Compare Different Denominators

lessonbunny.com

Answer Key & Explanations

Compare Different Denominators · Grade 4 · Worksheet 1

1. Mason is comparing two rectangular garden plots. Plot A is 7/8 of an acre, and Plot B is 5/6 of an acre. Which garden plot is larger? Answer: Plot A (7/8) Solution: Write the fractions: 7/8 and 5/6. Since the denominators (8 and 6) are different, find a common denominator. The least common multiple of 8 and 6 is 24.
   Full step-by-step solution

   Step 1: Write the fractions: 7/8 and 5/6. Since the denominators (8 and 6) are different, find a common denominator. The least common multiple of 8 and 6 is 24. Step 2: Convert 7/8 to a fraction with denominator 24: Multiply numerator and denominator by 3 to get 21/24. Step 3: Convert 5/6 to a fraction with denominator 24: Multiply numerator and denominator by 4 to get 20/24. Step 4: Compare the numerators: 21 > 20, so 21/24 > 20/24. Therefore, 7/8 > 5/6. Plot A is larger. Answer: Plot A (7/8)

2. 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

3. Aroha and Tane are planting flowers in their garden. Aroha has planted 3/5 of her flower bed. Tane has planted 5/7 of his flower bed. Each flower bed is the same size. Who has planted a larger fraction of their flower bed? Answer: Tane Solution: We need to compare 3/5 and 5/7. Since the denominators are different, we find a common denominator. The least common multiple of 5 and 7 is 35.
   Full step-by-step solution

   Step 1: We need to compare 3/5 and 5/7. Since the denominators are different, we 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: 3/5 = (3 × 7) / (5 × 7) = 21/35. Step 3: Convert 5/7 to an equivalent fraction with denominator 35: 5/7 = (5 × 5) / (7 × 5) = 25/35. Step 4: Compare 21/35 and 25/35. Since 25 > 21, 25/35 > 21/35, so 5/7 > 3/5. Therefore, Tane has planted a larger fraction of his flower bed. Answer: Tane

4. Hana and Matiu each have a rectangular garden of the same size. Hana plants flowers in 7/9 of her garden. Matiu plants flowers in 5/8 of his garden. Who planted flowers in a larger portion of their garden? Answer: Hana Solution: Write the fractions to compare: 7/9 and 5/8. Find a common denominator. The least common multiple of 9 and 8 is 72.
   Full step-by-step solution

   Step 1: Write the fractions to compare: 7/9 and 5/8. Step 2: Find a common denominator. The least common multiple of 9 and 8 is 72. Step 3: Convert each fraction to an equivalent fraction with denominator 72. For 7/9: Multiply numerator and denominator by 8: (7 × 8) / (9 × 8) = 56/72. For 5/8: Multiply numerator and denominator by 9: (5 × 9) / (8 × 9) = 45/72. Step 4: Compare the numerators: 56 > 45, so 56/72 > 45/72. Step 5: Therefore, 7/9 > 5/8. Hana planted flowers in a larger portion of her garden than Matiu. The answer is Hana.

5. Olivia has two identical rectangular gardens. She plants flowers in 3/5 of the first garden and in 5/9 of the second garden. Which garden has a larger fraction planted with flowers? Write your answer as 'first garden' or 'second garden'. Answer: first garden Solution: Write the fractions to compare: 3/5 and 5/9. Find a common denominator. The denominators are 5 and 9.
   Full step-by-step solution

   Step 1: Write the fractions to compare: 3/5 and 5/9. Step 2: Find a common denominator. The denominators are 5 and 9. The least common multiple of 5 and 9 is 45, because 5 x 9 = 45 and 9 x 5 = 45. Step 3: Convert 3/5 to an equivalent fraction with denominator 45. Multiply numerator and denominator by 9: (3 x 9) / (5 x 9) = 27/45. Step 4: Convert 5/9 to an equivalent fraction with denominator 45. Multiply numerator and denominator by 5: (5 x 5) / (9 x 5) = 25/45. Step 5: Compare 27/45 and 25/45. Since 27 > 25, 27/45 is greater than 25/45. Step 6: Therefore, 3/5 > 5/9. The first garden has a larger fraction planted with flowers. The answer is first garden.

6. Noah and Sophia each have a pizza of the same size. Noah eats 5/8 of his pizza, and Sophia eats 7/12 of her pizza. Who eats more pizza? Answer: Noah Solution: Compare 5/8 and 7/12. The denominators are different, so find a common denominator. The least common multiple of 8 and 12 is 24.
   Full step-by-step solution

   Step 1: Compare 5/8 and 7/12. The denominators are different, so find a common denominator. The least common multiple of 8 and 12 is 24. Step 2: Convert 5/8 to a fraction with denominator 24: 5/8 = (5 x 3)/(8 x 3) = 15/24. Step 3: Convert 7/12 to a fraction with denominator 24: 7/12 = (7 x 2)/(12 x 2) = 14/24. Step 4: Compare 15/24 and 14/24. Since 15 > 14, 15/24 > 14/24, so 5/8 > 7/12. Therefore, Noah eats more pizza. The answer is Noah.

7. Liam is looking at two identical rectangular garden beds. The first garden bed is divided into 9 equal sections, and 7 of them are planted with flowers. The second garden bed is divided into 15 equal sections, and 11 of them are planted with flowers. Which garden bed has a larger fraction of flower sections? Write your answer as 'first garden bed' or 'second garden bed'. Answer: first garden bed Solution: Write the fractions. First garden bed: 7/9. Second garden bed: 11/15.
   Full step-by-step solution

   Step 1: Write the fractions. First garden bed: 7/9. Second garden bed: 11/15. Step 2: Find a common denominator. The denominators are 9 and 15. The least common multiple of 9 and 15 is 45 (because 9 x 5 = 45 and 15 x 3 = 45). Step 3: Convert 7/9 to an equivalent fraction with denominator 45. Multiply numerator and denominator by 5: (7 x 5) / (9 x 5) = 35/45. Step 4: Convert 11/15 to an equivalent fraction with denominator 45. Multiply numerator and denominator by 3: (11 x 3) / (15 x 3) = 33/45. Step 5: Compare 35/45 and 33/45. Since 35 > 33, 35/45 is greater than 33/45. Step 6: Therefore, 7/9 > 11/15. The first garden bed has the larger fraction of flower sections. The answer is first garden bed.

8. Olivia is making two different batches of homemade granola bars. For the first batch, she uses 3/5 cup of honey. For the second batch, she uses 5/7 cup of honey. Which batch of granola bars uses more honey? 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: 3/5 = (3 × 7)/(5 × 7) = 21/35. Step 3: Convert 5/7 to an equivalent fraction with denominator 35: 5/7 = (5 × 5)/(7 × 5) = 25/35. Step 4: Now compare 21/35 and 25/35. Since 25/35 > 21/35, we know 5/7 > 3/5. The answer is 5/7.

9. 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.