Compare Different Denominators

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Compare Different Denominators · Grade 4 · Worksheet 3

1. Ava and Sophia are each making fruit punch for a party. Ava mixes 2/3 cup of orange juice with water. Sophia mixes 5/6 cup of orange juice with water. They both use the same size cup. Who uses more orange juice, Ava or Sophia? Answer: Sophia Solution: Compare 2/3 and 5/6. The denominators are 3 and 6. The least common denominator is 6.
   Full step-by-step solution

   Step 1: Compare 2/3 and 5/6. The denominators are 3 and 6. The least common denominator is 6. Step 2: Convert 2/3 to an equivalent fraction with denominator 6. Multiply numerator and denominator by 2: 2/3 = 4/6. Step 3: Now compare 4/6 and 5/6. Since 5/6 > 4/6, Sophia uses more orange juice. The answer is Sophia.

2. Emma and Liam are baking cookies for a school fundraiser. Emma uses 3/5 of a bag of chocolate chips for her batch, and Liam uses 5/8 of a bag of chocolate chips for his batch. Who used more chocolate chips, Emma or Liam? Answer: Liam Solution: Compare 3/5 and 5/8. The denominators are 5 and 8. Step 2: Find a common denominator.
   Full step-by-step solution

   Step 1: Compare 3/5 and 5/8. The denominators are 5 and 8. Step 2: Find a common denominator. The least common multiple of 5 and 8 is 40. Step 3: Convert each fraction. 3/5 = (3 x 8)/(5 x 8) = 24/40. 5/8 = (5 x 5)/(8 x 5) = 25/40. Step 4: Compare 24/40 and 25/40. Since 25/40 is greater than 24/40, Liam used more chocolate chips. The answer is Liam.

3. Mason is training for a fun run. He ran 2/7 of the track on Monday and 3/8 of the same track on Tuesday. On which day did he run a greater portion of the track? Answer: Tuesday Solution: Write the fractions: 2/7 and 3/8. Step 2: Find a common denominator. The denominators are 7 and 8, so multiply them: 7 × 8 = 56.
   Full step-by-step solution

   Step 1: Write the fractions: 2/7 and 3/8. Step 2: Find a common denominator. The denominators are 7 and 8, so multiply them: 7 × 8 = 56. Step 3: Convert 2/7 to an equivalent fraction with denominator 56. Multiply numerator and denominator by 8: 2/7 = (2 × 8)/(7 × 8) = 16/56. Step 4: Convert 3/8 to an equivalent fraction with denominator 56. Multiply numerator and denominator by 7: 3/8 = (3 × 7)/(8 × 7) = 21/56. Step 5: Compare 16/56 and 21/56. Since 21/56 > 16/56, 3/8 is greater than 2/7. Mason ran a greater portion of the track on Tuesday. Answer: Tuesday.

4. Noah and Ava are each making a fruit smoothie. Noah uses 5/6 of a cup of strawberries in his smoothie. Ava uses 7/9 of a cup of strawberries in her smoothie. Who uses more strawberries, Noah or Ava? Answer: Noah Solution: Compare 5/6 and 7/9 by finding a common denominator. The denominators are 6 and 9. The least common multiple of 6 and 9 is 18.
   Full step-by-step solution

   Step 1: Compare 5/6 and 7/9 by finding a common denominator. The denominators are 6 and 9. 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 x 3)/(6 x 3) = 15/18. Step 3: Convert 7/9 to an equivalent fraction with denominator 18: 7/9 = (7 x 2)/(9 x 2) = 14/18. Step 4: Compare 15/18 and 14/18. Since 15/18 > 14/18, we have 5/6 > 7/9. So Noah uses more strawberries. Answer: Noah.

