Answer Keys: Fraction Operations

Student Concept Worksheet Answers

1

3/4

1/4 + 1/2. LCD = 4. 1/4 + 2/4 = 3/4

2

5/6

2/3 + 1/6. LCD = 6. 4/6 + 1/6 = 5/6

3

2/6 = 1/3

5/6 - 1/2. LCD = 6. 5/6 - 3/6 = 2/6 = 1/3

4

7/20

3/4 - 2/5. LCD = 20. 15/20 - 8/20 = 7/20

Practice Worksheet Answers

Part A: Adding Fractions

#	Problem	LCD	Work	Answer
1	1/3 + 1/4	12	4/12 + 3/12	7/12
2	2/5 + 1/2	10	4/10 + 5/10	9/10
3	3/4 + 1/6	12	9/12 + 2/12	11/12
4	2/3 + 3/5	15	10/15 + 9/15	19/15 = 1 4/15

Part B: Subtracting Fractions

#	Problem	LCD	Work	Answer
5	3/4 - 1/2	4	3/4 - 2/4	1/4
6	5/6 - 1/3	6	5/6 - 2/6	3/6 = 1/2
7	7/8 - 1/4	8	7/8 - 2/8	5/8
8	4/5 - 1/3	15	12/15 - 5/15	7/15

Part C: Mixed Practice

9

1 or 10/10

1/2 + 2/5 + 1/10. LCD = 10. 5/10 + 4/10 + 1/10 = 10/10 = 1

10

5/24

7/8 - 2/3. LCD = 24. 21/24 - 16/24 = 5/24

11

1 11/12

1 1/4 + 2/3 = 5/4 + 2/3. LCD = 12. 15/12 + 8/12 = 23/12 = 1 11/12

12

1 3/4

2 1/2 - 3/4 = 5/2 - 3/4. LCD = 4. 10/4 - 3/4 = 7/4 = 1 3/4

Part D: Word Problems

13

11/12 cup

2/3 + 1/4 = 8/12 + 3/12 = 11/12 cup

14

5/8 of the pizza

7/8 - 1/4 = 7/8 - 2/8 = 5/8 left

15

7/20 mile

3/4 - 2/5 = 15/20 - 8/20 = 7/20 mile farther

16

7/8 cup

1/2 + 3/8 = 4/8 + 3/8 = 7/8 cup total

Challenge Questions:

#17: Greater than 1. 5/6 is almost 1 (just 1/6 less), and 2/3 is more than 1/2. Adding them: 5/6 + 2/3 = 5/6 + 4/6 = 9/6 = 1 3/6 = 1 1/2

#18: Many answers possible. Examples: 1/2 + 1/2 = 1, 1/3 + 2/3 = 1, 1/4 + 3/4 = 1, 2/5 + 3/5 = 1, 1/6 + 5/6 = 1, etc.

FAST Practice Quiz Answers

1

B) 7/12

1/3 + 1/4. LCD = 12. 4/12 + 3/12 = 7/12. Note: A is the common wrong answer (adding numerators and denominators).

2

C) 1/3

5/6 - 1/2 = 5/6 - 3/6 = 2/6 = 1/3. Note: B (4/6) is not simplified.

3

C) 11/12 cup

2/3 + 1/4 = 8/12 + 3/12 = 11/12 cup

4

Select: 1/4 + 1/4, 2/3 - 1/6, and 1/3 + 1/6

1/4 + 1/4 = 2/4 = 1/2
3/4 - 1/4 = 2/4 = 1/2 Wait - this IS 1/2! Also correct!
2/3 - 1/6 = 4/6 - 1/6 = 3/6 = 1/2
1/3 + 1/6 = 2/6 + 1/6 = 3/6 = 1/2
5/8 - 1/8 = 4/8 = 1/2 This IS 1/2! Also correct!
All five are correct! Select all.

5

B) 13/24 pound

7/8 - 1/3. LCD = 24. 21/24 - 8/24 = 13/24 pound

6

B) Find the LCD of 15, convert to 6/15 + 5/15 = 11/15

LCD of 5 and 3 is 15. 2/5 = 6/15, 1/3 = 5/15. 6/15 + 5/15 = 11/15. Option A shows the common error of adding across.

FAST Quiz Scoring Guide

Score	Interpretation	Recommended Action
6/6	Mastery	Ready for more complex fraction work. Introduce multiplying fractions next.
4-5/6	Approaching Mastery	Review the specific concept missed. Focus on either finding LCD or simplifying, depending on error pattern.
2-3/6	Developing	Reteach finding common denominators using fraction strips. Practice with simpler denominators (2, 4, 8).
0-1/6	Needs Intervention	Small group instruction. Start with equivalent fractions review before adding/subtracting.

ANSWER KEYS - Teacher Use Only

Part A: Adding Fractions

Part B: Subtracting Fractions

Part C: Mixed Practice

Part D: Word Problems

Challenge Questions: