Compare Like Numerators

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Answer Key & Explanations

Compare Like Numerators · Grade 3 · Worksheet 2

1. Charlotte and Isabella each have a large, identical chocolate bar. Charlotte eats 2/7 of her chocolate bar, and Isabella eats 2/5 of her chocolate bar. Who eats more chocolate, Charlotte or Isabella? Answer: Isabella Solution: Compare the fractions 2/7 and 2/5. Both have the same numerator (2), so we compare the denominators. The denominator tells how many equal parts the whole is divided into.
   Full step-by-step solution

   Step 1: Compare the fractions 2/7 and 2/5. Both have the same numerator (2), so we compare the denominators. Step 2: The denominator tells how many equal parts the whole is divided into. 2/7 means the chocolate bar is cut into 7 equal pieces, and Charlotte eats 2 of them. 2/5 means the bar is cut into 5 equal pieces, and Isabella eats 2 of them. Step 3: When the whole is divided into fewer pieces, each piece is larger. Since 5 is less than 7, each piece in Isabella's bar (cut into 5 pieces) is larger than each piece in Charlotte's bar (cut into 7 pieces). Step 4: Since both eat the same number of pieces (2), the person with the larger pieces eats more. Therefore, 2/5 > 2/7, so Isabella eats more chocolate. The answer is Isabella.

2. 3/4 > 3/8 ? Answer: B. yes Solution: We are comparing two fractions: 3/4 and 3/8. We need to determine if 3/4 is greater than 3/8. Compare fractions with the same numerator.
   Full step-by-step solution

   Step 1: Understand the problem. We are comparing two fractions: 3/4 and 3/8. We need to determine if 3/4 is greater than 3/8. Step 2: Compare fractions with the same numerator. Both fractions have the same numerator, which is 3. When numerators are the same, the fraction with the smaller denominator is the larger fraction. Here, 4 is smaller than 8, so 3/4 should be larger than 3/8. Step 3: Verify by finding a common denominator. Let's confirm by converting both fractions to have the same denominator. The least common denominator of 4 and 8 is 8. Convert 3/4 to eighths: Multiply numerator and denominator by 2 → (3×2)/(4×2) = 6/8. Now compare 6/8 and 3/8. Step 4: Compare the numerators. 6/8 vs 3/8: Since 6 > 3, we have 6/8 > 3/8. Therefore, 3/4 > 3/8. Step 5: Conclusion. The statement "3/4 > 3/8" is true. The correct answer is yes.

3. Mason and Charlotte each have an identical-sized chocolate cake. Mason cuts his cake into 7 equal slices and eats 2 of them. Charlotte cuts her cake into 12 equal slices and eats 2 of them. Who ate more cake, Mason or Charlotte? Answer: Mason Solution: Mason ate 2/7 of his cake. Charlotte ate 2/12 of her cake. Both fractions have the same numerator (2), so we compare the denominators.
   Full step-by-step solution

   Step 1: Mason ate 2/7 of his cake. Charlotte ate 2/12 of her cake. Step 2: Both fractions have the same numerator (2), so we compare the denominators. Step 3: The denominator tells how many equal slices the cake is cut into. 2/7 means Mason's cake is cut into 7 slices, and 2/12 means Charlotte's cake is cut into 12 slices. Step 4: When the numerators are the same, the fraction with the smaller denominator is larger because each piece is bigger. Since 7 is smaller than 12, each of Mason's slices is larger than each of Charlotte's slices. Step 5: Therefore, 2/7 > 2/12. Mason ate more cake. The answer is Mason.

4. Mason and Isabella each have a pizza of the same size. Mason cuts his pizza into 11 equal slices and eats 7 of them. Isabella cuts her pizza into 9 equal slices and eats 7 of them. Who eats more pizza, Mason or Isabella? Answer: Isabella Solution: Write the fractions. Mason eats 7/11 of his pizza. Isabella eats 7/9 of her pizza.
   Full step-by-step solution

   Step 1: Write the fractions. Mason eats 7/11 of his pizza. Isabella eats 7/9 of her pizza. Step 2: Both fractions have the same numerator (7). When numerators are the same, the fraction with the smaller denominator is larger because the whole is divided into fewer, bigger pieces. Step 3: Compare denominators: 9 < 11. So 7/9 > 7/11. Step 4: Therefore, Isabella eats more pizza than Mason. The answer is Isabella.

5. A rectangular classroom floor is 24 feet long and 18 feet wide. The teacher marks off a square reading area in one corner that measures 12 feet on each side. What is the area of the floor that is NOT part of the reading area? Answer: 288 Solution: Area = length × width = 24 × 18 24 × 18 = 432 square feet Area = side × side = 12 × 12 12 × 12 = 144 square feet 432 - 144 = 288 square feet The area of the floor that is NOT part of the reading area is 288 square feet.
   Full step-by-step solution

   Step 1: Find the total area of the classroom floor Area = length × width = 24 × 18 24 × 18 = 432 square feet Step 2: Find the area of the square reading area Area = side × side = 12 × 12 12 × 12 = 144 square feet Step 3: Subtract the reading area from the total area 432 - 144 = 288 square feet The area of the floor that is NOT part of the reading area is 288 square feet.

6. 3/4 > 3/5 = ? Answer: B. true Solution: Both fractions have the same numerator (3). Compare the denominators: 4 and 5. When numerators are equal, the fraction with the smaller denominator is larger.
   Full step-by-step solution

   Step 1: Both fractions have the same numerator (3). Step 2: Compare the denominators: 4 and 5. Step 3: When numerators are equal, the fraction with the smaller denominator is larger. Step 4: Since 4 is smaller than 5, 3/4 is greater than 3/5. Step 5: Therefore, the statement 3/4 > 3/5 is true.

7. Sophia and Noah each have an identical rectangular cake. Sophia cuts her cake into 11 equal slices and takes 6 of them for her party. Noah cuts his cake into 16 equal slices and takes 6 of them for his party. Who takes the larger total amount of cake: Sophia or Noah? Answer: Sophia Solution: Sophia cuts her cake into 11 equal slices, so each slice is 1/11 of the whole cake. She takes 6 slices, so she takes 6/11 of the cake. Noah cuts his cake into 16 equal slices, so each slice is 1/16 of the whole cake.
   Full step-by-step solution

   Step 1: Sophia cuts her cake into 11 equal slices, so each slice is 1/11 of the whole cake. She takes 6 slices, so she takes 6/11 of the cake. Step 2: Noah cuts his cake into 16 equal slices, so each slice is 1/16 of the whole cake. He takes 6 slices, so he takes 6/16 of the cake. Step 3: Both fractions have the same numerator (6), but different denominators (11 and 16). Step 4: When numerators are the same, the fraction with the smaller denominator is larger because the whole is divided into fewer, bigger pieces. Since 11 is smaller than 16, each slice in Sophia's cake is larger than each slice in Noah's cake. Step 5: Therefore, 6/11 is greater than 6/16, so Sophia takes a larger total amount of cake. The answer is Sophia.