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Fraction ÷ Fraction

Grade 6 · Fractions · Worksheet 3

  1. A construction crew is building a new community garden. They have 2 1/2 gallons of special waterproof sealant to protect the wooden planter boxes. Each planter box requires 3/8 of a gallon of sealant for proper coverage. How many complete planter boxes can the crew seal with the sealant they have? Answer: ______________
  2. Maria is creating a mosaic art project using small colored tiles. She has 2 1/4 square feet of blue tiles and needs to cut them into pieces that are each 3/8 of a square foot for her design. How many complete pieces of this size can Maria cut from her blue tiles? Answer: ______________
  3. A construction crew is building a new community garden. They have 3 1/2 cubic yards of soil to distribute evenly among several raised beds. Each raised bed requires 5/8 of a cubic yard of soil to be properly filled. How many complete raised beds can the construction crew fill with the soil they have available? Answer: ______________
  4. A rectangular garden is divided into two triangular sections by a diagonal path. The garden measures 18 2/3 meters by 14 1/4 meters. One triangular section is planted with sunflowers, and the other with daisies. If the sunflower section occupies 5/7 of the total garden area, what fraction of the garden is planted with daisies? Answer: ______________
  5. A construction crew is building a new community garden that requires dividing a large rectangular plot of land into smaller sections. The original plot measures 3 1/2 acres total. If each individual garden section needs to be exactly 2/5 of an acre, how many complete garden sections can the crew create from the original plot? Answer: ______________
  6. A construction crew is building a new bike path that requires a special concrete mixture. The recipe calls for 3/4 ton of gravel for every 2/5 ton of cement. If the crew has 5 tons of gravel available, how many tons of cement will they need to maintain the proper mixture ratio? Answer: ______________
  7. A rectangular garden is divided into two triangular sections by a diagonal path. The garden measures 18 2/3 meters by 12 1/4 meters. One triangular section is planted with roses, and the other with tulips. If the rose section occupies 7/10 of the total garden area, what fraction of the garden is planted with tulips? Answer: ______________
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Answer Key & Explanations

Fraction ÷ Fraction · Grade 6 · Worksheet 3

  1. A construction crew is building a new community garden. They have 2 1/2 gallons of special waterproof sealant to protect the wooden planter boxes. Each planter box requires 3/8 of a gallon of sealant for proper coverage. How many complete planter boxes can the crew seal with the sealant they have? Answer: 6 Solution: Convert 2 1/2 to an improper fraction: 2 1/2 = 5/2 Set up the division problem: (5/2) ÷ (3/8) To divide fractions, multiply by the reciprocal: (5/2) × (8/3) Multiply numerators: 5 × 8 = 40 Multiply denominators: 2 × 3 = 6 Simplify the fraction: 40/6 = 20/3 = 6 2/3 Since we can only seal complete…
    Full step-by-step solution

    Step 1: Convert 2 1/2 to an improper fraction: 2 1/2 = 5/2 Step 2: Set up the division problem: (5/2) ÷ (3/8) Step 3: To divide fractions, multiply by the reciprocal: (5/2) × (8/3) Step 4: Multiply numerators: 5 × 8 = 40 Step 5: Multiply denominators: 2 × 3 = 6 Step 6: Simplify the fraction: 40/6 = 20/3 = 6 2/3 Step 7: Since we can only seal complete boxes, we take the whole number part: 6 The crew can seal 6 complete planter boxes.

  2. Maria is creating a mosaic art project using small colored tiles. She has 2 1/4 square feet of blue tiles and needs to cut them into pieces that are each 3/8 of a square foot for her design. How many complete pieces of this size can Maria cut from her blue tiles? Answer: 6 Solution: 2 1/4 = (2 × 4 + 1)/4 = 9/4 square feet We need to divide 9/4 by 3/8 to find how many pieces Dividing by a fraction is the same as multiplying by its reciprocal 9/4 ÷ 3/8 = 9/4 × 8/3 (9 × 8)/(4 × 3) = 72/12 72/12 = 6 Maria can cut 6 complete pieces from her blue tiles.
    Full step-by-step solution

    Step 1: Convert the mixed number to an improper fraction 2 1/4 = (2 × 4 + 1)/4 = 9/4 square feet Step 2: Set up the division problem We need to divide 9/4 by 3/8 to find how many pieces Step 3: Apply the rule for dividing fractions Dividing by a fraction is the same as multiplying by its reciprocal 9/4 ÷ 3/8 = 9/4 × 8/3 Step 4: Multiply the fractions (9 × 8)/(4 × 3) = 72/12 Step 5: Simplify the fraction 72/12 = 6 Step 6: Interpret the result Maria can cut 6 complete pieces from her blue tiles. The answer is 6.

