ANSWER KEYS - Teacher Use Only

Multiplying Fractions | Grade 5

Student Concept Worksheet Answers
1
1/6
1/2 x 1/3 = (1x1)/(2x3) = 1/6
2
6/20 = 3/10
3/4 x 2/5 = (3x2)/(4x5) = 6/20 = 3/10 (simplified)
3
8/3 = 2 2/3
4 x 2/3 = 4/1 x 2/3 = 8/3 = 2 2/3
4
3/8 cup
1/2 x 3/4 = 3/8. Maria needs 3/8 cup of sugar.
Practice Worksheet Answers

Part A: Multiply Two Fractions

# Problem Work Answer
11/2 x 1/4(1x1)/(2x4)1/8
22/3 x 3/4(2x3)/(3x4) = 6/121/2
33/5 x 1/2(3x1)/(5x2)3/10
44/5 x 2/3(4x2)/(5x3)8/15

Part B: Multiply Fractions by Whole Numbers

# Problem Work Answer
53 x 2/53/1 x 2/5 = 6/51 1/5
63/4 x 83/4 x 8/1 = 24/46
76 x 5/66/1 x 5/6 = 30/65
82/3 x 122/3 x 12/1 = 24/38

Part C: Area Models

9
2/6 = 1/3
1/2 x 2/3: Shade 2 of 3 columns, 1 of 2 rows. Overlap = 2 out of 6 squares = 1/3
10
3/8
3/4 x 1/2: Shade 3 of 4 columns, 1 of 2 rows. Overlap = 3 out of 8 squares = 3/8

Part D: Word Problems

11
6/20 = 3/10 square yard
2/3 x 3/4 = 6/20 = 3/10 square yards (Area = length x width)
12
3/8 of the pizza
1/2 x 3/4 = 3/8 of the original pizza
13
8/3 = 2 2/3 cups
4 x 2/3 = 8/3 = 2 2/3 cups of oil
14
30/8 = 15/4 = 3 3/4 miles
6 x 5/8 = 30/8 = 15/4 = 3 3/4 miles

Challenge Questions:

#15: Less than 5/6. When you multiply by a fraction less than 1 (7/8 is less than 1), the product is smaller than the original. 5/6 x 7/8 = 35/48, which is less than 5/6 (which equals 40/48).

#16: 9/16. 3/4 x 3/4 = 9/16. Strategy: multiply numerators (3x3=9) and denominators (4x4=16).

FAST Practice Quiz Answers
1
C) 1/2
2/3 x 3/4 = 6/12 = 1/2. Note: B (6/12) is correct but not simplified. C is the best answer.
2
C) 3 1/3 or D) 10/3
5 x 2/3 = 10/3 = 3 1/3. Both C and D are correct (same value, different forms).
3
C) 3/10 square yard
Area = 3/4 x 2/5 = 6/20 = 3/10 square yard. Note: B (6/20) is correct but not simplified.
4
Select: 1/2 x 1/2, 1/2 x 3/4, and 2/5 x 1/3
1/2 x 1/2 = 1/4 (less than 1/2)
1/2 x 3/4 = 3/8 (less than 1/2 = 4/8)
3/4 x 2/3 = 6/12 = 1/2 (equal to, not less than)
2/5 x 1/3 = 2/15 (less than 1/2)
2 x 1/3 = 2/3 (greater than 1/2)
5
A) 1/4
1/3 x 3/4 = 3/12 = 1/4. Marcus ate 1/4 of the original pie. Note: B (3/12) is correct but not simplified.
6
B) When you multiply two fractions less than 1, the product is less than either fraction
A is wrong - you DON'T need common denominators for multiplication.
B is TRUE - 1/2 x 1/3 = 1/6, which is less than both 1/2 and 1/3.
C is wrong - multiplying fractions less than 1 gives smaller products.
D is wrong - you multiply (not add) numerators AND denominators.
FAST Quiz Scoring Guide
Score Interpretation Recommended Action
6/6 Mastery Ready for dividing fractions. Consider introducing mixed number multiplication.
4-5/6 Approaching Mastery Review the specific concept missed. Focus on simplifying or the "smaller product" concept.
2-3/6 Developing Reteach with area models and paper folding. Emphasize the algorithm: top x top, bottom x bottom.
0-1/6 Needs Intervention Small group instruction. Check if student is confusing with addition rules (finding common denominators).
FAST Success Kit | Grade 5 | FL B.E.S.T. Standard: MA.5.FR.2.2 | Answer Key - Teacher Use Only