Compare Different Denominators

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Answer Key & Explanations

Compare Different Denominators · Grade 4 · Worksheet 3

1. 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.

2. A baker is preparing two batches of cookies. For the chocolate chip cookies, she uses 3/5 of a cup of sugar. For the oatmeal cookies, she uses 7/10 of a cup of sugar. Which type of cookie uses more sugar? Answer: 7/10 Solution: We need to compare 3/5 and 7/10 to see which is larger. Since the denominators are different (5 and 10), we need to find a common denominator. The least common denominator of 5 and 10 is 10.
   Full step-by-step solution

   Step 1: We need to compare 3/5 and 7/10 to see which is larger. Step 2: Since the denominators are different (5 and 10), we need to find a common denominator. The least common denominator of 5 and 10 is 10. Step 3: Convert 3/5 to have a denominator of 10. Multiply both numerator and denominator by 2: 3/5 = (3 × 2)/(5 × 2) = 6/10. Step 4: Now we can compare 6/10 and 7/10. Since 7/10 is greater than 6/10, the oatmeal cookies use more sugar. The answer is 7/10.

3. Ava is making two different kinds of granola bars. One recipe calls for 1/6 cup of honey, and the other recipe calls for 1/11 cup of honey. Which recipe uses more honey? Answer: 1/6 Solution: Compare 1/6 and 1/11. Both have the same numerator (1).
   Full step-by-step solution

   Step 1: Compare 1/6 and 1/11. Both have the same numerator (1). Step 2: When numerators are the same, the fraction with the smaller denominator is larger, because the whole is divided into fewer equal parts, so each part is bigger. Step 3: 6 is less than 11, so 1/6 is greater than 1/11. The answer is 1/6.

4. Sophia is looking at two rectangular strips of fabric that are the same length. The first strip is divided into 6 equal sections, and she has colored 5 of them blue. The second strip is divided into 11 equal sections, and she has colored 9 of them red. Which strip has the larger fraction colored? Write your answer as 'first strip' or 'second strip'. Answer: second strip Solution: Write the fractions. First strip: 5/6. Second strip: 9/11.
   Full step-by-step solution

   Step 1: Write the fractions. First strip: 5/6. Second strip: 9/11. Step 2: Find a common denominator. The denominators are 6 and 11. The least common multiple of 6 and 11 is 66, because 6 x 11 = 66. Step 3: Convert 5/6 to an equivalent fraction with denominator 66. Multiply numerator and denominator by 11: (5 x 11) / (6 x 11) = 55/66. Step 4: Convert 9/11 to an equivalent fraction with denominator 66. Multiply numerator and denominator by 6: (9 x 6) / (11 x 6) = 54/66. Step 5: Compare 55/66 and 54/66. Since 55 > 54, 55/66 is greater than 54/66. Step 6: Therefore, 5/6 > 9/11. The first strip has a larger fraction colored. The answer is first strip.

5. Isabella is comparing two rectangular pieces of fabric that are the same size. The first piece is divided into 9 equal sections, and 4 of those sections are blue. The second piece is divided into 11 equal sections, and 5 of those sections are blue. Which piece of fabric has a larger fraction of blue sections? Write your answer as 'first piece' or 'second piece'. Answer: second piece Solution: Write the fractions. First piece: 4/9. Second piece: 5/11.
   Full step-by-step solution

   Step 1: Write the fractions. First piece: 4/9. Second piece: 5/11. Step 2: Find a common denominator. The denominators are 9 and 11. Since 9 and 11 have no common factors, the least common denominator is their product: 9 x 11 = 99. Step 3: Convert 4/9 to an equivalent fraction with denominator 99. Multiply numerator and denominator by 11: (4 x 11) / (9 x 11) = 44/99. Step 4: Convert 5/11 to an equivalent fraction with denominator 99. Multiply numerator and denominator by 9: (5 x 9) / (11 x 9) = 45/99. Step 5: Compare 44/99 and 45/99. Since 45 > 44, 45/99 is greater than 44/99. Step 6: Therefore, 5/11 > 4/9. The second piece has a larger fraction of blue sections. The answer is second piece.

6. Emma and Liam each have a rectangular garden plot of the same size. Emma planted carrots in 3/5 of her garden. Liam planted tomatoes in 5/8 of his garden. Who planted a larger fraction of their garden? Answer: Emma Solution: To compare 3/5 and 5/8, find a common denominator. The least common multiple of 5 and 8 is 40. Convert each fraction: 3/5 = (3 × 8)/(5 × 8) = 24/40.
   Full step-by-step solution

   To compare 3/5 and 5/8, find a common denominator. The least common multiple of 5 and 8 is 40. Convert each fraction: 3/5 = (3 × 8)/(5 × 8) = 24/40. 5/8 = (5 × 5)/(8 × 5) = 25/40. Now compare 24/40 and 25/40. Since 25/40 is greater than 24/40, 5/8 > 3/5. So Liam planted more of his garden than Emma did. The answer is Emma.

7. Mere is comparing two rectangular chocolate bars of the same size. The first bar is divided into 14 equal pieces, and she has eaten 5 pieces. The second bar is divided into 18 equal pieces, and she has eaten 7 pieces. Which chocolate bar has a larger fraction of pieces eaten? Write your answer as 'first bar' or 'second bar'. Answer: second bar Solution: Write the fractions. First bar: 5/14. Second bar: 7/18.
   Full step-by-step solution

   Step 1: Write the fractions. First bar: 5/14. Second bar: 7/18. Step 2: Find a common denominator. The denominators are 14 and 18. The least common multiple of 14 and 18 is 126, because 14 x 9 = 126 and 18 x 7 = 126. Step 3: Convert 5/14 to an equivalent fraction with denominator 126. Multiply numerator and denominator by 9: (5 x 9)/(14 x 9) = 45/126. Step 4: Convert 7/18 to an equivalent fraction with denominator 126. Multiply numerator and denominator by 7: (7 x 7)/(18 x 7) = 49/126. Step 5: Compare 45/126 and 49/126. Since 49 > 45, 49/126 is greater than 45/126. Step 6: Therefore, 7/18 > 5/14. The second bar has a larger fraction of pieces eaten. The answer is second bar.