# Multiplying Fractions and Whole Numbers - Grade 5
Section A: Multiple Choice Questions
Q1: What is \( \frac{1}{4} \times 8 \)? (a) 2 (b) 4 (c) 32 (d) \( \frac{1}{32} \)
Solution:
Ans: (a) Explanation: To multiply a fraction by a whole number, multiply the numerator by the whole number: \( \frac{1 \times 8}{4} = \frac{8}{4} = 2 \). Option (b) would be the result if we multiplied \( \frac{1}{2} \times 8 \). Option (c) incorrectly multiplies both numerator and denominator by 8. Option (d) incorrectly divides instead of multiplies.
Q2: Maria ate \( \frac{2}{5} \) of 15 cookies. How many cookies did she eat? (a) 5 cookies (b) 6 cookies (c) 7 cookies (d) 8 cookies
Solution:
Ans: (b) Explanation: Multiply \( \frac{2}{5} \times 15 = \frac{2 \times 15}{5} = \frac{30}{5} = 6 \) cookies. Option (a) would be \( \frac{1}{3} \times 15 \). Option (c) is not the correct product. Option (d) would be the result of a calculation error.
Q3: Which expression shows the correct way to multiply \( 12 \times \frac{3}{4} \)? (a) \( \frac{12}{3} \times 4 \) (b) \( \frac{12 \times 3}{4} \) (c) \( \frac{3}{12 \times 4} \) (d) \( 12 \times 3 \times 4 \)
Solution:
Ans: (b) Explanation: When multiplying a whole number by a fraction, we multiply the whole number by the numerator and keep the denominator: \( 12 \times \frac{3}{4} = \frac{12 \times 3}{4} \). Option (a) changes the operation incorrectly. Option (c) puts the whole number in the wrong position. Option (d) ignores the fraction completely.
Q4: What is \( 7 \times \frac{1}{2} \)? (a) 14 (b) \( \frac{7}{2} \) or \( 3\frac{1}{2} \) (c) \( \frac{1}{14} \) (d) 7
Solution:
Ans: (b) Explanation: Multiply the whole number by the numerator: \( 7 \times \frac{1}{2} = \frac{7 \times 1}{2} = \frac{7}{2} \), which equals \( 3\frac{1}{2} \) as a mixed number. Option (a) incorrectly multiplies 7 by 2. Option (c) incorrectly divides. Option (d) doesn't perform any operation.
Q5: A recipe needs \( \frac{3}{8} \) cup of sugar for one batch. How much sugar is needed for 4 batches? (a) \( \frac{3}{32} \) cups (b) \( \frac{7}{8} \) cups (c) \( \frac{12}{8} \) or \( 1\frac{1}{2} \) cups (d) \( \frac{3}{2} \) cups
Solution:
Ans: (c) Explanation: Multiply \( 4 \times \frac{3}{8} = \frac{4 \times 3}{8} = \frac{12}{8} = \frac{3}{2} = 1\frac{1}{2} \) cups. Option (a) incorrectly multiplies the denominator. Option (b) adds instead of multiplies. Option (d) is the simplified form but the question shows both forms in option (c).
Q6: What is \( \frac{5}{6} \times 18 \)? (a) 12 (b) 15 (c) 18 (d) 20
Solution:
Ans: (b) Explanation: Multiply \( \frac{5}{6} \times 18 = \frac{5 \times 18}{6} = \frac{90}{6} = 15 \). We can also think of this as dividing 18 by 6 to get 3, then multiplying by 5 to get 15. Option (a) would be \( \frac{4}{6} \times 18 \). Option (c) is the original whole number. Option (d) is too large.
Q7: If \( \frac{2}{3} \times 9 = 6 \), what does \( \frac{2}{3} \times 12 \) equal? (a) 6 (b) 8 (c) 9 (d) 10
Solution:
Ans: (b) Explanation: Multiply \( \frac{2}{3} \times 12 = \frac{2 \times 12}{3} = \frac{24}{3} = 8 \). We multiply the numerator (2) by the whole number (12) and divide by the denominator (3). Option (a) is the answer to the first problem. Option (c) is one of the factors. Option (d) is incorrect.
Q8: Which problem has the greatest product? (a) \( 5 \times \frac{3}{4} \) (b) \( 6 \times \frac{1}{2} \) (c) \( 4 \times \frac{7}{8} \) (d) \( 8 \times \frac{1}{3} \)
Q9: When multiplying a fraction by a whole number, multiply the __________ by the whole number and keep the denominator the same.
Solution:
Ans: numerator Explanation: The rule for multiplying a fraction by a whole number is to multiply the numerator by the whole number while keeping the denominator unchanged. For example, \( \frac{2}{5} \times 3 = \frac{2 \times 3}{5} = \frac{6}{5} \).
Q10: The product of \( 9 \times \frac{2}{3} \) is __________.
Solution:
Ans: 6 Explanation: Multiply \( 9 \times \frac{2}{3} = \frac{9 \times 2}{3} = \frac{18}{3} = 6 \). This demonstrates that multiplying a whole number by a fraction can result in a whole number when the numerator's product is divisible by the denominator.
Q11: If you multiply any whole number by \( \frac{1}{1} \), the product is __________.
Solution:
Ans: the same whole number (or the original number) Explanation: The fraction \( \frac{1}{1} \) equals 1, and any number multiplied by 1 equals itself. This is called the identity property of multiplication. For example, \( 7 \times \frac{1}{1} = 7 \).
Q12: \( \frac{4}{5} \times 20 = \) __________
Solution:
Ans: 16 Explanation: Multiply \( \frac{4}{5} \times 20 = \frac{4 \times 20}{5} = \frac{80}{5} = 16 \). We can also simplify by dividing 20 by 5 to get 4, then multiplying by 4 to get 16.
Q13: When you multiply a whole number by a fraction less than 1, the product is __________ than the whole number.
Solution:
Ans: less (or smaller) Explanation: When multiplying by a fraction less than 1, you are finding a part of the whole number, so the result is always smaller than the original whole number. For example, \( 10 \times \frac{1}{2} = 5 \), which is less than 10.
Q14: The expression \( 6 \times \frac{5}{8} \) can be rewritten as \( \frac{6 \times 5}{8} \) which simplifies to __________.
Solution:
Ans: \( \frac{30}{8} \) or \( \frac{15}{4} \) or \( 3\frac{3}{4} \) Explanation: Calculate \( \frac{6 \times 5}{8} = \frac{30}{8} \). This can be simplified by dividing both numerator and denominator by 2 to get \( \frac{15}{4} \), which equals \( 3\frac{3}{4} \) as a mixed number.
Section C: Word Problems
Q15: A rope is 24 feet long. If Sarah cuts off \( \frac{5}{6} \) of the rope, how many feet of rope did she cut off?
Solution:
Ans: Step 1: Multiply the fraction by the whole number: \( \frac{5}{6} \times 24 \) Step 2: \( \frac{5 \times 24}{6} = \frac{120}{6} \) Step 3: \( \frac{120}{6} = 20 \) Final Answer: 20 feet
Q16: A farmer has 18 acres of land. He plants corn on \( \frac{2}{9} \) of his land. How many acres are planted with corn?
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