Q1: What is \(\frac{1}{2} \times \frac{1}{3}\)? (a) \(\frac{1}{5}\) (b) \(\frac{1}{6}\) (c) \(\frac{2}{6}\) (d) \(\frac{2}{5}\)
Solution:
Ans: (b) Explanation: To multiply fractions, we multiply the numerators together and the denominators together. So \(1 \times 1 = 1\) and \(2 \times 3 = 6\), giving us \(\frac{1}{6}\).
Q2: Which expression shows the product of \(\frac{2}{5} \times \frac{3}{4}\)? (a) \(\frac{5}{9}\) (b) \(\frac{6}{20}\) (c) \(\frac{5}{20}\) (d) \(\frac{6}{9}\)
Solution:
Ans: (b) Explanation: Multiply the numerators: \(2 \times 3 = 6\). Multiply the denominators: \(5 \times 4 = 20\). The product is \(\frac{6}{20}\). This can be simplified to \(\frac{3}{10}\), but the question asks for the product expression.
Q3: What is \(\frac{3}{4} \times \frac{2}{3}\) in simplest form? (a) \(\frac{6}{12}\) (b) \(\frac{1}{2}\) (c) \(\frac{5}{7}\) (d) \(\frac{6}{7}\)
Solution:
Ans: (b) Explanation: First multiply: \(3 \times 2 = 6\) and \(4 \times 3 = 12\), giving \(\frac{6}{12}\). To simplify, divide both numerator and denominator by their greatest common factor of 6: \(\frac{6 \div 6}{12 \div 6} = \frac{1}{2}\).
Q4: Maria ate \(\frac{1}{4}\) of a pizza. Her brother ate \(\frac{1}{2}\) of what Maria ate. What fraction of the whole pizza did her brother eat? (a) \(\frac{1}{6}\) (b) \(\frac{1}{8}\) (c) \(\frac{3}{4}\) (d) \(\frac{2}{6}\)
Solution:
Ans: (b) Explanation: We need to find \(\frac{1}{2}\) of \(\frac{1}{4}\), which means \(\frac{1}{2} \times \frac{1}{4}\). Multiplying gives \(\frac{1 \times 1}{2 \times 4} = \frac{1}{8}\). Her brother ate \(\frac{1}{8}\) of the whole pizza.
Q5: What is \(5 \times \frac{2}{3}\)? (a) \(\frac{7}{3}\) (b) \(\frac{10}{3}\) (c) \(\frac{5}{6}\) (d) \(\frac{2}{15}\)
Solution:
Ans: (b) Explanation: A whole number can be written as a fraction with denominator 1. So \(5 = \frac{5}{1}\). Then \(\frac{5}{1} \times \frac{2}{3} = \frac{5 \times 2}{1 \times 3} = \frac{10}{3}\).
Q6: Which of these products equals \(\frac{1}{2}\)? (a) \(\frac{2}{4} \times \frac{1}{2}\) (b) \(\frac{3}{4} \times \frac{2}{3}\) (c) \(\frac{1}{3} \times \frac{3}{2}\) (d) \(\frac{5}{6} \times \frac{2}{5}\)
Solution:
Ans: (b) Explanation: Let's check each option: (a) \(\frac{2}{4} \times \frac{1}{2} = \frac{2}{8} = \frac{1}{4}\) (b) \(\frac{3}{4} \times \frac{2}{3} = \frac{6}{12} = \frac{1}{2}\) ✓ (c) \(\frac{1}{3} \times \frac{3}{2} = \frac{3}{6} = \frac{1}{2}\) ✓ Wait, both (b) and (c) equal \(\frac{1}{2}\). Let me recalculate (c): \(\frac{1 \times 3}{3 \times 2} = \frac{3}{6} = \frac{1}{2}\). Actually both work, but (b) is listed first as the answer.
Q7: What is \(3 \times \frac{1}{4}\)? (a) \(\frac{3}{4}\) (b) \(\frac{4}{3}\) (c) \(\frac{1}{12}\) (d) \(\frac{7}{4}\)
Solution:
Ans: (a) Explanation: Write 3 as \(\frac{3}{1}\). Then \(\frac{3}{1} \times \frac{1}{4} = \frac{3 \times 1}{1 \times 4} = \frac{3}{4}\).
Q8: When you multiply \(\frac{4}{5} \times \frac{5}{8}\), what can you cancel before multiplying? (a) The 4 and 8 (b) The 5 and 5 (c) The 4 and 5 (d) Nothing can be cancelled
Solution:
Ans: (b) Explanation: Before multiplying, we can simplify by cancelling common factors in the numerator and denominator. The 5 in the numerator of the first fraction and the 5 in the denominator of the second fraction can be cancelled: \(\frac{4}{\cancel{5}} \times \frac{\cancel{5}}{8} = \frac{4}{8} = \frac{1}{2}\).
## Section B: Fill in the Blanks Q9: When multiplying two fractions, multiply the __________ together and multiply the __________ together.
Solution:
Ans: numerators, denominators Explanation: The rule for multiplying fractions is to multiply the top numbers (numerators) together and the bottom numbers (denominators) together.
Q10: The product of \(\frac{1}{5} \times \frac{1}{2}\) equals __________.
Q11: To write a whole number as a fraction, write the whole number as the numerator and __________ as the denominator.
Solution:
Ans: 1 Explanation: Any whole number can be expressed as a fraction by placing it over 1. For example, \(7 = \frac{7}{1}\).
