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Dividing Fractions | Grade 5

Student Concept Worksheet Answers
1
1/6
1/3 / 2 = 1/(3 x 2) = 1/6. Splitting 1/3 between 2 people gives each person 1/6.
2
8
4 / 1/2 = 4 x 2 = 8. There are 8 halves in 4 wholes.
3
Type 1: 1/4 / 5 = 1/20 meter
The ribbon (1/4 meter) is being cut into 5 pieces, so each piece = 1/4 / 5 = 1/20 meter.
4
Type 2: 6 / 1/3 = 18 pillowcases
Finding how many 1/3 yard pieces fit in 6 yards: 6 / 1/3 = 6 x 3 = 18.
Practice Worksheet Answers

Part A: Unit Fraction / Whole Number

# Problem Answer Work
11/2 / 31/61/(2 x 3) = 1/6
21/4 / 21/81/(4 x 2) = 1/8
31/3 / 51/151/(3 x 5) = 1/15
41/6 / 21/121/(6 x 2) = 1/12

Part B: Whole Number / Unit Fraction

# Problem Answer Work
52 / 1/482 x 4 = 8
65 / 1/3155 x 3 = 15
73 / 1/5153 x 5 = 15
86 / 1/2126 x 2 = 12

Part C: Visual Models

9
1/3 / 2 = 1/6
Dividing 1/3 equally among 2 people gives each 1/6 of the whole.
10
2 / 1/4 = 8
Two whole bars divided into fourths: 4 + 4 = 8 pieces total.

Part D: Word Problems

11
1/2 / 4 = 1/8
Maria has 1/2 pan, shares among 4 friends: 1/2 / 4 = 1/8 of the pan each.
12
4 / 1/3 = 12 pizzas
4 pounds / (1/3 pound per pizza) = 4 x 3 = 12 pizzas.
13
1/4 / 3 = 1/12 yard
Cutting 1/4 yard into 3 pieces: 1/4 / 3 = 1/12 yard each.
14
5 / 1/4 = 20 muffins
5 cups / (1/4 cup per muffin) = 5 x 4 = 20 muffins.

Challenge Questions:

#15: 6 / 1/2 = 12 is greater than 1/2 / 6 = 1/12. When you divide a whole by a fraction, you get a bigger number. When you divide a fraction by a whole, you get a smaller number.

#16: 1 / 1/2 = 2, 2 / 1/2 = 4, 3 / 1/2 = 6, 4 / 1/2 = 8. Pattern: The answer is always double the whole number (multiply by 2).

FAST Practice Quiz Answers
1
C) 1/12
1/4 / 3 = 1/(4 x 3) = 1/12. Dividing a unit fraction by a whole number multiplies the denominator.
2
C) 18
6 / 1/3 = 6 x 3 = 18. There are 18 thirds in 6 wholes.
3
C) 8 batches
4 / 1/2 = 4 x 2 = 8. There are 8 half-cups in 4 cups.
4
Select: 5 / 1/2 and 3 / 1/4
1/2 / 5 = 1/10 (less than 1)
5 / 1/2 = 10 (greater than 1)
1/3 / 2 = 1/6 (less than 1)
3 / 1/4 = 12 (greater than 1)
1/6 / 6 = 1/36 (less than 1)
5
B) 1/9
Lisa has 1/3 pie shared among 3 people: 1/3 / 3 = 1/9 of the whole pie each.
6
A) 3 / 1/4 = 12
The model shows how many fourths are in 3 wholes: 3 / 1/4 = 12 fourths total.
FAST Quiz Scoring Guide
Score Interpretation Recommended Action
6/6 Mastery Ready for mixed fraction operations. Consider extension to dividing non-unit fractions.
4-5/6 Approaching Mastery Review the type that was missed (fraction/whole vs. whole/fraction). Use visual models to reinforce.
2-3/6 Developing Reteach with manipulatives. Focus on understanding the difference between the two types of division.
0-1/6 Needs Intervention Small group instruction with concrete models. Start with "sharing" scenarios (Type 1) before "how many fit" (Type 2).
FAST Success Kit | Grade 5 | FL B.E.S.T. Standard: MA.5.FR.2.3 | Answer Key - Teacher Use Only