Compare Like Numerators

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Answer Key & Explanations

Compare Like Numerators · Grade 3 · Worksheet 1

1. Aroha is making two different types of fruit punch for a party. For the first punch, she uses 7/9 of a cup of orange juice concentrate. For the second punch, she uses 7/12 of a cup of orange juice concentrate. Which fruit punch uses more orange juice concentrate: the one with 7/9 of a cup or the one with 7/12 of a cup? Answer: 7/9 of a cup Solution: We are comparing 7/9 and 7/12. Both fractions have the same numerator (7), so we compare the denominators. The denominator tells us how many equal pieces the whole is divided into.
   Full step-by-step solution

   We are comparing 7/9 and 7/12. Both fractions have the same numerator (7), so we compare the denominators. The denominator tells us how many equal pieces the whole is divided into. For 7/9, the whole is divided into 9 equal pieces, so each piece is 1/9. For 7/12, the whole is divided into 12 equal pieces, so each piece is 1/12. Since 1/9 is larger than 1/12 (because 9 pieces are bigger than 12 pieces from the same whole), 7 pieces of size 1/9 is more than 7 pieces of size 1/12. Therefore, 7/9 is greater than 7/12. The answer is 7/9 of a cup.

2. 2/3 > 2/6 ? Answer: A. yes Solution: Both fractions have the same numerator (2). Compare the denominators: 3 and 6. A smaller denominator means larger pieces when the numerators are equal.
   Full step-by-step solution

   Step 1: Both fractions have the same numerator (2). Step 2: Compare the denominators: 3 and 6. Step 3: A smaller denominator means larger pieces when the numerators are equal. Step 4: Since 3 is smaller than 6, 2/3 represents larger pieces than 2/6. Step 5: Therefore, 2/3 is greater than 2/6. The answer is yes.

3. Mason and Isabella each have an identical-sized orange. Mason cuts his orange into 8 equal slices and eats 5 of them. Isabella cuts her orange into 11 equal slices and eats 5 of them. Who ate more orange, Mason or Isabella? Answer: Mason Solution: Write the fractions. Mason eats 5/8 of his orange. Isabella eats 5/11 of her orange.
   Full step-by-step solution

   Step 1: Write the fractions. Mason eats 5/8 of his orange. Isabella eats 5/11 of her orange. Both fractions have the same numerator (5). Step 2: Compare the denominators. The denominator tells how many equal parts the whole is divided into. A smaller denominator means fewer, larger pieces. A larger denominator means more, smaller pieces. Step 3: 8 is smaller than 11. So each slice of Mason's orange (1/8) is larger than each slice of Isabella's orange (1/11). Step 4: Since both eat 5 slices, Mason eats 5 larger slices, which is a greater amount. Therefore, 5/8 is greater than 5/11. The answer is Mason.

4. Isabella and Mason each have a rectangular garden of the same size. Isabella plants carrots in 5/8 of her garden. Mason plants carrots in 5/11 of his garden. Who planted carrots in a larger portion of their garden, Isabella or Mason? Answer: Isabella Solution: The fractions to compare are 5/8 and 5/11. 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.
   Full step-by-step solution

   Step 1: The fractions to compare are 5/8 and 5/11. 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 garden is divided into 8 equal parts, and Isabella plants carrots in 5 of those parts. 5/11 means the garden is divided into 11 equal parts, and Mason plants carrots in 5 of those parts. Step 3: When the numerators are the same, the fraction with the smaller denominator is larger because each part is bigger. Since 8 is less than 11, each part in Isabella's garden is larger than each part in Mason's garden. Step 4: Therefore, 5/8 > 5/11. Isabella planted carrots in a larger portion of her garden. 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 is 12 feet on each side. What is the area of the remaining floor space in square feet? Answer: 288 Solution: Area = length × width = 24 ft × 18 ft 24 × 18 = 432 square feet Area = side × side = 12 ft × 12 ft 12 × 12 = 144 square feet Remaining area = total area - reading area 432 - 144 = 288 square feet The answer is 288 square feet.
   Full step-by-step solution

   Step 1: Find the total area of the classroom floor Area = length × width = 24 ft × 18 ft 24 × 18 = 432 square feet Step 2: Find the area of the square reading area Area = side × side = 12 ft × 12 ft 12 × 12 = 144 square feet Step 3: Subtract the reading area from the total area Remaining area = total area - reading area 432 - 144 = 288 square feet The answer is 288 square feet.

6. Kaia and Aroha each have a chocolate bar of the same size. Kaia eats 5/9 of her chocolate bar, and Aroha eats 5/12 of her chocolate bar. Who ate more chocolate? Answer: Kaia Solution: Compare the fractions 5/9 and 5/12. They have the same numerator (5), so we compare the denominators. Step 2: The denominator tells how many equal parts the whole is divided into.
   Full step-by-step solution

   Step 1: Compare the fractions 5/9 and 5/12. They have the same numerator (5), so we compare the denominators. Step 2: The denominator tells how many equal parts the whole is divided into. 5/9 means the chocolate bar is cut into 9 equal pieces, and Kaia eats 5 of them. 5/12 means the bar is cut into 12 equal pieces, and Aroha eats 5 of them. Step 3: The smaller the denominator, the larger each piece. Since 9 is less than 12, each piece in Kaia's bar is larger. So 5 pieces from a bar cut into 9 pieces is more than 5 pieces from a bar cut into 12 pieces. Therefore, 5/9 > 5/12. The answer is Kaia.

7. Olivia and Emma each have a large pizza of the same size. Olivia cuts her pizza into 10 equal slices and eats 3 slices. Emma cuts her pizza into 5 equal slices and eats 3 slices. Who eats more pizza, Olivia or Emma? Answer: Emma Solution: Write the fractions. Olivia eats 3/10 of her pizza. Emma eats 3/5 of her pizza.
   Full step-by-step solution

   Step 1: Write the fractions. Olivia eats 3/10 of her pizza. Emma eats 3/5 of her pizza. Step 2: Both fractions have the same numerator (3). When numerators are the same, the fraction with the smaller denominator is larger. Step 3: Compare denominators: 5 is smaller than 10. So 3/5 is larger than 3/10. Step 4: Therefore, Emma eats more pizza. The answer is Emma.