Fraction Applications

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Fraction Applications · Grade 5 · Worksheet 3

1. A construction project requires 3/4 ton of gravel for each section of foundation. If the project needs 2 2/3 sections completed, how many total tons of gravel 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 gravel per section (3/4 ton) 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 gravel per section (3/4 ton) by the number of sections (8/3). 3/4 × 8/3 = (3 × 8)/(4 × 3) = 24/12 Step 3: Simplify the fraction 24/12 by dividing numerator and denominator by 12. 24 ÷ 12 = 2 12 ÷ 12 = 1 24/12 = 2/1 = 2 Step 4: The total gravel needed is 2 tons.

2. A recipe calls for 3/4 cup of sugar per batch of cookies. If you need to make 2 2/3 batches for a party, how many total cups of sugar 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 sugar 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 sugar 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 by dividing numerator and denominator by 12. 24 ÷ 12 = 2 12 ÷ 12 = 1 24/12 = 2/1 = 2 Step 4: The total sugar needed is 2 cups.

3. A rectangular garden is 12 meters long and 8 meters wide. The gardener plants tomatoes in a square section that is 4 meters on each side in one corner. The rest of the garden is planted with flowers. What fraction of the total garden area is planted with flowers? Answer: 5/6 Solution: Find the total area of the garden. Total area = length × width = 12 m × 8 m = 96 square meters. Find the area used for tomatoes.
   Full step-by-step solution

   Step 1: Find the total area of the garden. Total area = length × width = 12 m × 8 m = 96 square meters. Step 2: Find the area used for tomatoes. Tomato area = side × side = 4 m × 4 m = 16 square meters. Step 3: Find the area used for flowers. Flower area = total area - tomato area = 96 - 16 = 80 square meters. Step 4: Find the fraction of the garden planted with flowers. Fraction = flower area / total area = 80 / 96. Step 5: Simplify the fraction. 80/96 = (80 ÷ 16) / (96 ÷ 16) = 5/6. The answer is 5/6.

4. Aroha is making a traditional kapa haka costume. Each costume requires 5/6 of a meter of fabric for the skirt and 2/3 of a meter for the top. If she needs to make 12 costumes for the performance, how many total meters of fabric does she need? Answer: 18 Solution: Find the fabric needed for one costume. Add the skirt fabric (5/6 meter) and top fabric (2/3 meter). Convert 2/3 to an equivalent fraction with denominator 6: 2/3 = 4/6.
   Full step-by-step solution

   Step 1: Find the fabric needed for one costume. Add the skirt fabric (5/6 meter) and top fabric (2/3 meter). Convert 2/3 to an equivalent fraction with denominator 6: 2/3 = 4/6. So 5/6 + 4/6 = 9/6 = 3/2 = 1 1/2 meters per costume. Step 2: Multiply the fabric per costume by the number of costumes: 3/2 × 12 = (3 × 12)/2 = 36/2 = 18. Step 3: Aroha needs 18 meters of fabric in total.

5. Emma is making a quilt for her grandmother. She has a piece of fabric that is 5/6 yard long. She needs to cut it into pieces that are each 1/4 yard long for the quilt squares. How many complete quilt squares can Emma cut from her fabric? Answer: 3 Solution: Identify the total fabric length: 5/6 yard. Identify the length needed for one quilt square: 1/4 yard. To find how many squares she can cut, divide the total fabric by the fabric per square: (5/6) ÷ (1/4).
   Full step-by-step solution

   Step 1: Identify the total fabric length: 5/6 yard. Step 2: Identify the length needed for one quilt square: 1/4 yard. Step 3: To find how many squares she can cut, divide the total fabric by the fabric per square: (5/6) ÷ (1/4). Step 4: Dividing by a fraction is the same as multiplying by its reciprocal. So, (5/6) × (4/1) = (5 × 4) / (6 × 1) = 20/6. Step 5: Simplify the fraction: 20/6 = 10/3. Step 6: Convert the improper fraction to a mixed number: 10/3 = 3 and 1/3. Step 7: Since Emma can only make complete squares, we take the whole number part. The answer is 3 complete quilt squares.

6. A recipe calls for 2/3 cup of olive oil per batch of salad dressing. If you need to make 3 1/4 batches for a restaurant order, how many cups of olive oil are needed in total? Answer: 13/6 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 olive oil per batch (2/3 cup) by the number of batches (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 olive oil per batch (2/3 cup) by the number of batches (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 26/12 = 13/6 Step 4: The total olive oil needed is 13/6 cups.

7. Max is filling water balloons for a water fight. Each water balloon holds 3 cup of water. Max has a container with 24 cups of water. How many water balloons can Max fill completely? Answer: 8 Solution: Each water balloon holds 3 cup of water. Max has 24 cups of water total. Divide the total water by the amount per balloon: 24 ÷ 3 = 8.
   Full step-by-step solution

   Step 1: Each water balloon holds 3 cup of water. Step 2: Max has 24 cups of water total. Step 3: Divide the total water by the amount per balloon: 24 ÷ 3 = 8. Step 4: Max can fill 8 water balloons completely.