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. (2/3) ÷ (4/5) = ? Answer: ______________
  2. Aisha is creating a scale model of her neighborhood for a school project. The scale requires that 3/4 inch on the model represents 1/8 mile in real life. If Aisha's actual street is 2 miles long, how many inches should she make the street on her model? Answer: ______________
  3. Liam is baking cookies and needs to divide 3/4 cup of chocolate chips equally among several batches. Each batch requires 1/8 cup of chocolate chips. How many batches of cookies can Liam make with the chocolate chips he has? Answer: ______________
  4. Liam is making a special salad dressing for his family's restaurant. The recipe requires 3/4 cup of olive oil, but he only has small bottles that each contain 1/8 cup of oil. How many bottles of olive oil does Liam need to measure out for the recipe? Answer: ______________
  5. Aisha is creating a large mural for her school's art fair. She has 4 1/2 gallons of blue paint that she needs to divide into smaller containers. Each container can hold exactly 3/5 of a gallon. How many complete containers can Aisha fill with her blue paint? Answer: ______________
  6. Matiu is a conservationist restoring a native forest. He has 7/9 of a kilogram of rare native tree seeds. Each planting pouch requires exactly 1/6 of a kilogram of seeds to grow one tree seedling. How many complete planting pouches can Matiu fill with the seeds he has? Answer: ______________
  7. Liam is making a special fruit punch for a school event. The recipe requires 3/4 cup of pineapple juice for every 1/2 cup of orange juice. If Liam wants to use exactly 2 cups of orange juice, how many cups of pineapple juice should he use? Answer: ______________
  8. Aisha is designing a mural for her school's art festival. She has 4 1/2 gallons of blue paint and needs to divide it into smaller containers that each hold 3/5 of a gallon for the student volunteers. How many complete containers can Aisha fill with her blue paint? Answer: ______________
lessonbunny.com

Answer Key & Explanations

Fraction ÷ Fraction · Grade 6 · Worksheet 1

  1. (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.

  2. Aisha is creating a scale model of her neighborhood for a school project. The scale requires that 3/4 inch on the model represents 1/8 mile in real life. If Aisha's actual street is 2 miles long, how many inches should she make the street on her model? Answer: 12 Solution: Identify the scale ratio: 3/4 inch on model represents 1/8 mile in real life Convert this to a unit rate: (3/4) ÷ (1/8) = (3/4) × (8/1) = 24/4 = 6 inches per mile Multiply the unit rate by the actual street length: 6 inches/mile × 2 miles = 12 inches The street should be 12 inches long on the model.
    Full step-by-step solution

    Step 1: Identify the scale ratio: 3/4 inch on model represents 1/8 mile in real life Step 2: Convert this to a unit rate: (3/4) ÷ (1/8) = (3/4) × (8/1) = 24/4 = 6 inches per mile Step 3: Multiply the unit rate by the actual street length: 6 inches/mile × 2 miles = 12 inches Step 4: The street should be 12 inches long on the model.

  3. Liam is baking cookies and needs to divide 3/4 cup of chocolate chips equally among several batches. Each batch requires 1/8 cup of chocolate chips. How many batches of cookies can Liam make with the chocolate chips he has? Answer: 6 Solution: We are told Liam has 3/4 cup of chocolate chips and each batch needs 1/8 cup. We want to know how many batches he can make. We need to divide the total amount of chocolate chips by the amount per batch.
    Full step-by-step solution

    We are told Liam has 3/4 cup of chocolate chips and each batch needs 1/8 cup. We want to know how many batches he can make. Step 1: Understand the problem. We need to divide the total amount of chocolate chips by the amount per batch. That is: (3/4) ÷ (1/8) Step 2: Recall that dividing by a fraction is the same as multiplying by its reciprocal. The reciprocal of 1/8 is 8/1, or 8. 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 divided by 4 equals 6. Step 5: Conclusion. Liam can make 6 batches of cookies. Answer: 6

  4. Liam is making a special salad dressing for his family's restaurant. The recipe requires 3/4 cup of olive oil, but he only has small bottles that each contain 1/8 cup of oil. How many bottles of olive oil does Liam need to measure out for the recipe? Answer: 6 Solution: We need to find how many bottles of oil Liam needs. Each bottle holds 1/8 cup. The recipe requires 3/4 cup of oil.
    Full step-by-step solution

    We need to find how many bottles of oil Liam needs. Each bottle holds 1/8 cup. The recipe requires 3/4 cup of oil. Step 1: Write the problem as a division. We want: total cups needed ÷ cups per bottle That is: (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. Liam needs 6 bottles of oil to get 3/4 cup. Answer: 6

