Equivalent Fractions

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Answer Key & Explanations

Equivalent Fractions · Grade 4 · Worksheet 3

1. Charlotte is making a large batch of fruit punch for her birthday party. The recipe calls for 4/7 cup of orange juice for each serving. She wants to make 14 servings. How many cups of orange juice does Charlotte need in total? Write your answer as a fraction in simplest form. Answer: 8 Solution: Charlotte needs 4/7 cup of orange juice for each serving, and she wants to make 14 servings. So we need to multiply 4/7 by 14. Write 14 as a fraction: 14 = 14/1.
   Full step-by-step solution

   Step 1: Charlotte needs 4/7 cup of orange juice for each serving, and she wants to make 14 servings. So we need to multiply 4/7 by 14. Step 2: Write 14 as a fraction: 14 = 14/1. Step 3: Multiply the numerators: 4 × 14 = 56. The new numerator is 56. Step 4: Multiply the denominators: 7 × 1 = 7. The denominator stays 7. Step 5: The product is 56/7. Step 6: Simplify 56/7 by dividing both numerator and denominator by 7: 56 ÷ 7 = 8, and 7 ÷ 7 = 1. So 56/7 = 8/1 = 8. Charlotte needs 8 cups of orange juice.

2. 3/8 = __/96 Answer: 36 Solution: The original fraction is 3/8 and the new denominator is 96. Find what number you multiply the original denominator (8) by to get the new denominator (96). 8 × 12 = 96.
   Full step-by-step solution

   Step 1: The original fraction is 3/8 and the new denominator is 96. Step 2: Find what number you multiply the original denominator (8) by to get the new denominator (96). 8 × 12 = 96. Step 3: Multiply the original numerator (3) by the same number (12). 3 × 12 = 36. Step 4: The equivalent fraction is 36/96. The missing numerator is 36.

3. 3/7 = __/56 Answer: 24 Solution: The original fraction is 3/7 and the new denominator is 56. Find what number you multiply the original denominator (7) by to get the new denominator (56). 7 × 8 = 56.
   Full step-by-step solution

   Step 1: The original fraction is 3/7 and the new denominator is 56. Step 2: Find what number you multiply the original denominator (7) by to get the new denominator (56). 7 × 8 = 56. Step 3: Multiply the original numerator (3) by the same number (8). 3 × 8 = 24. Step 4: The equivalent fraction is 24/56. The missing numerator is 24.

4. Noah is helping his aunt prepare bags of rice for a community food drive. They have a large bag that contains 6/8 of a kilogram of rice. Noah's aunt asks him to divide the rice into smaller bags, each holding 1/4 of a kilogram. How many smaller bags can Noah fill? Answer: 3 Solution: We need to find how many 1/4 kilogram bags fit into 6/8 kilogram of rice. This is the same as dividing 6/8 by 1/4. To divide fractions, it helps to have the same denominator.
   Full step-by-step solution

   Step 1: We need to find how many 1/4 kilogram bags fit into 6/8 kilogram of rice. This is the same as dividing 6/8 by 1/4. Step 2: To divide fractions, it helps to have the same denominator. Write 1/4 as an equivalent fraction with denominator 8. Multiply numerator and denominator by 2: 1/4 = (1 x 2)/(4 x 2) = 2/8. Step 3: Now the problem becomes: how many times does 2/8 fit into 6/8? Divide the numerators: 6 ÷ 2 = 3. Step 4: So Noah can fill 3 smaller bags of rice. The answer is 3.

5. 7/8 = __/96 Answer: 84 Solution: The original fraction is 7/8 and the new denominator is 96. Find what number you multiply the original denominator (8) by to get the new denominator (96). 8 × 12 = 96.
   Full step-by-step solution

   Step 1: The original fraction is 7/8 and the new denominator is 96. Step 2: Find what number you multiply the original denominator (8) by to get the new denominator (96). 8 × 12 = 96. Step 3: Multiply the original numerator (7) by the same number (12). 7 × 12 = 84. Step 4: The equivalent fraction is 84/96. The missing numerator is 84.

6. Hana is helping her grandmother make traditional coconut candy. The recipe calls for 3/4 cup of sugar, but Hana only has a 1/8 cup measuring spoon. How many scoops of the 1/8 cup spoon does Hana need to measure out the correct amount of sugar? Answer: 6 Solution: We need to find how many 1/8 cup scoops equal 3/4 cup. This is the same as finding an equivalent fraction for 3/4 with a denominator of 8. To change the denominator from 4 to 8, we multiply by 2: 4 x 2 = 8.
   Full step-by-step solution

   Step 1: We need to find how many 1/8 cup scoops equal 3/4 cup. This is the same as finding an equivalent fraction for 3/4 with a denominator of 8. Step 2: To change the denominator from 4 to 8, we multiply by 2: 4 x 2 = 8. Step 3: Multiply the numerator by the same number: 3 x 2 = 6. Step 4: So 3/4 = 6/8. Step 5: Since 6/8 means 6 parts of 1/8 each, Hana needs 6 scoops of the 1/8 cup spoon. The answer is 6.

7. 5/6 = __/42 Answer: 35 Solution: The original fraction is 5/6 and the new denominator is 42. Find what number you multiply the original denominator (6) by to get the new denominator (42). 6 × 7 = 42.
   Full step-by-step solution

   Step 1: The original fraction is 5/6 and the new denominator is 42. Step 2: Find what number you multiply the original denominator (6) by to get the new denominator (42). 6 × 7 = 42. Step 3: Multiply the original numerator (5) by the same number (7). 5 × 7 = 35. Step 4: The equivalent fraction is 35/42. The missing numerator is 35.

8. 5/8 = __/72 Answer: 45 Solution: The original fraction is 5/8 and the new denominator is 72. Find what number you multiply the original denominator (8) by to get the new denominator (72). 8 × 9 = 72.
   Full step-by-step solution

   Step 1: The original fraction is 5/8 and the new denominator is 72. Step 2: Find what number you multiply the original denominator (8) by to get the new denominator (72). 8 × 9 = 72. Step 3: Multiply the original numerator (5) by the same number (9). 5 × 9 = 45. Step 4: The equivalent fraction is 45/72. The missing numerator is 45.

9. Emma is making lemonade for a school fundraiser. She needs 2/3 cup of lemon juice for each pitcher. If she wants to make 5 pitchers of lemonade, how many cups of lemon juice does Emma need in total? Answer: 10/3 or 3 1/3 Solution: Emma needs 2/3 cup of lemon juice for each pitcher She wants to make 5 pitchers Multiply the amount per pitcher by the number of pitchers: 2/3 × 5 Write 5 as a fraction: 5 = 5/1 Multiply the fractions: (2/3) × (5/1) = (2 × 5)/(3 × 1) = 10/3 Convert to a mixed number: 10/3 = 3 1/3 Emma needs 3…
   Full step-by-step solution

   Step 1: Emma needs 2/3 cup of lemon juice for each pitcher Step 2: She wants to make 5 pitchers Step 3: Multiply the amount per pitcher by the number of pitchers: 2/3 × 5 Step 4: Write 5 as a fraction: 5 = 5/1 Step 5: Multiply the fractions: (2/3) × (5/1) = (2 × 5)/(3 × 1) = 10/3 Step 6: Convert to a mixed number: 10/3 = 3 1/3 Emma needs 3 1/3 cups of lemon juice in total.