Compare Different Denominators

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Answer Key & Explanations

Compare Different Denominators · Grade 4 · Worksheet 2

1. 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.

2. Emma is looking at two rectangular chocolate bars that are the same size. The first bar is divided into 10 equal pieces, and she eats 3 pieces. The second bar is divided into 5 equal pieces, and she eats 2 pieces. Which chocolate bar has more chocolate left? Answer: 3/10 Solution: Find the fraction left of the first bar. She eats 3 out of 10 pieces, so 10 - 3 = 7 pieces remain. That is 7/10 of the bar left.
   Full step-by-step solution

   Step 1: Find the fraction left of the first bar. She eats 3 out of 10 pieces, so 10 - 3 = 7 pieces remain. That is 7/10 of the bar left. Step 2: Find the fraction left of the second bar. She eats 2 out of 5 pieces, so 5 - 2 = 3 pieces remain. That is 3/5 of the bar left. Step 3: Compare 7/10 and 3/5. The denominators are different, so find a common denominator. The least common multiple of 10 and 5 is 10. Convert 3/5 to tenths: 3/5 = (3 x 2)/(5 x 2) = 6/10. Step 4: Now compare 7/10 and 6/10. Since 7 > 6, 7/10 is greater than 6/10. So the first bar (7/10 left) has more chocolate left than the second bar (6/10 left). The answer is 3/10.

3. 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.

4. Aroha and Tane are each making a fruit smoothie. Aroha drinks 7/9 of her smoothie, and Tane drinks 9/11 of his smoothie. Who drank more of their smoothie? Answer: Tane Solution: Compare 7/9 and 9/11. Find a common denominator. The least common multiple of 9 and 11 is 99.
   Full step-by-step solution

   Step 1: Compare 7/9 and 9/11. Find a common denominator. The least common multiple of 9 and 11 is 99. Step 2: Convert 7/9 to an equivalent fraction: 7/9 = (7 x 11)/(9 x 11) = 77/99. Step 3: Convert 9/11 to an equivalent fraction: 9/11 = (9 x 9)/(11 x 9) = 81/99. Step 4: Compare 77/99 and 81/99. Since 81 > 77, we have 81/99 > 77/99, so 9/11 > 7/9. Step 5: Therefore, Tane drank more of his smoothie. Answer: Tane

5. Matiu is looking at a rectangular chocolate bar divided into 12 equal squares. He eats 5/12 of the bar. Mere has an identical chocolate bar, but hers is divided into 8 equal squares, and she eats 3/8 of her bar. Who ate more chocolate? Answer: Matiu Solution: Write the fractions: Matiu ate 5/12, Mere ate 3/8. Find a common denominator. The denominators are 12 and 8.
   Full step-by-step solution

   Step 1: Write the fractions: Matiu ate 5/12, Mere ate 3/8. Step 2: Find a common denominator. The denominators are 12 and 8. The least common multiple of 12 and 8 is 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: Convert 3/8 to an equivalent fraction with denominator 24: 3/8 = (3 x 3)/(8 x 3) = 9/24. Step 5: Compare 10/24 and 9/24. Since 10 > 9, 10/24 > 9/24, so 5/12 > 3/8. Step 6: Therefore, Matiu ate more chocolate than Mere. The answer is Matiu.

6. Hana and Matiu each have a chocolate bar of the same size. Hana eats 7/12 of her chocolate bar. Matiu eats 5/8 of his chocolate bar. Who ate more chocolate? Answer: Matiu Solution: Compare 7/12 and 5/8. Find a common denominator. The least common multiple of 12 and 8 is 24.
   Full step-by-step solution

   Step 1: Compare 7/12 and 5/8. Find a common denominator. The least common multiple of 12 and 8 is 24. Step 2: Convert 7/12 to an equivalent fraction with denominator 24: 7/12 = (7 x 2)/(12 x 2) = 14/24. Step 3: Convert 5/8 to an equivalent fraction with denominator 24: 5/8 = (5 x 3)/(8 x 3) = 15/24. Step 4: Compare 14/24 and 15/24. Since 14 < 15, 14/24 < 15/24, so 7/12 < 5/8. Therefore, Matiu ate more chocolate.

7. Sophia and Noah each have a small chocolate bar of the same size. Sophia eats 3/8 of her chocolate bar. Noah eats 1/6 of his chocolate bar. Who eats the larger amount of chocolate? Answer: Sophia Solution: We need to compare 3/8 and 1/6. Since the denominators are different (8 and 6), find a common denominator. The least common multiple of 8 and 6 is 24.
   Full step-by-step solution

   Step 1: We need to compare 3/8 and 1/6. Since the denominators are different (8 and 6), find a common denominator. 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 × 3) / (8 × 3) = 9/24. Step 3: Convert 1/6 to an equivalent fraction with denominator 24: Multiply numerator and denominator by 4: (1 × 4) / (6 × 4) = 4/24. Step 4: Compare 9/24 and 4/24. Since 9 > 4, 9/24 is greater than 4/24. Step 5: Therefore, 3/8 > 1/6. Sophia ate the larger amount. The answer is Sophia.

8. Olivia is making two different types of granola bars. One recipe calls for 5/7 cup of honey, and the other recipe calls for 3/5 cup of honey. Which recipe requires more honey? Answer: 5/7 Solution: Compare 5/7 and 3/5. The denominators are different (7 and 5), so we need to find a common denominator. Find the least common multiple of 7 and 5.
   Full step-by-step solution

   Step 1: Compare 5/7 and 3/5. The denominators are different (7 and 5), so we need to find a common denominator. Step 2: Find the least common multiple of 7 and 5. Since 7 and 5 are both prime numbers, the LCM is 7 × 5 = 35. Step 3: Convert each fraction to an equivalent fraction with denominator 35. - For 5/7: Multiply numerator and denominator by 5: (5 × 5) / (7 × 5) = 25/35. - For 3/5: Multiply numerator and denominator by 7: (3 × 7) / (5 × 7) = 21/35. Step 4: Now compare 25/35 and 21/35. Since 25 > 21, we know 25/35 > 21/35. Step 5: Therefore, 5/7 > 3/5. The recipe that uses 5/7 cup of honey requires more honey. The answer is 5/7.

9. 3/4 > 2/3 ? Answer: A. yes Solution: To determine if 3/4 is greater than 2/3, we need to compare the two fractions. The easiest way is to express both fractions with the same denominator. Find a common denominator.
   Full step-by-step solution

   To determine if 3/4 is greater than 2/3, we need to compare the two fractions. The easiest way is to express both fractions with the same denominator. Step 1: Find a common denominator. The denominators are 4 and 3. The smallest number that both 4 and 3 divide into is 12. So, 12 is our common denominator. Step 2: Convert 3/4 to an equivalent fraction with denominator 12. To change the denominator from 4 to 12, we multiply 4 by 3. To keep the fraction equivalent, we must also multiply the numerator by 3. 3/4 = (3 * 3) / (4 * 3) = 9/12 Step 3: Convert 2/3 to an equivalent fraction with denominator 12. To change the denominator from 3 to 12, we multiply 3 by 4. To keep the fraction equivalent, we must also multiply the numerator by 4. 2/3 = (2 * 4) / (3 * 4) = 8/12 Step 4: Compare the two fractions. Now we compare 9/12 and 8/12. Since the denominators are the same, we simply compare the numerators. 9 is greater than 8. Therefore, 9/12 is greater than 8/12. Conclusion: Because 9/12 > 8/12, the original statement 3/4 > 2/3 is correct. ANSWER: yes