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Compare Different Denominators

Grade 4 · Fractions · Worksheet 1

  1. Sophia and Noah each have a chocolate bar of the same size. Sophia eats 5/6 of her chocolate bar. Noah eats 7/9 of his chocolate bar. Who ate more chocolate? Answer: ______________
  2. Mere is making two different types of fruit punch for a party. She uses 2/3 of a cup of orange juice for the first recipe and 3/4 of a cup of orange juice for the second recipe. Which recipe uses more orange juice? Answer: ______________
  3. Liam and Olivia are each making a fruit drink for a picnic. Liam mixes 3/5 of a cup of orange juice with water. Olivia mixes 5/7 of a cup of apple juice with water. They want to know who uses more juice in their drink. Which fraction is greater, 3/5 or 5/7? Answer: ______________
  4. Hana and Matiu each have a chocolate bar of the same size. Hana eats 3/8 of her chocolate bar. Matiu eats 2/6 of his chocolate bar. Who ate more chocolate? Answer: ______________
  5. Tane is looking at two rectangular chocolate bars that are the same size. The first bar is divided into 11 equal pieces, and Tane has eaten 4 of them. The second bar is divided into 13 equal pieces, and Tane has eaten 5 of them. Which chocolate bar has more chocolate remaining? Write the fraction of chocolate remaining for each bar and compare them using >, <, or =. Answer: ______________
  6. 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: ______________
  7. Sophia is baking two different kinds of granola bars. She uses 3/8 of a cup of honey in the first batch and 5/12 of a cup of honey in the second batch. For which batch does Sophia use more honey? Answer: ______________
  8. Isabella and Mason each have a chocolate bar of the same size. Isabella ate 7/9 of her chocolate bar. Mason ate 5/7 of his chocolate bar. Who ate more chocolate? Answer: ______________
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Answer Key & Explanations

Compare Different Denominators · Grade 4 · Worksheet 1

  1. Sophia and Noah each have a chocolate bar of the same size. Sophia eats 5/6 of her chocolate bar. Noah eats 7/9 of his chocolate bar. Who ate more chocolate? Answer: Sophia Solution: Compare 5/6 and 7/9. They have different denominators, so we need a common denominator. Find the least common multiple (LCM) of 6 and 9.
    Full step-by-step solution

    Step 1: Compare 5/6 and 7/9. They have different denominators, so we need a common denominator. Step 2: Find the least common multiple (LCM) of 6 and 9. Multiples of 6: 6, 12, 18, 24... Multiples of 9: 9, 18, 27... The LCM is 18. Step 3: Rewrite 5/6 with denominator 18: 5/6 = (5 x 3)/(6 x 3) = 15/18. Step 4: Rewrite 7/9 with denominator 18: 7/9 = (7 x 2)/(9 x 2) = 14/18. Step 5: Compare 15/18 and 14/18. 15/18 is greater than 14/18. Step 6: So, 5/6 > 7/9. Sophia ate more chocolate. Answer: Sophia

  2. Mere is making two different types of fruit punch for a party. She uses 2/3 of a cup of orange juice for the first recipe and 3/4 of a cup of orange juice for the second recipe. Which recipe uses more orange juice? Answer: 3/4 Solution: We need to compare 2/3 and 3/4. The denominators are 3 and 4, which are different. Step 2: Find a common denominator.
    Full step-by-step solution

    Step 1: We need to compare 2/3 and 3/4. The denominators are 3 and 4, which are different. Step 2: Find a common denominator. The least common multiple of 3 and 4 is 12. Step 3: Rewrite each fraction with denominator 12. For 2/3, multiply numerator and denominator by 4: (2 x 4)/(3 x 4) = 8/12. For 3/4, multiply numerator and denominator by 3: (3 x 3)/(4 x 3) = 9/12. Step 4: Now compare 8/12 and 9/12. Since 9/12 is greater than 8/12, 3/4 is greater than 2/3. Therefore, the second recipe uses more orange juice. The answer is 3/4.

  3. Liam and Olivia are each making a fruit drink for a picnic. Liam mixes 3/5 of a cup of orange juice with water. Olivia mixes 5/7 of a cup of apple juice with water. They want to know who uses more juice in their drink. Which fraction is greater, 3/5 or 5/7? Answer: 5/7 Solution: Compare 3/5 and 5/7. Since the denominators are different, find a common denominator. The least common multiple of 5 and 7 is 35.
    Full step-by-step solution

    Step 1: Compare 3/5 and 5/7. Since the denominators are different, find a common denominator. The least common multiple of 5 and 7 is 35. Step 2: Convert 3/5 to an equivalent fraction with denominator 35: Multiply numerator and denominator by 7 to get (3 x 7)/(5 x 7) = 21/35. Step 3: Convert 5/7 to an equivalent fraction with denominator 35: Multiply numerator and denominator by 5 to get (5 x 5)/(7 x 5) = 25/35. Step 4: Compare 21/35 and 25/35. Since 25 is greater than 21, 25/35 > 21/35, so 5/7 > 3/5. The answer is 5/7.