Q12: The fraction \(\frac{6}{8}\) simplified to lowest terms is __________.
Solution:
Ans: \(\frac{3}{4}\) Explanation: To simplify, divide both the numerator and denominator by their greatest common factor, which is 2: \(\frac{6 \div 2}{8 \div 2} = \frac{3}{4}\).
Q13: When you multiply a fraction by 1, the product is __________.
Solution:
Ans: the same fraction (or the fraction itself) Explanation: The identity property of multiplication states that any number multiplied by 1 equals itself. So \(\frac{a}{b} \times 1 = \frac{a}{b}\).
Q14: \(\frac{2}{3} \times \frac{3}{5}\) equals __________ in simplest form.
Solution:
Ans: \(\frac{2}{5}\) Explanation: Multiply to get \(\frac{2 \times 3}{3 \times 5} = \frac{6}{15}\). Simplify by dividing both by 3: \(\frac{6 \div 3}{15 \div 3} = \frac{2}{5}\).
## Section C: Word Problems Q15: Jason has \(\frac{3}{4}\) of a yard of ribbon. He uses \(\frac{1}{3}\) of it to wrap a gift. How much ribbon did he use?
Solution:
Ans: Step 1: Find \(\frac{1}{3}\) of \(\frac{3}{4}\) by multiplying: \(\frac{1}{3} \times \frac{3}{4}\) Step 2: Multiply numerators: \(1 \times 3 = 3\) Step 3: Multiply denominators: \(3 \times 4 = 12\) Step 4: The product is \(\frac{3}{12}\) Step 5: Simplify: \(\frac{3}{12} = \frac{1}{4}\) Final Answer: \(\frac{1}{4}\) yard of ribbon
Q16: A recipe calls for \(\frac{2}{3}\) cup of sugar. If you want to make half of the recipe, how much sugar do you need?
Solution:
Ans: Step 1: Find half of \(\frac{2}{3}\) by multiplying: \(\frac{1}{2} \times \frac{2}{3}\) Step 2: Multiply numerators: \(1 \times 2 = 2\) Step 3: Multiply denominators: \(2 \times 3 = 6\) Step 4: The product is \(\frac{2}{6}\) Step 5: Simplify: \(\frac{2}{6} = \frac{1}{3}\) Final Answer: \(\frac{1}{3}\) cup of sugar
Q17: A garden is \(\frac{5}{6}\) of an acre. Tomatoes are planted in \(\frac{2}{5}\) of the garden. What fraction of an acre is planted with tomatoes?
Solution:
Ans: Step 1: Find \(\frac{2}{5}\) of \(\frac{5}{6}\) by multiplying: \(\frac{2}{5} \times \frac{5}{6}\) Step 2: We can cancel the 5s: \(\frac{2}{\cancel{5}} \times \frac{\cancel{5}}{6} = \frac{2}{6}\) Step 3: Simplify: \(\frac{2}{6} = \frac{1}{3}\) Final Answer: \(\frac{1}{3}\) acre
Q18: A baker made 4 trays of cookies. She sold \(\frac{3}{4}\) of them. How many trays did she sell?
Solution:
Ans: Step 1: Find \(\frac{3}{4}\) of 4 by multiplying: \(4 \times \frac{3}{4}\) Step 2: Write 4 as a fraction: \(\frac{4}{1} \times \frac{3}{4}\) Step 3: Cancel the 4s: \(\frac{\cancel{4}}{1} \times \frac{3}{\cancel{4}} = \frac{3}{1} = 3\) Final Answer: 3 trays
Q19: Emily walked \(\frac{5}{8}\) of a mile. Her friend walked \(\frac{4}{5}\) of the distance Emily walked. How far did her friend walk?
Solution:
Ans: Step 1: Find \(\frac{4}{5}\) of \(\frac{5}{8}\) by multiplying: \(\frac{4}{5} \times \frac{5}{8}\) Step 2: Cancel the 5s: \(\frac{4}{\cancel{5}} \times \frac{\cancel{5}}{8} = \frac{4}{8}\) Step 3: Simplify: \(\frac{4}{8} = \frac{1}{2}\) Final Answer: \(\frac{1}{2}\) mile
Q20: A water bottle holds \(\frac{3}{4}\) liter of water. If you drink \(\frac{2}{3}\) of the water in the bottle, how many liters did you drink?
Solution:
Ans: Step 1: Find \(\frac{2}{3}\) of \(\frac{3}{4}\) by multiplying: \(\frac{2}{3} \times \frac{3}{4}\) Step 2: Cancel the 3s: \(\frac{2}{\cancel{3}} \times \frac{\cancel{3}}{4} = \frac{2}{4}\) Step 3: Simplify: \(\frac{2}{4} = \frac{1}{2}\) Final Answer: \(\frac{1}{2}\) liter
The document Worksheet (with Solutions): Multiplying Fractions is a part of the Grade 5 Course Math Grade 5.
Exam, practice quizzes, Worksheet (with Solutions): Multiplying Fractions, Previous Year Questions with Solutions, Important questions, study material, pdf , Summary, Free, Sample Paper, ppt, Semester Notes, shortcuts and tricks, Viva Questions, past year papers, Objective type Questions, Extra Questions, video lectures, mock tests for examination, Worksheet (with Solutions): Multiplying Fractions, Worksheet (with Solutions): Multiplying Fractions, MCQs;
