Q1: What is a common denominator? (a) The largest number in a fraction (b) A denominator that is the same in two or more fractions (c) The numerator of a fraction (d) A number that can only be divided by 1
Solution:
Ans: (b) Explanation: A common denominator is a denominator that is shared by two or more fractions. This makes it easier to compare, add, or subtract fractions.
Q2: Which pair of fractions already has a common denominator? (a) \(\frac{1}{3}\) and \(\frac{1}{4}\) (b) \(\frac{2}{5}\) and \(\frac{3}{5}\) (c) \(\frac{1}{2}\) and \(\frac{1}{6}\) (d) \(\frac{3}{8}\) and \(\frac{2}{3}\)
Solution:
Ans: (b) Explanation: Both fractions \(\frac{2}{5}\) and \(\frac{3}{5}\) have the same denominator of 5, so they already share a common denominator. The other pairs have different denominators.
Q3: What is the least common denominator (LCD) of \(\frac{1}{4}\) and \(\frac{1}{6}\)? (a) 10 (b) 12 (c) 24 (d) 8
Solution:
Ans: (b) Explanation: The least common denominator is the smallest number that both 4 and 6 divide into evenly. The multiples of 4 are 4, 8, 12, 16... and the multiples of 6 are 6, 12, 18... The smallest common multiple is 12.
Q4: To rewrite \(\frac{2}{3}\) with a denominator of 12, what do you multiply both the numerator and denominator by? (a) 2 (b) 3 (c) 4 (d) 6
Solution:
Ans: (c) Explanation: Since \(3 \times 4 = 12\), you need to multiply both the numerator and denominator by 4. So \(\frac{2}{3} = \frac{2 \times 4}{3 \times 4} = \frac{8}{12}\).
Q5: What is \(\frac{3}{5}\) rewritten with a denominator of 20? (a) \(\frac{6}{20}\) (b) \(\frac{12}{20}\) (c) \(\frac{15}{20}\) (d) \(\frac{9}{20}\)
Solution:
Ans: (b) Explanation: To change the denominator from 5 to 20, multiply by 4 (since \(5 \times 4 = 20\)). Multiply the numerator by 4 as well: \(3 \times 4 = 12\). So \(\frac{3}{5} = \frac{12}{20}\).
Q6: What is the least common multiple (LCM) of 8 and 12? (a) 24 (b) 48 (c) 96 (d) 20
Solution:
Ans: (a) Explanation: The least common multiple is the smallest number that both 8 and 12 divide into evenly. Multiples of 8: 8, 16, 24, 32... Multiples of 12: 12, 24, 36... The smallest shared multiple is 24.
Q7: Which fraction is NOT equivalent to \(\frac{1}{2}\)? (a) \(\frac{2}{4}\) (b) \(\frac{5}{10}\) (c) \(\frac{3}{5}\) (d) \(\frac{4}{8}\)
Solution:
Ans: (c) Explanation:Equivalent fractions represent the same value. \(\frac{2}{4}\), \(\frac{5}{10}\), and \(\frac{4}{8}\) all simplify to \(\frac{1}{2}\), but \(\frac{3}{5}\) does not equal \(\frac{1}{2}\).
Q8: To find a common denominator for \(\frac{2}{9}\) and \(\frac{1}{3}\), which of these denominators would work? (a) 12 (b) 18 (c) 6 (d) 27
Solution:
Ans: (b) Explanation: A common denominator must be divisible by both 9 and 3. While 27 also works, 18 is the least common denominator. Both 9 and 3 divide evenly into 18.
Section B: Fill in the Blanks
Q9:The smallest common denominator of two or more fractions is called the __________.
Solution:
Ans: least common denominator (or LCD) Explanation: The least common denominator is the smallest number that can be used as a common denominator for two or more fractions.
Q10:To create equivalent fractions, you must multiply or divide both the __________ and the __________ by the same number.
Solution:
Ans: numerator and denominator Explanation: When creating equivalent fractions, you must multiply or divide both the numerator and denominator by the same non-zero number to maintain the same value.
Q11:The least common multiple of 6 and 9 is __________.
Solution:
Ans: 18 Explanation: The least common multiple (LCM) is found by listing multiples: 6, 12, 18, 24... and 9, 18, 27... The smallest common multiple is 18.