  5. Aisha is creating a large mural for her school's art fair. She has 4 1/2 gallons of blue paint that she needs to divide into smaller containers. Each container can hold exactly 3/5 of a gallon. How many complete containers can Aisha fill with her blue paint? Answer: 7 Solution: Convert the mixed number to an improper fraction: 4 1/2 = 9/2 Set up the division problem: (9/2) ÷ (3/5) When dividing fractions, multiply by the reciprocal: (9/2) × (5/3) Multiply the numerators: 9 × 5 = 45 Multiply the denominators: 2 × 3 = 6 Simplify the fraction: 45/6 = 7 3/6 = 7 1/2 Since…
    Full step-by-step solution

    Step 1: Convert the mixed number to an improper fraction: 4 1/2 = 9/2 Step 2: Set up the division problem: (9/2) ÷ (3/5) Step 3: When dividing fractions, multiply by the reciprocal: (9/2) × (5/3) Step 4: Multiply the numerators: 9 × 5 = 45 Step 5: Multiply the denominators: 2 × 3 = 6 Step 6: Simplify the fraction: 45/6 = 7 3/6 = 7 1/2 Step 7: Since we need complete containers, we take the whole number part: 7 The answer is 7 complete containers.

  6. Matiu is a conservationist restoring a native forest. He has 7/9 of a kilogram of rare native tree seeds. Each planting pouch requires exactly 1/6 of a kilogram of seeds to grow one tree seedling. How many complete planting pouches can Matiu fill with the seeds he has? Answer: 4 Solution: Identify the total amount of seeds: 7/9 kg. Each pouch needs 1/6 kg. Step 2: To find the number of pouches, divide the total seeds by the seeds per pouch: (7/9) ÷ (1/6).
    Full step-by-step solution

    Step 1: Identify the total amount of seeds: 7/9 kg. Each pouch needs 1/6 kg. Step 2: To find the number of pouches, divide the total seeds by the seeds per pouch: (7/9) ÷ (1/6). Step 3: When dividing fractions, multiply by the reciprocal of the second fraction. The reciprocal of 1/6 is 6/1. Step 4: So, (7/9) × (6/1) = (7 × 6) / (9 × 1) = 42/9. Step 5: Simplify the fraction: 42 ÷ 9 = 4 remainder 6, so 42/9 = 4 6/9 = 4 2/3. Since Matiu can only fill complete pouches, he can fill 4 pouches. The answer is 4.

  7. Liam is making a special fruit punch for a school event. The recipe requires 3/4 cup of pineapple juice for every 1/2 cup of orange juice. If Liam wants to use exactly 2 cups of orange juice, how many cups of pineapple juice should he use? Answer: 3 Solution: The recipe says: 3/4 cup pineapple juice for every 1/2 cup orange juice. This means the ratio of pineapple juice to orange juice is (3/4) : (1/2). Find how many "1/2 cups" are in 2 cups of orange juice.
    Full step-by-step solution

    Step 1: Understand the ratio from the recipe. The recipe says: 3/4 cup pineapple juice for every 1/2 cup orange juice. This means the ratio of pineapple juice to orange juice is (3/4) : (1/2). Step 2: Find how many "1/2 cups" are in 2 cups of orange juice. Since 1 cup = two 1/2 cups, 2 cups = 4 half-cups. So, 2 cups orange juice = 4 × (1/2 cup orange juice). Step 3: Multiply the pineapple juice amount by the same factor. For each 1/2 cup orange juice, use 3/4 cup pineapple juice. So for 4 times the orange juice, use 4 × (3/4) cup pineapple juice. Step 4: Calculate 4 × (3/4). 4 × 3/4 = 12/4 = 3 cups. Step 5: Conclusion. Liam should use 3 cups of pineapple juice.

  8. Aisha is designing a mural for her school's art festival. She has 4 1/2 gallons of blue paint and needs to divide it into smaller containers that each hold 3/5 of a gallon for the student volunteers. How many complete containers can Aisha fill with her blue paint? Answer: 7 Solution: Convert the mixed number to an improper fraction. 4 1/2 = (4 × 2 + 1)/2 = 9/2 gallons. Divide the total paint by the container size: 9/2 ÷ 3/5.
    Full step-by-step solution

    Step 1: Convert the mixed number to an improper fraction. 4 1/2 = (4 × 2 + 1)/2 = 9/2 gallons. Step 2: Divide the total paint by the container size: 9/2 ÷ 3/5. Step 3: To divide fractions, multiply by the reciprocal: 9/2 × 5/3. Step 4: Multiply numerators: 9 × 5 = 45. Step 5: Multiply denominators: 2 × 3 = 6. Step 6: Simplify the fraction: 45/6 = 7 3/6 = 7 1/2. Step 7: Since we need complete containers, we take the whole number part: 7 containers. The answer is 7 complete containers.