Compare Different Denominators

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Answer Key & Explanations

Compare Different Denominators · Grade 4 · Worksheet 2

1. Noah and Ava each have a garden of the same size. Noah planted flowers in 7/11 of his garden. Ava planted flowers in 5/6 of her garden. Who planted flowers in a larger fraction of their garden? Answer: Ava Solution: Compare 7/11 and 5/6. Since the denominators are different (11 and 6), find a common denominator. The least common multiple of 11 and 6 is 66.
   Full step-by-step solution

   Step 1: Compare 7/11 and 5/6. Since the denominators are different (11 and 6), find a common denominator. The least common multiple of 11 and 6 is 66. Step 2: Convert 7/11 to a fraction with denominator 66: Multiply numerator and denominator by 6: 7/11 = (7 x 6)/(11 x 6) = 42/66. Step 3: Convert 5/6 to a fraction with denominator 66: Multiply numerator and denominator by 11: 5/6 = (5 x 11)/(6 x 11) = 55/66. Step 4: Compare 42/66 and 55/66. Since 55 > 42, 55/66 > 42/66, so 5/6 > 7/11. Therefore, Ava planted flowers in a larger fraction of her garden. The answer is Ava.

2. Olivia is making two different kinds of trail mix. The first batch uses 3/8 cup of almonds, and the second batch uses 2/5 cup of almonds. Which batch uses more almonds? Answer: 2/5 Solution: We need to compare 3/8 and 2/5. Since the denominators are different (8 and 5), we find a common denominator. Step 2: The least common multiple of 8 and 5 is 40.
   Full step-by-step solution

   Step 1: We need to compare 3/8 and 2/5. Since the denominators are different (8 and 5), we find a common denominator. Step 2: The least common multiple of 8 and 5 is 40. Step 3: Convert 3/8 to an equivalent fraction: 3/8 = (3 x 5)/(8 x 5) = 15/40. Step 4: Convert 2/5 to an equivalent fraction: 2/5 = (2 x 8)/(5 x 8) = 16/40. Step 5: Now compare 15/40 and 16/40. Since 16/40 is larger, 2/5 > 3/8. The answer is 2/5.

3. Ava is making two different fruit salads for a picnic. For the first salad, she uses 5/9 of a cup of blueberries. For the second salad, she uses 3/7 of a cup of blueberries. Which fruit salad uses more blueberries, the first or the second? Answer: first Solution: Compare 5/9 and 3/7. Since the denominators are different (9 and 7), find a common denominator by multiplying: 9 x 7 = 63. Rewrite 5/9 as an equivalent fraction with denominator 63: 5/9 = (5 x 7)/(9 x 7) = 35/63.
   Full step-by-step solution

   Step 1: Compare 5/9 and 3/7. Since the denominators are different (9 and 7), find a common denominator by multiplying: 9 x 7 = 63. Step 2: Rewrite 5/9 as an equivalent fraction with denominator 63: 5/9 = (5 x 7)/(9 x 7) = 35/63. Step 3: Rewrite 3/7 as an equivalent fraction with denominator 63: 3/7 = (3 x 9)/(7 x 9) = 27/63. Step 4: Compare 35/63 and 27/63. Since 35 > 27, 35/63 is greater, so 5/9 > 3/7. Step 5: The first fruit salad (5/9 cup) uses more blueberries than the second (3/7 cup). The answer is first.

4. Mason is making two different batches of homemade granola bars. One batch uses 3/8 cup of honey, and the other batch uses 5/12 cup of honey. Which batch requires more honey? Answer: 5/12 Solution: Compare 3/8 and 5/12 by finding a common denominator. The denominators are 8 and 12. The least common multiple of 8 and 12 is 24.
   Full step-by-step solution

   Step 1: Compare 3/8 and 5/12 by finding a common denominator. The denominators are 8 and 12. The least common multiple of 8 and 12 is 24. Step 2: Convert 3/8 to an equivalent fraction with denominator 24: 3/8 = (3 x 3)/(8 x 3) = 9/24. Step 3: Convert 5/12 to an equivalent fraction with denominator 24: 5/12 = (5 x 2)/(12 x 2) = 10/24. Step 4: Compare 9/24 and 10/24. Since 9 < 10, we have 9/24 < 10/24, so 3/8 < 5/12. Step 5: Therefore, the batch that uses 5/12 cup of honey requires more honey. The answer is 5/12.