Q12:When \(\frac{1}{4}\) is rewritten with a denominator of 16, the numerator becomes __________.
Solution:
Ans: 4 Explanation: Since \(4 \times 4 = 16\), multiply both the numerator and denominator by 4: \(\frac{1 \times 4}{4 \times 4} = \frac{4}{16}\).
Q13:The fractions \(\frac{3}{8}\) and \(\frac{5}{8}\) already have a common denominator of __________.
Solution:
Ans: 8 Explanation: Both fractions already share the same denominator of 8, so no conversion is needed.
Q14:To compare fractions with different denominators, you must first find a __________ __________.
Solution:
Ans: common denominator Explanation: A common denominator allows you to rewrite fractions so they can be easily compared, added, or subtracted.
Section C: Word Problems
Q15:Maria ate \(\frac{1}{3}\) of a pizza and her brother ate \(\frac{1}{4}\) of the same pizza. To find out how much pizza they ate together, Maria needs to find a common denominator. What is the least common denominator for these two fractions?
Solution:
Ans: Step 1: List multiples of 3: 3, 6, 9, 12, 15... Step 2: List multiples of 4: 4, 8, 12, 16... Step 3: The smallest common multiple is 12. Final Answer: 12
Q16:Jason ran \(\frac{2}{5}\) of a mile on Monday. He wants to compare this to the \(\frac{3}{10}\) of a mile he ran on Tuesday. Rewrite \(\frac{2}{5}\) with a denominator of 10.
Solution:
Ans: Step 1: Find what to multiply: \(5 \times 2 = 10\) Step 2: Multiply the numerator by the same number: \(2 \times 2 = 4\) Step 3: Write the new fraction: \(\frac{4}{10}\) Final Answer: \(\frac{4}{10}\)
Q17:Sarah has two ribbon pieces. One piece is \(\frac{3}{8}\) of a yard long and the other is \(\frac{1}{2}\) of a yard long. What is the least common denominator she should use to compare the lengths?
Solution:
Ans: Step 1: List multiples of 8: 8, 16, 24... Step 2: List multiples of 2: 2, 4, 6, 8, 10... Step 3: The smallest common multiple is 8. Final Answer: 8
Q18:A recipe calls for \(\frac{1}{6}\) cup of sugar and \(\frac{1}{4}\) cup of butter. To add these amounts, Carlos needs a common denominator. Find the least common denominator and rewrite both fractions with this denominator.
Solution:
Ans: Step 1: Find LCM of 6 and 4. Multiples of 6: 6, 12, 18... Multiples of 4: 4, 8, 12, 16... LCD = 12 Step 2: Convert \(\frac{1}{6}\): \(6 \times 2 = 12\), so \(\frac{1 \times 2}{6 \times 2} = \frac{2}{12}\) Step 3: Convert \(\frac{1}{4}\): \(4 \times 3 = 12\), so \(\frac{1 \times 3}{4 \times 3} = \frac{3}{12}\) Final Answer: \(\frac{2}{12}\) and \(\frac{3}{12}\)
Q19:Emma practiced piano for \(\frac{3}{4}\) of an hour on Saturday. She wants to write this with a denominator of 12 to compare with her Sunday practice time. Rewrite \(\frac{3}{4}\) with a denominator of 12.
Solution:
Ans: Step 1: Determine what to multiply: \(4 \times 3 = 12\) Step 2: Multiply the numerator: \(3 \times 3 = 9\) Step 3: Write the equivalent fraction: \(\frac{9}{12}\) Final Answer: \(\frac{9}{12}\)
Q20:Two friends are sharing a cake. Alex ate \(\frac{2}{9}\) of the cake and Jordan ate \(\frac{1}{3}\) of the cake. Find the least common denominator for these fractions and rewrite both fractions using this common denominator.
Solution:
Ans: Step 1: Find LCM of 9 and 3. Since 9 is a multiple of 3, LCD = 9 Step 2: \(\frac{2}{9}\) already has denominator 9, so it stays \(\frac{2}{9}\) Step 3: Convert \(\frac{1}{3}\): \(3 \times 3 = 9\), so \(\frac{1 \times 3}{3 \times 3} = \frac{3}{9}\) Final Answer: \(\frac{2}{9}\) and \(\frac{3}{9}\)
The document Worksheet (with Solutions): Common Denominators is a part of the Grade 5 Course Math Grade 5.
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