike in 5 hours?
b. At this rate, how long will it take to bike 30 miles? Write your answer in hours and minutes.
Academic Worksheet 6.4
Given 𝐸𝐹𝐺𝐻~𝐽𝐾𝐿𝑀, tell whether the statement is true or false.
1. ∠𝐹 and ∠𝐽 are corresponding angles.
2. ̅̅̅̅
𝐺𝐻 and ̅̅̅̅
𝐿𝑀 are corresponding sides.
3. ∠𝐻 and ∠M are corresponding angles.
4. ̅̅̅̅
𝐻𝐸 and ̅̅̅̅
𝑀𝐽 are corresponding sides.
̅̅̅̅ and 𝐾𝐿
̅̅̅̅ are corresponding sides.
6. ∠𝐺 and ∠𝐾 are corresponding angles.
5. 𝐹𝐺
7.
Given 𝐷𝐸𝐹𝐺~𝑅𝑆𝑇𝑈, name the corresponding angles and the corresponding sides.
Tell whether the figures are similar. If they are, find the ratio of the lengths of the corresponding sides of
figure A to figure B.
Copy and complete the statement using always, sometimes, or never.
12. Congruent figures are __?__ similar.
13. Similar figures are __?__ congruent.
14. Two squares are __?__ similar.
15. Two rectangles are __?__ congruent.
16. Given 𝐸𝐹𝐺𝐻 ≅ 𝑃𝑄𝑅𝑆, find the indicated measure.
a. 𝑅𝑄
b. 𝑚∠𝐹