Worksheet 1Worksheet 2Worksheet 3

The download includes this worksheet followed by the answer key with explanations. In the print dialog choose “Save as PDF” to download.

lessonbunny.com
Name: ______________________________ Date: ______________

Fraction ÷ Fraction

Grade 6 · Fractions · Worksheet 1

  1. 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: ______________
  2. A construction crew is building a new community garden and needs to divide a 5 1/3 foot long wooden beam into equal sections for fence posts. Each section must be exactly 2/3 of a foot long. How many complete sections can the crew cut from the wooden beam? Answer: ______________
  3. Liam is making a special salad dressing that requires 3/4 cup of olive oil. He only has a 1/8 cup measuring cup. How many scoops of the 1/8 cup does Liam need to measure out the required 3/4 cup of olive oil? Answer: ______________
  4. Liam is making a special fruit punch for a school event. The recipe requires 3/4 cup of orange juice for every 1/2 cup of pineapple juice. If Liam wants to use exactly 2 cups of pineapple juice, how many cups of orange juice should he use? Answer: ______________
  5. 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: ______________
  6. (2/3) ÷ (4/5) = ? Answer: ______________
  7. A construction crew is building a new bike path that needs to be exactly 3/4 mile long. Each section of the path requires 1/12 of a mile of concrete. How many complete sections can the crew build along the entire bike path? Answer: ______________
  8. A construction crew is building a new community garden. They need to divide a 5 1/3 meter long wooden beam into equal sections, with each section being 2/3 of a meter long for the garden fence posts. How many complete sections can they cut from the beam? Answer: ______________
lessonbunny.com

Answer Key & Explanations

Fraction ÷ Fraction · Grade 6 · Worksheet 1

  1. 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.

  2. A construction crew is building a new community garden and needs to divide a 5 1/3 foot long wooden beam into equal sections for fence posts. Each section must be exactly 2/3 of a foot long. How many complete sections can the crew cut from the wooden beam? Answer: 8 Solution: Convert the mixed number 5 1/3 to an improper fraction 5 1/3 = (5 × 3 + 1)/3 = (15 + 1)/3 = 16/3 We need to divide 16/3 by 2/3 Dividing by a fraction is the same as multiplying by its reciprocal 16/3 ÷ 2/3 = 16/3 × 3/2 16/3 × 3/2 = (16 × 3)/(3 × 2) = 48/6 48/6 = 8 Since we're looking for…
    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: Set up the division problem We need to divide 16/3 by 2/3 Step 3: Apply the rule for dividing fractions Dividing by a fraction is the same as multiplying by its reciprocal 16/3 ÷ 2/3 = 16/3 × 3/2 Step 4: Multiply the fractions 16/3 × 3/2 = (16 × 3)/(3 × 2) = 48/6 Step 5: Simplify the fraction 48/6 = 8 Step 6: Interpret the result Since we're looking for complete sections, and we got exactly 8, the crew can cut 8 complete sections. The answer is 8 complete sections.

  3. Liam is making a special salad dressing that requires 3/4 cup of olive oil. He only has a 1/8 cup measuring cup. How many scoops of the 1/8 cup does Liam need to measure out the required 3/4 cup of olive oil? Answer: 6 Solution: We need to find how many 1/8-cup scoops make 3/4 cup. Write the problem as a division. We want: (3/4) ÷ (1/8) Dividing by a fraction is the same as multiplying by its reciprocal.
    Full step-by-step solution

    We need to find how many 1/8-cup scoops make 3/4 cup. Step 1: Write the problem as a division. We want: (3/4) ÷ (1/8) Step 2: Dividing by a fraction is the same as multiplying by its reciprocal. So, (3/4) ÷ (1/8) = (3/4) × (8/1) Step 3: Multiply the fractions. Multiply numerators: 3 × 8 = 24 Multiply denominators: 4 × 1 = 4 So we have 24/4 Step 4: Simplify 24/4. 24 ÷ 4 = 6 Step 5: Interpret the result. This means Liam needs 6 scoops of the 1/8 cup to get 3/4 cup of olive oil. Answer: 6

  4. Liam is making a special fruit punch for a school event. The recipe requires 3/4 cup of orange juice for every 1/2 cup of pineapple juice. If Liam wants to use exactly 2 cups of pineapple juice, how many cups of orange juice should he use? Answer: 3 Solution: 1. Orange juice / Pineapple juice = (3/4) / (1/2). 2.
    Full step-by-step solution

