Fraction Applications

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Fraction Applications · Grade 5 · Worksheet 2

1. A construction project requires 3/4 of a ton of gravel for each section. If there are 5 1/3 sections to complete, how many tons of gravel are needed in total? Answer: 4 Solution: Convert the mixed number 5 1/3 to an improper fraction. 5 1/3 = (5 × 3 + 1)/3 = (15 + 1)/3 = 16/3 Multiply the gravel per section by the number of sections. 3/4 × 16/3 = (3 × 16)/(4 × 3) = 48/12 Simplify the fraction.
   Full step-by-step solution

   Step 1: Convert the mixed number 5 1/3 to an improper fraction. 5 1/3 = (5 × 3 + 1)/3 = (15 + 1)/3 = 16/3 Step 2: Multiply the gravel per section by the number of sections. 3/4 × 16/3 = (3 × 16)/(4 × 3) = 48/12 Step 3: Simplify the fraction. 48/12 = 4 Step 4: The total gravel needed is 4 tons.

2. A construction project requires 3/4 yard of concrete per section. If the project has 2 2/3 sections, how many total yards of concrete are needed? Answer: 2 Solution: Convert the mixed number 2 2/3 to an improper fraction. 2 2/3 = (2 × 3 + 2)/3 = (6 + 2)/3 = 8/3 Multiply the concrete per section (3/4 yard) by the number of sections (8/3).
   Full step-by-step solution

   Step 1: Convert the mixed number 2 2/3 to an improper fraction. 2 2/3 = (2 × 3 + 2)/3 = (6 + 2)/3 = 8/3 Step 2: Multiply the concrete per section (3/4 yard) by the number of sections (8/3). 3/4 × 8/3 = (3 × 8)/(4 × 3) = 24/12 Step 3: Simplify the fraction 24/12. 24 ÷ 12 = 2 Step 4: The total concrete needed is 2 yards.

3. A recipe calls for 3/4 cup of flour per batch. If you need to make 2 2/3 batches, how many cups of flour are needed in total? Answer: 2 Solution: Convert the mixed number 2 2/3 to an improper fraction. 2 2/3 = (2 × 3 + 2)/3 = (6 + 2)/3 = 8/3 Multiply the flour per batch (3/4 cup) by the number of batches (8/3).
   Full step-by-step solution

   Step 1: Convert the mixed number 2 2/3 to an improper fraction. 2 2/3 = (2 × 3 + 2)/3 = (6 + 2)/3 = 8/3 Step 2: Multiply the flour per batch (3/4 cup) by the number of batches (8/3). 3/4 × 8/3 = (3 × 8)/(4 × 3) = 24/12 Step 3: Simplify the fraction 24/12. 24 ÷ 12 = 2 Step 4: The total flour needed is 2 cups.

4. Emma is making a quilt for her grandmother. She needs 3/4 yard of blue fabric and 2/3 yard of red fabric. If she already has 1/2 yard of blue fabric from another project, how many more yards of blue fabric does Emma need to buy? Answer: 1/4 Solution: Emma needs 3/4 yard of blue fabric total. She already has 1/2 yard of blue fabric.
   Full step-by-step solution

   Step 1: Emma needs 3/4 yard of blue fabric total. Step 2: She already has 1/2 yard of blue fabric. Step 3: To find how much more she needs, subtract what she has from what she needs: 3/4 - 1/2 Step 4: Convert 1/2 to fourths: 1/2 = 2/4 Step 5: Subtract: 3/4 - 2/4 = 1/4 Step 6: Emma needs to buy 1/4 yard more of blue fabric. The answer is 1/4.

5. Hana is making a traditional woven mat. Each section requires 5/6 meter of ribbon. If she needs to complete 7 1/5 sections, how many total meters of ribbon does she need? Answer: 6 Solution: Convert the mixed number 7 1/5 to an improper fraction. 7 1/5 = (7 × 5 + 1)/5 = (35 + 1)/5 = 36/5. Multiply the ribbon per section (5/6 meter) by the number of sections (36/5).
   Full step-by-step solution

   Step 1: Convert the mixed number 7 1/5 to an improper fraction. 7 1/5 = (7 × 5 + 1)/5 = (35 + 1)/5 = 36/5. Step 2: Multiply the ribbon per section (5/6 meter) by the number of sections (36/5). 5/6 × 36/5 = (5 × 36)/(6 × 5) = 180/30. Step 3: Simplify the fraction 180/30 by dividing numerator and denominator by 30. 180 ÷ 30 = 6, 30 ÷ 30 = 1. So 180/30 = 6/1 = 6. Step 4: The total ribbon needed is 6 meters.