5. Noah is making two different kinds of fruit punch for a party. One recipe calls for 5/6 cup of orange juice, and the other recipe calls for 7/9 cup of pineapple juice. Which recipe uses more juice: the one with orange juice or the one with pineapple juice? Answer: 5/6 Solution: Compare 5/6 and 7/9. Since the denominators are different (6 and 9), find a common denominator. The least common multiple of 6 and 9 is 18.
   Full step-by-step solution

   Step 1: Compare 5/6 and 7/9. Since the denominators are different (6 and 9), find a common denominator. The least common multiple of 6 and 9 is 18. Step 2: Convert 5/6 to an equivalent fraction with denominator 18: 5/6 = (5 × 3)/(6 × 3) = 15/18. Step 3: Convert 7/9 to an equivalent fraction with denominator 18: 7/9 = (7 × 2)/(9 × 2) = 14/18. Step 4: Compare the numerators: 15/18 > 14/18, so 5/6 > 7/9. Therefore, the orange juice recipe uses more juice.

6. Isabella and Charlotte are each making a fruit smoothie. Isabella uses 2/7 of a cup of strawberries, and Charlotte uses 3/5 of a cup of strawberries. Who uses more strawberries? Answer: Charlotte Solution: The fractions to compare are 2/7 and 3/5. They have different denominators (7 and 5). Step 2: Find a common denominator by multiplying the denominators: 7 x 5 = 35.
   Full step-by-step solution

   Step 1: The fractions to compare are 2/7 and 3/5. They have different denominators (7 and 5). Step 2: Find a common denominator by multiplying the denominators: 7 x 5 = 35. Step 3: Rewrite 2/7 as an equivalent fraction with denominator 35: 2/7 = (2 x 5)/(7 x 5) = 10/35. Step 4: Rewrite 3/5 as an equivalent fraction with denominator 35: 3/5 = (3 x 7)/(5 x 7) = 21/35. Step 5: Compare 10/35 and 21/35. Since 21/35 is greater than 10/35, Charlotte uses more strawberries. The answer is Charlotte.

7. A farmer has two fields of the same size. In the first field, he planted corn in 3/4 of the field. In the second field, he planted wheat in 5/6 of the field. Which crop takes up more of its field - corn or wheat? Answer: 5/6 Solution: Write the fractions for each crop's portion of its field. Corn: 3/4 of the first field. Wheat: 5/6 of the second field.
   Full step-by-step solution

   Let's compare the fractions to see which is larger. Step 1: Write the fractions for each crop's portion of its field. Corn: 3/4 of the first field. Wheat: 5/6 of the second field. Step 2: To compare 3/4 and 5/6, we need a common denominator. The denominators are 4 and 6. The least common multiple of 4 and 6 is 12. Step 3: Convert each fraction to have denominator 12. For 3/4: Multiply numerator and denominator by 3 → (3 × 3)/(4 × 3) = 9/12. For 5/6: Multiply numerator and denominator by 2 → (5 × 2)/(6 × 2) = 10/12. Step 4: Compare 9/12 and 10/12. Since 10/12 is greater than 9/12, we have 5/6 > 3/4. Step 5: Conclusion. Wheat (5/6 of the field) takes up more of its field than corn (3/4 of the field). Answer: 5/6

8. Mason is baking two different kinds of cookies. For the first batch, he uses 3/4 cup of chocolate chips. For the second batch, he uses 2/3 cup of chocolate chips. Which batch uses more chocolate chips? Answer: 3/4 Solution: We need to compare 3/4 and 2/3. Find a common denominator. The denominators are 4 and 3.
   Full step-by-step solution

   We need to compare 3/4 and 2/3. Step 1: Find a common denominator. The denominators are 4 and 3. The least common denominator is 12. Step 2: Convert 3/4 to an equivalent fraction with denominator 12. Multiply numerator and denominator by 3: 3/4 = 9/12. Step 3: Convert 2/3 to an equivalent fraction with denominator 12. Multiply numerator and denominator by 4: 2/3 = 8/12. Step 4: Compare 9/12 and 8/12. Since 9 > 8, we know 9/12 > 8/12, so 3/4 > 2/3. The first batch with 3/4 cup of chocolate chips uses more chocolate chips. Answer: 3/4

9. Mason is making two different kinds of trail mix. For the first batch, he uses 7/9 of a cup of almonds. For the second batch, he uses 5/8 of a cup of almonds. In which batch does Mason use more almonds? Answer: 7/9 Solution: The fractions to compare are 7/9 and 5/8. Since they have different denominators, we need to find a common denominator. The least common multiple of 9 and 8 is 72.
   Full step-by-step solution

   Step 1: The fractions to compare are 7/9 and 5/8. Since they have different denominators, we need to find a common denominator. The least common multiple of 9 and 8 is 72. Step 2: Convert 7/9 to an equivalent fraction with denominator 72. Multiply numerator and denominator by 8: 7/9 = (7 x 8)/(9 x 8) = 56/72. Step 3: Convert 5/8 to an equivalent fraction with denominator 72. Multiply numerator and denominator by 9: 5/8 = (5 x 9)/(8 x 9) = 45/72. Step 4: Compare 56/72 and 45/72. Since 56 is greater than 45, 56/72 > 45/72. Step 5: Therefore, 7/9 > 5/8. Mason uses more almonds in the first batch. The answer is 7/9.