Compare Like Numerators

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Answer Key & Explanations

Compare Like Numerators · Grade 3 · Worksheet 2

1. 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.

2. Olivia baked two trays of brownies for a school bake sale. On the first tray, she cut the brownies into 9 equal pieces. On the second tray, she cut the brownies into 7 equal pieces. Olivia's friend Emma bought 3 pieces from the first tray, and Liam bought 3 pieces from the second tray. Who bought the larger total amount of brownie, Emma or Liam? Answer: Liam Solution: Emma bought 3 pieces from the first tray, which was cut into 9 equal pieces. So Emma's brownie amount is 3/9 of the whole tray. Liam bought 3 pieces from the second tray, which was cut into 7 equal pieces.
   Full step-by-step solution

   Step 1: Emma bought 3 pieces from the first tray, which was cut into 9 equal pieces. So Emma's brownie amount is 3/9 of the whole tray. Step 2: Liam bought 3 pieces from the second tray, which was cut into 7 equal pieces. So Liam's brownie amount is 3/7 of the whole tray. Step 3: We need to compare 3/9 and 3/7. Both fractions have the same numerator (3), so the fraction with the smaller denominator represents the larger amount because the whole is divided into fewer, bigger pieces. Step 4: Since 7 is less than 9, 3/7 is greater than 3/9. Step 5: Therefore, Liam bought the larger total amount of brownie. The answer is Liam.

3. Emma has two identical chocolate bars. She cuts one into 5 equal pieces and eats 3 of them. She cuts the other into 10 equal pieces and eats 3 of them. From which chocolate bar did Emma eat the greater amount? Answer: 3/5 Solution: Emma eats 3 pieces from the bar cut into 5 equal pieces. That is the fraction 3/5. Emma eats 3 pieces from the bar cut into 10 equal pieces.
   Full step-by-step solution

   Step 1: Emma eats 3 pieces from the bar cut into 5 equal pieces. That is the fraction 3/5. Step 2: Emma eats 3 pieces from the bar cut into 10 equal pieces. That is the fraction 3/10. Step 3: Compare 3/5 and 3/10. Both fractions have the same numerator (3). When numerators are the same, the fraction with the smaller denominator is larger, because the whole is divided into fewer pieces, so each piece is bigger. Step 4: Since 5 is less than 10, 3/5 is greater than 3/10. Final answer: Emma ate the greater amount from the bar cut into 5 pieces, which is 3/5.

4. 3/4 > 3/7 = ? Answer: B. true Solution: Both fractions have the same numerator (3). When numerators are equal, the fraction with the smaller denominator is larger. Compare denominators: 4 and 7.
   Full step-by-step solution

   Step 1: Both fractions have the same numerator (3). Step 2: When numerators are equal, the fraction with the smaller denominator is larger. Step 3: Compare denominators: 4 and 7. Since 4 is smaller than 7, 3/4 is larger than 3/7. Step 4: Therefore, the statement 3/4 > 3/7 is true. The answer is true.

5. Emma and Liam each have a whole pizza of the same size. Emma cuts her pizza into 11 equal slices and eats 7 of them. Liam cuts his pizza into 9 equal slices and eats 7 of them. Who ate more pizza, Emma or Liam? Answer: Liam Solution: Emma ate 7/11 of her pizza. Liam ate 7/9 of his pizza. Both fractions have the same numerator (7).
   Full step-by-step solution

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

6. 2/3 > 2/5 ? Answer: A. yes Solution: We need to determine if the statement "2/3 > 2/5" is true. Compare the two fractions. Both fractions have the same numerator (2).
   Full step-by-step solution

   Step 1: Understand the problem. We need to determine if the statement "2/3 > 2/5" is true. Step 2: Compare the two fractions. Both fractions have the same numerator (2). When the numerators are the same, the fraction with the smaller denominator is the larger fraction. Step 3: Compare denominators. The denominators are 3 and 5. Since 3 < 5, the fraction 2/3 is larger than 2/5. Step 4: Verify by finding a common denominator. The least common denominator of 3 and 5 is 15. Convert 2/3: (2 × 5)/(3 × 5) = 10/15 Convert 2/5: (2 × 3)/(5 × 3) = 6/15 Step 5: Compare the converted fractions. 10/15 > 6/15, so 2/3 > 2/5. Conclusion: The statement "2/3 > 2/5" is correct. Answer: yes

7. Emma and Liam are each making fruit punch for a party. Emma's recipe uses 3/10 of a cup of lemon juice. Liam's recipe uses 3/5 of a cup of lemon juice. Whose recipe uses more lemon juice, Emma's or Liam's? Answer: Liam's Solution: Both fractions have the same numerator (3), so we compare the denominators. Step 2: Emma's recipe uses 3/10 of a cup. This means the cup is split into 10 equal parts, and she uses 3 of those parts.
   Full step-by-step solution

   Step 1: Both fractions have the same numerator (3), so we compare the denominators. Step 2: Emma's recipe uses 3/10 of a cup. This means the cup is split into 10 equal parts, and she uses 3 of those parts. Step 3: Liam's recipe uses 3/5 of a cup. This means the cup is split into 5 equal parts, and he uses 3 of those parts. Step 4: When the numerator is the same, the fraction with the smaller denominator is larger because the parts are bigger. Since 5 is smaller than 10, each fifth is larger than each tenth. Step 5: 3/5 is greater than 3/10. Therefore, Liam's recipe uses more lemon juice. The answer is Liam's.

8. Mere and Hana each have an identical-sized fruit bar. Mere eats 5/11 of her fruit bar, and Hana eats 5/8 of her fruit bar. Who eats more of their fruit bar, Mere or Hana? Answer: Hana Solution: We compare the fractions 5/11 and 5/8. Both have the same numerator (5), so we compare the denominators. The denominator tells how many equal pieces the whole fruit bar is divided into.
   Full step-by-step solution

   Step 1: We compare the fractions 5/11 and 5/8. Both have the same numerator (5), so we compare the denominators. Step 2: The denominator tells how many equal pieces the whole fruit bar is divided into. 5/11 means the bar is cut into 11 equal pieces, and Mere eats 5 of them. 5/8 means the bar is cut into 8 equal pieces, and Hana eats 5 of them. Step 3: When the whole is the same size, cutting it into fewer pieces makes each piece larger. Since 8 is less than 11, each piece in the bar cut into 8 pieces is larger than each piece in the bar cut into 11 pieces. Step 4: So, 5 pieces from a bar cut into 8 pieces is a greater amount than 5 pieces from a bar cut into 11 pieces. Therefore, 5/8 > 5/11. The answer is Hana.

9. Emma and Olivia each have a glass of lemonade of the same size. Emma drinks 5/8 of her glass, and Olivia drinks 5/12 of her glass. Who drinks more lemonade? Answer: Emma Solution: Compare the fractions 5/8 and 5/12. Both have the same numerator (5), 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 5/8 and 5/12. Both have the same numerator (5), so we compare the denominators. Step 2: The denominator tells how many equal parts the whole is divided into. 5/8 means the glass is divided into 8 equal parts, and Emma drinks 5 of them. 5/12 means the glass is divided into 12 equal parts, and Olivia drinks 5 of them. Step 3: When the numerator is the same, the fraction with the smaller denominator has larger pieces. Since 8 is less than 12, each piece in Emma's glass is larger. Step 4: Therefore, 5/8 is greater than 5/12. Emma drinks more lemonade. The answer is Emma.