6. Emma is making a quilt for her grandmother. She needs 3/4 yard of blue fabric and 2/3 yard of red fabric for the main design. Then she needs 1/2 yard of green fabric for the border. How many total yards of fabric does Emma need for her quilt? Answer: 23/12 Solution: Write the fractions to add: 3/4 + 2/3 + 1/2 Find a common denominator for 4, 3, and 2. The least common multiple is 12.
   Full step-by-step solution

   Step 1: Write the fractions to add: 3/4 + 2/3 + 1/2 Step 2: Find a common denominator for 4, 3, and 2. The least common multiple is 12. Step 3: Convert each fraction to have denominator 12: 3/4 = 9/12 (multiply numerator and denominator by 3) 2/3 = 8/12 (multiply numerator and denominator by 4) 1/2 = 6/12 (multiply numerator and denominator by 6) Step 4: Add the fractions: 9/12 + 8/12 + 6/12 = 23/12 Step 5: The answer is 23/12 yards, which can also be written as 1 11/12 yards. The total fabric needed is 23/12 yards.

7. A farmer harvested 750 kilograms of apples from his orchard. He sold 3/5 of the harvest to a grocery store and used 1/4 of the remaining apples to make apple pies. What fraction of the original harvest was used for apple pies? Answer: 1/10 Solution: 1. The farmer harvested 750 kg of apples. He sold 3/5 of the harvest to a grocery store.
   Full step-by-step solution

   Let's go step-by-step. 1. The farmer harvested 750 kg of apples. He sold 3/5 of the harvest to a grocery store. Amount sold = 3/5 × 750 = (3 × 750) / 5 = 2250 / 5 = 450 kg. 2. Remaining apples after selling to grocery store: Remaining = 750 − 450 = 300 kg. 3. He used 1/4 of the remaining apples to make apple pies. Amount used for pies = 1/4 × 300 = 300 / 4 = 75 kg. 4. We need the fraction of the original harvest used for pies. Fraction = (Amount for pies) / (Original harvest) = 75 / 750. 5. Simplify 75/750: Divide numerator and denominator by 75: 75 ÷ 75 = 1, 750 ÷ 75 = 10. So, 75/750 = 1/10. Therefore, the fraction of the original harvest used for apple pies is 1/10.

8. A rectangular garden is divided into 8 equal sections. If 3 sections are planted with tomatoes and 2 sections are planted with carrots, what fraction of the garden is planted with vegetables? Answer: 5/8 Solution: The garden is divided into 8 equal sections. So, each section is 1/8 of the garden. Identify the vegetable sections.
   Full step-by-step solution

   Step 1: Understand the problem. The garden is divided into 8 equal sections. So, each section is 1/8 of the garden. Step 2: Identify the vegetable sections. Tomatoes are planted in 3 sections. Carrots are planted in 2 sections. Step 3: Add the vegetable sections together. 3 sections (tomatoes) + 2 sections (carrots) = 5 sections. Step 4: Convert to a fraction of the whole garden. Since each section is 1/8, 5 sections = 5 × (1/8) = 5/8. Step 5: Conclusion. The fraction of the garden planted with vegetables is 5/8.

9. Liam is building a rectangular garden bed that is 3/4 meters long and 2/5 meters wide. He wants to cover the entire garden with soil. What is the area of Liam's garden bed in square meters? Answer: 3/10 Solution: To find the area of a rectangle, we multiply the length by the width. Write down the given measurements. Length = 3/4 meters Width = 2/5 meters Set up the area calculation.
   Full step-by-step solution

   To find the area of a rectangle, we multiply the length by the width. Step 1: Write down the given measurements. Length = 3/4 meters Width = 2/5 meters Step 2: Set up the area calculation. Area = Length × Width Area = (3/4) × (2/5) Step 3: Multiply the fractions. To multiply fractions, multiply the numerators together and multiply the denominators together. Numerator: 3 × 2 = 6 Denominator: 4 × 5 = 20 So, Area = 6/20 Step 4: Simplify the fraction. Find the greatest common factor (GCF) of 6 and 20. The GCF is 2. Divide both the numerator and the denominator by 2. 6 ÷ 2 = 3 20 ÷ 2 = 10 So, 6/20 simplifies to 3/10. Step 5: State the final answer. Therefore, the area of Liam's garden bed is 3/10 square meters.