Answer Keys: Understanding Ratios

Student Concept Worksheet Answers

1

a) 2:4 or 1:2 | b) 4:2 or 2:1 | c) 2:6 or 1:3

There are 2 green and 4 red circles. Total = 6. Green to red = 2:4 = 1:2. Red to green = 4:2 = 2:1. Green to total = 2:6 = 1:3.

2

a) 14:16 or 7:8 | b) 16:14 or 8:7 | c) 14:30 or 7:15

14 boys, 16 girls. Total = 30. Boys to girls = 14:16 = 7:8. Girls to boys = 16:14 = 8:7. Boys to total = 14:30 = 7:15.

3

8:10, 12:15, 16:20 (or any equivalent)

Multiply both parts by the same number: 4x2:5x2=8:10, 4x3:5x3=12:15, 4x4:5x4=16:20

4

a) 2:3 | b) 4:3 | c) 4:7

a) 10:15 - divide both by 5 = 2:3. b) 24:18 - divide both by 6 = 4:3. c) 20:35 - divide both by 5 = 4:7.

Practice Worksheet Answers

Part A: Writing Ratios from Pictures

#	Problem	Answer	Explanation
1a	Red to blue (colon)	4:6 or 2:3	4 red, 6 blue circles
1b	Blue to red (using "to")	6 to 4 or 3 to 2	Reverse order
1c	Red to total (fraction)	4/10 or 2/5	4 red out of 10 total
2a	Squares to triangles	3:5	3 squares, 5 triangles
2b	Triangles to total	5:8	5 triangles out of 8 total
2c	Squares to total	3:8	3 squares out of 8 total

Part B: Writing Ratios from Word Problems

#	Problem	Answer	Explanation
3	12 apples, 8 oranges	12:8 or 3:2	Apples to oranges, simplified by dividing by 4
4	15 boys, 20 girls - boys to total	15:35 or 3:7	15 boys out of 35 total (15+20), simplified
5	Sugar to flour	3:2	3 cups sugar to 2 cups flour (reversed from given)
6	Trucks to total vehicles	16:40 or 2:5	16 trucks out of 40 total (24+16)

Part C: Finding Equivalent Ratios

7

12

3:4 = 9:? Since 3x3=9, multiply 4x3=12

8

15

5:6 = ?:18. Since 6x3=18, multiply 5x3=15

9

3

8:12 = 2:? Since 8/4=2, divide 12/4=3

10

12

?:15 = 4:5. Since 5x3=15, multiply 4x3=12

Part D: Writing Equivalent Ratios

11

4:10, 6:15, 8:20 (or other equivalent ratios)

Multiply both parts of 2:5 by 2, 3, 4, etc.

12

Simplified: 3:2. Equivalent: 9:6, 12:8, 15:10

6:4 simplifies to 3:2. Then multiply to get equivalents.

Part E: Word Problems

13

8 cups of bananas

3:2 = 12:? Since 3x4=12, multiply 2x4=8

14

40 dogs

5:3 = ?:24. Since 3x8=24, multiply 5x8=40

15

44 people total

7:4 means 7+4=11 parts total. If 28 prefer pizza and 7 parts=28, then 1 part=4. Tacos = 4x4=16. Total = 28+16=44

16

100 6th graders

2:9 = ?:450. Since 9x50=450, multiply 2x50=100

Challenge Questions:

#17: Class A: 3:4 = 0.75 (3 divided by 4). Class B: 2:3 = 0.667 (2 divided by 3). Since 0.75 > 0.667, Class A has a greater ratio of boys to girls.

#18: Red:Blue = 2:3 and Blue:Green = 3:4. The blue values are the same (3), so we can combine: Red:Blue:Green = 2:3:4. Therefore, Red:Green = 2:4 = 1:2.

FAST Practice Quiz Answers

1

B) 2:3

8:12 simplified by dividing both by 4 = 2:3. Note: A is correct but not in simplest form. C reverses the order. D adds incorrectly.

2

C) 5:8

5 green out of 8 total (5+3=8). This is part-to-whole. A and B are part-to-part ratios. D is red to total.

3

B) 8 cups

3:2 = 12:? Since 3x4=12, we need 2x4=8 cups of sugar.

4

Select: 2:3, 12:18, and 6:9

2:3 = 4:6 (divide by 2)
8:10 does not equal 4:6
12:18 = 4:6 (divide by 3)
6:9 = 4:6 (multiply by 1.5 or simplify both to 2:3)
10:15 = 2:3 which equals 4:6 - Actually this IS equivalent!
Correction: 2:3, 12:18, 6:9, and 10:15 are all equivalent to 4:6 (all simplify to 2:3)

5

A) 25 boys

5:7 = ?:35. Since 7x5=35, multiply 5x5=25 boys.

6

B) For every 3 cats, there are 5 dogs

The ratio 3/5 for cats to dogs means "3 cats for every 5 dogs." A confuses total. C describes a part-to-whole fraction. D reverses the order.

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