  3. A construction crew is building a new community garden. They have 3 1/2 cubic yards of soil to distribute evenly among several raised beds. Each raised bed requires 5/8 of a cubic yard of soil to be properly filled. How many complete raised beds can the construction crew fill with the soil they have available? Answer: 5 Solution: Convert the mixed number to an improper fraction: 3 1/2 = 7/2 Set up the division problem: (7/2) ÷ (5/8) When dividing fractions, multiply by the reciprocal: (7/2) × (8/5) Multiply the numerators: 7 × 8 = 56 Multiply the denominators: 2 × 5 = 10 Simplify the fraction: 56/10 = 28/5 = 5 3/5 Since…
    Full step-by-step solution

    Step 1: Convert the mixed number to an improper fraction: 3 1/2 = 7/2 Step 2: Set up the division problem: (7/2) ÷ (5/8) Step 3: When dividing fractions, multiply by the reciprocal: (7/2) × (8/5) Step 4: Multiply the numerators: 7 × 8 = 56 Step 5: Multiply the denominators: 2 × 5 = 10 Step 6: Simplify the fraction: 56/10 = 28/5 = 5 3/5 Step 7: Since we can only fill complete beds, we take the whole number part: 5 The construction crew can fill 5 complete raised beds.

  4. A rectangular garden is divided into two triangular sections by a diagonal path. The garden measures 18 2/3 meters by 14 1/4 meters. One triangular section is planted with sunflowers, and the other with daisies. If the sunflower section occupies 5/7 of the total garden area, what fraction of the garden is planted with daisies? Answer: 2/7 Solution: The entire garden represents 1 whole unit of area. The sunflower section occupies 5/7 of the total garden area.
    Full step-by-step solution

    Step 1: The entire garden represents 1 whole unit of area. Step 2: The sunflower section occupies 5/7 of the total garden area. Step 3: To find the daisy section's fraction, subtract the sunflower fraction from the whole: 1 - 5/7 Step 4: Convert 1 to a fraction with denominator 7: 1 = 7/7 Step 5: Subtract: 7/7 - 5/7 = 2/7 Step 6: The daisy section occupies 2/7 of the total garden area. The answer is 2/7.

  5. A construction crew is building a new community garden that requires dividing a large rectangular plot of land into smaller sections. The original plot measures 3 1/2 acres total. If each individual garden section needs to be exactly 2/5 of an acre, how many complete garden sections can the crew create from the original plot? Answer: 8 Solution: Convert the mixed number to an improper fraction: 3 1/2 = (3 × 2 + 1)/2 = 7/2 acres Set up the division problem: (7/2) ÷ (2/5) To divide fractions, multiply by the reciprocal: (7/2) × (5/2) Multiply the numerators: 7 × 5 = 35 Multiply the denominators: 2 × 2 = 4 Simplify the fraction: 35/4 = 8…
    Full step-by-step solution

    Step 1: Convert the mixed number to an improper fraction: 3 1/2 = (3 × 2 + 1)/2 = 7/2 acres Step 2: Set up the division problem: (7/2) ÷ (2/5) Step 3: To divide fractions, multiply by the reciprocal: (7/2) × (5/2) Step 4: Multiply the numerators: 7 × 5 = 35 Step 5: Multiply the denominators: 2 × 2 = 4 Step 6: Simplify the fraction: 35/4 = 8 3/4 Step 7: Since we need complete garden sections, we take the whole number part: 8 Step 8: The 3/4 represents a partial section that cannot be used, so the answer is 8 complete garden sections.

  6. A construction crew is building a new bike path that requires a special concrete mixture. The recipe calls for 3/4 ton of gravel for every 2/5 ton of cement. If the crew has 5 tons of gravel available, how many tons of cement will they need to maintain the proper mixture ratio? Answer: 8/3 Solution: Set up the proportion based on the given ratio: gravel/cement = (3/4)/(2/5) We know we have 5 tons of gravel, so we write: 5/cement = (3/4)/(2/5) Simplify the right side: (3/4) ÷ (2/5) = (3/4) × (5/2) = 15/8 So 5/cement = 15/8 Cross multiply: 5 × 8 = 15 × cement 40 = 15 × cement Divide both…
    Full step-by-step solution

    Step 1: Set up the proportion based on the given ratio: gravel/cement = (3/4)/(2/5) Step 2: We know we have 5 tons of gravel, so we write: 5/cement = (3/4)/(2/5) Step 3: Simplify the right side: (3/4) ÷ (2/5) = (3/4) × (5/2) = 15/8 Step 4: So 5/cement = 15/8 Step 5: Cross multiply: 5 × 8 = 15 × cement Step 6: 40 = 15 × cement Step 7: Divide both sides by 15: cement = 40/15 Step 8: Simplify the fraction: 40/15 = 8/3 Step 9: The crew needs 8/3 tons of cement, which is 2 2/3 tons. The answer is 8/3.

  7. A rectangular garden is divided into two triangular sections by a diagonal path. The garden measures 18 2/3 meters by 12 1/4 meters. One triangular section is planted with roses, and the other with tulips. If the rose section occupies 7/10 of the total garden area, what fraction of the garden is planted with tulips? Answer: 3/10 Solution: The entire garden represents 1 whole. The rose section occupies 7/10 of the garden. Since there are only two sections (roses and tulips), the tulip section must be the remaining part of the garden.
    Full step-by-step solution

    Step 1: The entire garden represents 1 whole. Step 2: The rose section occupies 7/10 of the garden. Step 3: Since there are only two sections (roses and tulips), the tulip section must be the remaining part of the garden. Step 4: Calculate the tulip fraction: 1 - 7/10 = 10/10 - 7/10 = 3/10 Step 5: The tulip section occupies 3/10 of the total garden area. The answer is 3/10.