ANSWER KEYS - Teacher Use Only

Dividing Fractions | Grade 6

Student Concept Worksheet Answers
1
3/2 or 1 1/2
3/4 / 1/2 = 3/4 x 2/1 = 6/4 = 3/2 = 1 1/2
2
5/4 or 1 1/4
5/6 / 2/3 = 5/6 x 3/2 = 15/12 = 5/4 = 1 1/4
3
2
4/5 / 2/5 = 4/5 x 5/2 = 20/10 = 2
4
6
2 1/4 = 9/4. Then 9/4 / 3/8 = 9/4 x 8/3 = 72/12 = 6
Practice Worksheet Answers

Part A: Divide Fractions by Fractions

# Problem Keep-Change-Flip Answer
11/2 / 1/41/2 x 4/1 = 4/22
23/4 / 1/23/4 x 2/1 = 6/43/2 = 1 1/2
32/3 / 1/62/3 x 6/1 = 12/34
45/8 / 3/45/8 x 4/3 = 20/245/6
54/5 / 2/34/5 x 3/2 = 12/106/5 = 1 1/5
67/8 / 1/47/8 x 4/1 = 28/87/2 = 3 1/2

Part B: Divide with Mixed Numbers

# Problem Convert & Solve Answer
71 1/2 / 1/43/2 x 4/1 = 12/26
82 1/3 / 2/37/3 x 3/2 = 21/67/2 = 3 1/2
93 3/4 / 1 1/215/4 / 3/2 = 15/4 x 2/3 = 30/125/2 = 2 1/2
105/6 / 2 1/25/6 / 5/2 = 5/6 x 2/5 = 10/301/3

Part C: Word Problems

11
6 craft projects
3/4 / 1/8 = 3/4 x 8/1 = 24/4 = 6 projects
12
4 scoops
2/3 / 1/6 = 2/3 x 6/1 = 12/3 = 4 scoops
13
6 bows
2 1/4 = 9/4. Then 9/4 / 3/8 = 9/4 x 8/3 = 72/12 = 6 bows
14
2 1/2 times farther
5/6 / 1/3 = 5/6 x 3/1 = 15/6 = 5/2 = 2 1/2 times
15
6 water bottles
4 1/2 = 9/2. Then 9/2 / 3/4 = 9/2 x 4/3 = 36/6 = 6 bottles

Challenge Questions:

#16: Greater than the original fraction. When you divide by a fraction less than 1, you get more pieces (a larger number). Example: 1/2 / 1/4 = 2. You're finding how many 1/4s fit in 1/2, which is more than 1.

#17: Many answers possible. Example: "I have 1 1/2 cups of flour. Each muffin needs 1/4 cup. How many muffins can I make?" Answer: 1 1/2 / 1/4 = 3/2 x 4/1 = 6 muffins.

FAST Practice Quiz Answers
1
B) 3/2 (or 1 1/2)
3/4 / 1/2 = 3/4 x 2/1 = 6/4 = 3/2. Note: A (3/8) is the common error of multiplying instead of dividing.
2
B) 5/6
2/3 / 4/5 = 2/3 x 5/4 = 10/12 = 5/6. Note: A (8/15) is the multiplication answer, not division.
3
A) 10 pieces
5/6 / 1/12 = 5/6 x 12/1 = 60/6 = 10 pieces
4
Select: 1/2 / 1/4, 2/3 / 1/3, 3/4 / 3/8, 4/5 / 2/5, 5/6 / 5/12
1/2 / 1/4 = 1/2 x 4/1 = 2
2/3 / 1/3 = 2/3 x 3/1 = 2
3/4 / 3/8 = 3/4 x 8/3 = 24/12 = 2
4/5 / 2/5 = 4/5 x 5/2 = 20/10 = 2
5/6 / 5/12 = 5/6 x 12/5 = 60/30 = 2
All five equal 2! Select all.
5
B) 3 1/3
2 1/2 = 5/2. Then 5/2 / 3/4 = 5/2 x 4/3 = 20/6 = 10/3 = 3 1/3
6
A) Multiply 3/5 by the reciprocal of 2/7, which is 7/2, to get 21/10
This correctly describes Keep-Change-Flip: 3/5 x 7/2 = 21/10 = 2 1/10. Option B flips the wrong fraction. Option C describes multiplication. Option D describes subtraction.
FAST Quiz Scoring Guide
Score Interpretation Recommended Action
6/6 Mastery Ready for complex fraction problems. Introduce dividing with decimals next.
4-5/6 Approaching Mastery Review the specific concept missed. Focus on mixed number conversion if that was the issue.
2-3/6 Developing Reteach Keep-Change-Flip with visual models. Practice finding reciprocals first.
0-1/6 Needs Intervention Small group instruction. Review multiplication of fractions before division.
FAST Success Kit | Grade 6 | FL B.E.S.T. Standards: MA.6.NSO.2.1, MA.6.NSO.2.2 | Answer Key - Teacher Use Only