5. Olivia is baking two different types of cookies. She uses 2/5 cup of brown sugar for the chocolate chip cookies and 3/10 cup of brown sugar for the oatmeal cookies. Which type of cookie uses more brown sugar? Answer: chocolate chip cookies (2/5 is greater than 3/10) Solution: Compare 2/5 and 3/10. The denominators are different, so find a common denominator. The least common multiple of 5 and 10 is 10.
   Full step-by-step solution

   Step 1: Compare 2/5 and 3/10. The denominators are different, so find a common denominator. The least common multiple of 5 and 10 is 10. Step 2: Convert 2/5 to an equivalent fraction with denominator 10. Multiply numerator and denominator by 2: 2/5 = (2 x 2)/(5 x 2) = 4/10. Step 3: Now compare 4/10 and 3/10. Since 4 > 3, 4/10 > 3/10. Step 4: Therefore, 2/5 > 3/10. The chocolate chip cookies use more brown sugar. Answer: chocolate chip cookies

6. Matiu is looking at two rectangular pizzas that are the same size. The first pizza is cut into 12 equal slices, and Matiu has eaten 7 of those slices. The second pizza is cut into 16 equal slices, and Matiu has eaten 9 of those slices. Which pizza did Matiu eat more of: the first pizza (7/12) or the second pizza (9/16)? Answer: 7/12 Solution: We need to compare 7/12 and 9/16. Find a common denominator. The denominators are 12 and 16.
   Full step-by-step solution

   Step 1: We need to compare 7/12 and 9/16. Step 2: Find a common denominator. The denominators are 12 and 16. The least common multiple of 12 and 16 is 48, because 12 x 4 = 48 and 16 x 3 = 48. Step 3: Convert 7/12 to an equivalent fraction with denominator 48. Multiply numerator and denominator by 4: (7 x 4) / (12 x 4) = 28/48. Step 4: Convert 9/16 to an equivalent fraction with denominator 48. Multiply numerator and denominator by 3: (9 x 3) / (16 x 3) = 27/48. Step 5: Now compare 28/48 and 27/48. Since 28 > 27, 28/48 is greater than 27/48. Step 6: Therefore, 7/12 > 9/16. Matiu ate more of the first pizza. The answer is 7/12.

7. A bakery made two batches of cookies. The first batch used 3/4 cup of chocolate chips. The second batch used 7/10 cup of chocolate chips. Which batch used more chocolate chips? Answer: 3/4 Solution: We need to compare 3/4 and 7/10 Find a common denominator.
   Full step-by-step solution

   Step 1: We need to compare 3/4 and 7/10 Step 2: Find a common denominator. The denominators are 4 and 10 Step 3: The least common multiple of 4 and 10 is 20 Step 4: Convert 3/4 to twentieths: 3/4 = (3 × 5)/(4 × 5) = 15/20 Step 5: Convert 7/10 to twentieths: 7/10 = (7 × 2)/(10 × 2) = 14/20 Step 6: Compare 15/20 and 14/20 Step 7: Since 15/20 is greater than 14/20, 3/4 is greater than 7/10 The answer is 3/4.

8. Mason is comparing two rectangular chocolate bars of the same size. The first bar is divided into 7 equal pieces, and he eats 2 of them. The second bar is divided into 8 equal pieces, and he eats 3 of them. Which bar has more chocolate eaten? Write your answer as 'first bar' or 'second bar'. Answer: second bar Solution: Write the fractions. Mason eats 2/7 of the first bar and 3/8 of the second bar. To compare 2/7 and 3/8, find a common denominator.
   Full step-by-step solution

   Step 1: Write the fractions. Mason eats 2/7 of the first bar and 3/8 of the second bar. Step 2: To compare 2/7 and 3/8, find a common denominator. The denominators are 7 and 8. Multiply: 7 x 8 = 56. So use 56 as the common denominator. Step 3: Convert 2/7 to an equivalent fraction with denominator 56. Multiply numerator and denominator by 8: (2 x 8) / (7 x 8) = 16/56. Step 4: Convert 3/8 to an equivalent fraction with denominator 56. Multiply numerator and denominator by 7: (3 x 7) / (8 x 7) = 21/56. Step 5: Compare 16/56 and 21/56. Since 21 > 16, we have 21/56 > 16/56, so 3/8 > 2/7. Step 6: Therefore, the second bar has more chocolate eaten. The answer is second bar.