Fraction Applications

lessonbunny.com

Answer Key & Explanations

Fraction Applications · Grade 5 · Worksheet 1

1. Zoe is following a recipe for granola bars that calls for 1 cup of honey. Zoe wants to make 3 batches of the recipe. How many cups of honey does Zoe need in total? Answer: 3 Solution: The recipe uses 1 cup of honey for one batch. To make 3 batches, multiply the honey per batch by the number of batches: 1 × 3 = 3. So Zoe needs 3 cups of honey in total.
   Full step-by-step solution

   Step 1: The recipe uses 1 cup of honey for one batch. Step 2: To make 3 batches, multiply the honey per batch by the number of batches: 1 × 3 = 3. Step 3: So Zoe needs 3 cups of honey in total.

2. A shipping company has 840 packages to deliver. In the morning, they delivered 3/7 of all packages. In the afternoon, they delivered 2/5 of the remaining packages. What fraction of the original 840 packages were delivered in the afternoon? Answer: 8/35 Solution: Morning delivery was 3/7 of all packages Remaining packages after morning = 1 - 3/7 = 7/7 - 3/7 = 4/7 of original Afternoon delivery was 2/5 of the remaining packages Fraction of original delivered in afternoon = 2/5 × 4/7 = 8/35 Check: 8/35 is in simplest form since 8 and 35 share no common…
   Full step-by-step solution

   Step 1: Morning delivery was 3/7 of all packages Step 2: Remaining packages after morning = 1 - 3/7 = 7/7 - 3/7 = 4/7 of original Step 3: Afternoon delivery was 2/5 of the remaining packages Step 4: Fraction of original delivered in afternoon = 2/5 × 4/7 = 8/35 Step 5: Check: 8/35 is in simplest form since 8 and 35 share no common factors The answer is 8/35.

3. A recipe calls for 2/3 cup of sugar. If you want to make 3 1/4 times the recipe, how many cups of sugar do you need? Answer: 2 1/6 Solution: Convert the mixed number 3 1/4 to an improper fraction. 3 1/4 = (3 × 4 + 1)/4 = (12 + 1)/4 = 13/4 Multiply the original amount of sugar (2/3 cup) by the scaling factor (13/4).
   Full step-by-step solution

   Step 1: Convert the mixed number 3 1/4 to an improper fraction. 3 1/4 = (3 × 4 + 1)/4 = (12 + 1)/4 = 13/4 Step 2: Multiply the original amount of sugar (2/3 cup) by the scaling factor (13/4). 2/3 × 13/4 = (2 × 13)/(3 × 4) = 26/12 Step 3: Simplify the fraction 26/12 by dividing numerator and denominator by 2. 26 ÷ 2 = 13 12 ÷ 2 = 6 So 26/12 = 13/6 Step 4: Convert the improper fraction 13/6 to a mixed number. 13 ÷ 6 = 2 with remainder 1, so 13/6 = 2 1/6 The final answer is 2 1/6 cups of sugar.

4. A rectangular garden is divided into sections for different vegetables. The garden is 8 meters long and 6 meters wide. Three-fourths of the garden is planted with tomatoes, and the remaining area is divided equally between carrots and lettuce. What fraction of the total garden area is planted with carrots? Answer: 1/8 Solution: Find the total area of the garden. The garden is a rectangle with length 8 m and width 6 m. Area = length × width = 8 × 6 = 48 square meters.
   Full step-by-step solution

   Step 1: Find the total area of the garden. The garden is a rectangle with length 8 m and width 6 m. Area = length × width = 8 × 6 = 48 square meters. Step 2: Find the area planted with tomatoes. Three-fourths of the garden is tomatoes. Tomato area = 3/4 × 48 = 36 square meters. Step 3: Find the remaining area for carrots and lettuce. Remaining area = total area − tomato area = 48 − 36 = 12 square meters. Step 4: Divide the remaining area equally between carrots and lettuce. Each gets half of the remaining area. Carrot area = 12 ÷ 2 = 6 square meters. Step 5: Find the fraction of the total garden planted with carrots. Fraction = carrot area / total area = 6 / 48. Simplify: divide numerator and denominator by 6 → 1/8. Final answer: 1/8

5. Kaia has a board that is 18 feet long. Kaia cuts it into pieces that are each 2 foot long. How many pieces does Kaia get? Answer: 9 Solution: The board is 18 feet long total. Each piece is 2 foot long. Divide the total length by the length of each piece: 18 ÷ 2 = 9.
   Full step-by-step solution

   Step 1: The board is 18 feet long total. Step 2: Each piece is 2 foot long. Step 3: Divide the total length by the length of each piece: 18 ÷ 2 = 9. Step 4: Kaia gets 9 pieces.

6. Isabella has a board that is 10 feet long. Isabella cuts it into pieces that are each 1 foot long. How many pieces does Isabella get? Answer: 10 Solution: The board is 10 feet long total. Each piece is 1 foot long. Divide the total length by the length of each piece: 10 ÷ 1 = 10.
   Full step-by-step solution

   Step 1: The board is 10 feet long total. Step 2: Each piece is 1 foot long. Step 3: Divide the total length by the length of each piece: 10 ÷ 1 = 10. Step 4: Isabella gets 10 pieces.

7. A construction project requires 3/5 of a ton of gravel for each section. If there are 6 2/3 sections to complete, how many tons of gravel are needed in total? Answer: 4 Solution: Convert the mixed number 6 2/3 to an improper fraction. 6 2/3 = (6 × 3 + 2)/3 = (18 + 2)/3 = 20/3 Multiply the gravel per section (3/5 ton) by the number of sections (20/3).
   Full step-by-step solution

   Step 1: Convert the mixed number 6 2/3 to an improper fraction. 6 2/3 = (6 × 3 + 2)/3 = (18 + 2)/3 = 20/3 Step 2: Multiply the gravel per section (3/5 ton) by the number of sections (20/3). 3/5 × 20/3 = (3 × 20)/(5 × 3) = 60/15 Step 3: Simplify the fraction 60/15. 60 ÷ 15 = 4 Step 4: The total gravel needed is 4 tons.