Compare Like Denominators

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Answer Key & Explanations

Compare Like Denominators · Grade 3 · Worksheet 3

1. A farmer harvested 7/8 of her cornfield on Monday and 5/8 of her cornfield on Tuesday. On which day did she harvest a larger fraction of her cornfield? Answer: 7/8 Solution: Identify the fractions harvested each day. On Monday: 7/8 of the cornfield. On Tuesday: 5/8 of the cornfield.
   Full step-by-step solution

   Step 1: Identify the fractions harvested each day. On Monday: 7/8 of the cornfield. On Tuesday: 5/8 of the cornfield. Step 2: Compare the two fractions. Both fractions have the same denominator (8), so we can compare them by looking at the numerators. Numerator for Monday: 7 Numerator for Tuesday: 5 Step 3: Reasoning. When two fractions have the same denominator, the larger numerator means the fraction is larger. Since 7 is greater than 5, 7/8 is greater than 5/8. Step 4: Conclusion. Therefore, the farmer harvested a larger fraction of her cornfield on Monday. Final answer: 7/8

2. Sophia and Noah are helping their teacher organize the classroom library. There are 66 books to sort. Sophia sorted 7/11 of the books onto the shelf, and Noah sorted 4/11 of the books into the reading corner. Who sorted a larger portion of the books? Answer: Sophia Solution: Both fractions have the same denominator of 11. This means the books are divided into 11 equal groups. Step 2: Compare the numerators: Sophia sorted 7/11 (7 out of 11 groups) and Noah sorted 4/11 (4 out of 11 groups).
   Full step-by-step solution

   Step 1: Both fractions have the same denominator of 11. This means the books are divided into 11 equal groups. Step 2: Compare the numerators: Sophia sorted 7/11 (7 out of 11 groups) and Noah sorted 4/11 (4 out of 11 groups). Step 3: Since 7 is greater than 4, 7/11 is greater than 4/11. Step 4: Therefore, Sophia sorted a larger portion of the books.

3. Isabella has a rectangular garden divided into 12 equal square plots. She plants sunflowers in 7 of the plots and daisies in the remaining 5 plots. Looking at the garden layout, which flower takes up more space: sunflowers or daisies? Answer: sunflowers Solution: The garden is divided into 12 equal square plots, so each plot represents 1/12 of the whole garden. Sunflowers are planted in 7 plots, which is 7/12 of the garden.
   Full step-by-step solution

   Step 1: The garden is divided into 12 equal square plots, so each plot represents 1/12 of the whole garden. Step 2: Sunflowers are planted in 7 plots, which is 7/12 of the garden. Step 3: Daisies are planted in the remaining 5 plots, which is 5/12 of the garden. Step 4: Both fractions have the same denominator (12), so compare the numerators: 7 and 5. Step 5: 7 is greater than 5, so 7/12 is greater than 5/12. Step 6: Therefore, the sunflowers take up more space than the daisies. The answer is sunflowers.

4. 3/5 > 2/5 ? Answer: B. yes Solution: Identify the fractions to compare. We are comparing 3/5 and 2/5. Compare the denominators.
   Full step-by-step solution

   Step 1: Identify the fractions to compare. We are comparing 3/5 and 2/5. Step 2: Compare the denominators. Both fractions have the same denominator, which is 5. When denominators are the same, we only need to compare the numerators. Step 3: Compare the numerators. Numerator of first fraction: 3 Numerator of second fraction: 2 Since 3 > 2, the fraction with numerator 3 is larger. Step 4: Write the conclusion. 3/5 > 2/5 is true. Final Answer: yes

5. 9/11 ? 7/11 Answer: > Solution: Both fractions have the same denominator of 11. Compare the numerators: 9 and 7. Since 9 is greater than 7, 9/11 is greater than 7/11.
   Full step-by-step solution

   Step 1: Both fractions have the same denominator of 11. Step 2: Compare the numerators: 9 and 7. Step 3: Since 9 is greater than 7, 9/11 is greater than 7/11. Step 4: The correct symbol is >. The answer is >.

6. Liam and Emma are painting a mural on their school wall. Liam painted 7/10 of the wall with blue paint, while Emma painted 5/10 of the wall with yellow paint. Which student painted a larger portion of the wall? Answer: D. Liam Solution: Both fractions have the same denominator of 10, which means they represent parts of the same whole wall. Compare the numerators: 7 (Liam's portion) and 5 (Emma's portion).
   Full step-by-step solution

   Step 1: Both fractions have the same denominator of 10, which means they represent parts of the same whole wall. Step 2: Compare the numerators: 7 (Liam's portion) and 5 (Emma's portion). Step 3: Since 7 is greater than 5, 7/10 is greater than 5/10. Step 4: Therefore, Liam painted a larger portion of the wall than Emma. The correct answer is Liam.

7. Which fraction is greater: 7/12 or 5/12? Answer: C. 7/12 Solution: Both fractions have the same denominator of 12 Compare the numerators: 7 and 5 Since 7 is greater than 5, 7/12 is greater than 5/12 Therefore, 7/12 is the greater fraction The correct answer is 7/12.
   Full step-by-step solution

   Step 1: Both fractions have the same denominator of 12 Step 2: Compare the numerators: 7 and 5 Step 3: Since 7 is greater than 5, 7/12 is greater than 5/12 Step 4: Therefore, 7/12 is the greater fraction The correct answer is 7/12.

8. Liam and Emma are painting a mural on the school wall. Liam painted 7/10 of the mural, while Emma painted 5/10 of the mural. Who painted a greater portion of the mural? Answer: A. Liam Solution: Both fractions have the same denominator of 10, which means the mural is divided into 10 equal parts. Compare the numerators: 7 versus 5. Since 7 is greater than 5, 7/10 is greater than 5/10.
   Full step-by-step solution

   Step 1: Both fractions have the same denominator of 10, which means the mural is divided into 10 equal parts. Step 2: Compare the numerators: 7 versus 5. Step 3: Since 7 is greater than 5, 7/10 is greater than 5/10. Step 4: Therefore, Liam painted a greater portion of the mural than Emma. The correct answer is Liam.