  4. Hana and Matiu each have a chocolate bar of the same size. Hana eats 3/8 of her chocolate bar. Matiu eats 2/6 of his chocolate bar. Who ate more chocolate? Answer: Hana Solution: Compare 3/8 and 2/6. Find a common denominator. The denominators are 8 and 6.
    Full step-by-step solution

    Step 1: Compare 3/8 and 2/6. Find a common denominator. The denominators are 8 and 6. The least common multiple of 8 and 6 is 24. Step 2: Convert 3/8 to an equivalent fraction with denominator 24. Multiply numerator and denominator by 3: (3 x 3)/(8 x 3) = 9/24. Step 3: Convert 2/6 to an equivalent fraction with denominator 24. Multiply numerator and denominator by 4: (2 x 4)/(6 x 4) = 8/24. Step 4: Compare 9/24 and 8/24. Since 9 is greater than 8, 9/24 is greater than 8/24. So 3/8 is greater than 2/6. Step 5: Therefore, Hana ate more chocolate than Matiu. Answer: Hana.

  5. Tane is looking at two rectangular chocolate bars that are the same size. The first bar is divided into 11 equal pieces, and Tane has eaten 4 of them. The second bar is divided into 13 equal pieces, and Tane has eaten 5 of them. Which chocolate bar has more chocolate remaining? Write the fraction of chocolate remaining for each bar and compare them using >, <, or =. Answer: 4/11 > 5/13 Solution: Write the fractions. First bar has 11 pieces, 4 eaten, so 11 - 4 = 7 pieces remaining. Fraction remaining = 7/11.
    Full step-by-step solution

    Step 1: Write the fractions. First bar has 11 pieces, 4 eaten, so 11 - 4 = 7 pieces remaining. Fraction remaining = 7/11. Second bar has 13 pieces, 5 eaten, so 13 - 5 = 8 pieces remaining. Fraction remaining = 8/13. Step 2: Compare 7/11 and 8/13 by finding a common denominator. The denominators are 11 and 13. Multiply: 11 x 13 = 143. So common denominator is 143. Step 3: Convert 7/11 to denominator 143: 7 x 13 = 91, so 7/11 = 91/143. Step 4: Convert 8/13 to denominator 143: 8 x 11 = 88, so 8/13 = 88/143. Step 5: Compare 91/143 and 88/143. Since 91 > 88, we have 91/143 > 88/143, so 7/11 > 8/13. Step 6: So the first bar has more chocolate remaining. The answer is 7/11 > 8/13.

  6. 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.

  7. Sophia is baking two different kinds of granola bars. She uses 3/8 of a cup of honey in the first batch and 5/12 of a cup of honey in the second batch. For which batch does Sophia use more honey? Answer: 5/12 Solution: Compare 3/8 and 5/12. The denominators are 8 and 12. Find the least common multiple (LCM) of 8 and 12.
    Full step-by-step solution

    Step 1: Compare 3/8 and 5/12. The denominators are 8 and 12. Find the least common multiple (LCM) of 8 and 12. Multiples of 8: 8, 16, 24, 32... Multiples of 12: 12, 24, 36... The LCM is 24. Step 2: Convert 3/8 to a fraction with denominator 24. 8 x 3 = 24, so multiply numerator and denominator by 3: 3/8 = (3 x 3)/(8 x 3) = 9/24. Step 3: Convert 5/12 to a fraction with denominator 24. 12 x 2 = 24, so multiply numerator and denominator by 2: 5/12 = (5 x 2)/(12 x 2) = 10/24. Step 4: Compare the numerators: 9/24 and 10/24. Since 10 > 9, 10/24 is greater than 9/24. Therefore, 5/12 > 3/8. Sophia uses more honey in the second batch (5/12 cup). Answer: 5/12

  8. Isabella and Mason each have a chocolate bar of the same size. Isabella ate 7/9 of her chocolate bar. Mason ate 5/7 of his chocolate bar. Who ate more chocolate? Answer: Isabella Solution: To compare 7/9 and 5/7, find a common denominator. The denominators are 9 and 7. The least common multiple of 9 and 7 is 63.
    Full step-by-step solution

    To compare 7/9 and 5/7, find a common denominator. The denominators are 9 and 7. The least common multiple of 9 and 7 is 63. Convert each fraction: 7/9 = (7 x 7)/(9 x 7) = 49/63. 5/7 = (5 x 9)/(7 x 9) = 45/63. Since 49/63 > 45/63, 7/9 > 5/7. So Isabella ate more chocolate.