    Let's go step-by-step. 1. Understand the ratio: The recipe says 3/4 cup orange juice for every 1/2 cup pineapple juice. This means: Orange juice / Pineapple juice = (3/4) / (1/2). 2. Calculate the unit ratio: (3/4) ÷ (1/2) = (3/4) × (2/1) = 6/4 = 3/2. So for every 1 cup of pineapple juice, Liam needs 3/2 cups of orange juice. 3. Apply to 2 cups of pineapple juice: Orange juice needed = (3/2) × 2 = 3 cups. 4. Final check: With 2 cups pineapple juice, which is 4 times the original 1/2 cup amount (since 2 ÷ 1/2 = 4), Orange juice needed = 4 × (3/4) = 12/4 = 3 cups. Both methods match. ANSWER: 3

  5. 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.

  6. (2/3) ÷ (4/5) = ? Answer: 5/6 Solution: To divide fractions, we use the rule: dividing by a fraction is the same as multiplying by its reciprocal. Write down the problem. (2/3) ÷ (4/5) Change the division to multiplication by the reciprocal of the second fraction.
    Full step-by-step solution

    To divide fractions, we use the rule: dividing by a fraction is the same as multiplying by its reciprocal. Step 1: Write down the problem. (2/3) ÷ (4/5) Step 2: Change the division to multiplication by the reciprocal of the second fraction. The reciprocal of a fraction is found by swapping its numerator and denominator. The reciprocal of 4/5 is 5/4. So, the problem becomes: (2/3) × (5/4) Step 3: Multiply the two fractions. To multiply fractions, multiply the numerators together and multiply the denominators together. Numerator: 2 × 5 = 10 Denominator: 3 × 4 = 12 This gives us the new fraction: 10/12 Step 4: Simplify the fraction to its lowest terms. Find the greatest common factor (GCF) of 10 and 12. The GCF is 2. Divide both the numerator and the denominator by 2: 10 ÷ 2 = 5 12 ÷ 2 = 6 So, 10/12 simplifies to 5/6. Therefore, the final answer is 5/6.

  7. A construction crew is building a new bike path that needs to be exactly 3/4 mile long. Each section of the path requires 1/12 of a mile of concrete. How many complete sections can the crew build along the entire bike path? Answer: 9 Solution: We need to find how many 1/12 mile sections fit into 3/4 mile. This means we need to divide 3/4 by 1/12.
    Full step-by-step solution

    Step 1: We need to find how many 1/12 mile sections fit into 3/4 mile. Step 2: This means we need to divide 3/4 by 1/12. Step 3: To divide fractions, we multiply by the reciprocal: 3/4 ÷ 1/12 = 3/4 × 12/1 Step 4: Multiply the numerators: 3 × 12 = 36 Step 5: Multiply the denominators: 4 × 1 = 4 Step 6: Simplify the fraction: 36/4 = 9 Step 7: The crew can build 9 complete sections. The answer is 9.

  8. A construction crew is building a new community garden. They need to divide a 5 1/3 meter long wooden beam into equal sections, with each section being 2/3 of a meter long for the garden fence posts. How many complete sections can they cut from the beam? Answer: 8 Solution: Convert the mixed number to an improper fraction: 5 1/3 = (5 × 3 + 1)/3 = 16/3 Set up the division problem: (16/3) ÷ (2/3) When dividing fractions, multiply by the reciprocal: (16/3) × (3/2) Multiply the numerators: 16 × 3 = 48 Multiply the denominators: 3 × 2 = 6 Simplify the fraction: 48/6 = 8…
    Full step-by-step solution

    Step 1: Convert the mixed number to an improper fraction: 5 1/3 = (5 × 3 + 1)/3 = 16/3 Step 2: Set up the division problem: (16/3) ÷ (2/3) Step 3: When dividing fractions, multiply by the reciprocal: (16/3) × (3/2) Step 4: Multiply the numerators: 16 × 3 = 48 Step 5: Multiply the denominators: 3 × 2 = 6 Step 6: Simplify the fraction: 48/6 = 8 Step 7: Since the problem asks for complete sections, and 8 is a whole number, we have exactly 8 complete sections. The answer is 8.