Compare Like Numerators

lessonbunny.com

Answer Key & Explanations

Compare Like Numerators · Grade 3 · Worksheet 1

1. 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.

2. 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.

3. 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.

4. A rectangular classroom floor is 24 feet long and 18 feet wide. The teacher marks off a square reading corner that is 12 feet on each side. What is the area of the floor that is NOT part of the reading corner? 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 Subtract the reading corner area from the total area 432 - 144 = 288 square feet The area of the floor that is NOT part of the reading corner 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 corner Area = side × side = 12 ft × 12 ft 12 × 12 = 144 square feet Step 3: Subtract the reading corner area from the total area 432 - 144 = 288 square feet The area of the floor that is NOT part of the reading corner is 288 square feet.

5. Aroha and Tane each have identical chocolate bars of the same size. Aroha eats 4/9 of her chocolate bar. Tane eats 4/7 of his chocolate bar. Who ate more chocolate, Aroha or Tane? Explain your reasoning. Answer: Tane Solution: Aroha ate 4/9 of her bar. This means her bar was cut into 9 equal pieces, and she ate 4 of them. Tane ate 4/7 of his bar.
   Full step-by-step solution

   Step 1: Aroha ate 4/9 of her bar. This means her bar was cut into 9 equal pieces, and she ate 4 of them. Step 2: Tane ate 4/7 of his bar. This means his bar was cut into 7 equal pieces, and he ate 4 of them. Step 3: When comparing fractions with the same numerator (both are 4), the fraction with the smaller denominator represents larger pieces. Because 7 is smaller than 9, each piece of Tane's bar is larger than each piece of Aroha's bar. Step 4: Since both ate 4 pieces, Tane ate 4 larger pieces, so he ate more chocolate. Final answer: Tane ate more chocolate.

6. 2/3 > 2/6 = ? Answer: A. yes Solution: Both fractions have the same numerator (2). Compare the denominators: 3 and 6. 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 (2). Step 2: Compare the denominators: 3 and 6. Step 3: When numerators are equal, the fraction with the smaller denominator is larger. Step 4: Since 3 is smaller than 6, 2/3 is larger than 2/6. Step 5: Therefore, 2/3 > 2/6 is true. The answer is Yes.

7. Aroha and Tane each have a chocolate bar of the same size. Aroha cuts her bar into 9 equal pieces and eats 5 of them. Tane cuts his bar into 11 equal pieces and eats 5 of them. Who ate more chocolate: Aroha or Tane? Answer: Aroha Solution: Both chocolate bars are the same size. Aroha cuts hers into 9 equal pieces, so each piece is 1/9 of the bar. She eats 5 pieces, which is 5/9 of the bar.
   Full step-by-step solution

   Step 1: Both chocolate bars are the same size. Aroha cuts hers into 9 equal pieces, so each piece is 1/9 of the bar. She eats 5 pieces, which is 5/9 of the bar. Step 2: Tane cuts his bar into 11 equal pieces, so each piece is 1/11 of the bar. He eats 5 pieces, which is 5/11 of the bar. Step 3: Compare the fractions 5/9 and 5/11. Since both numerators are the same (5), the fraction with the smaller denominator is larger. 9 is smaller than 11, so 5/9 is greater than 5/11. Step 4: Therefore, Aroha ate more chocolate than Tane. The answer is Aroha.