Fraction ÷ Fraction

lessonbunny.com

Answer Key & Explanations

Fraction ÷ Fraction · Grade 6 · Worksheet 3

1. Liam is baking cookies for a school fundraiser. He has 3/4 of a cup of chocolate chips left in one bag. Each batch of cookies requires 1/8 of a cup of chocolate chips. How many full batches of cookies can Liam make with the chocolate chips he has? Answer: 6 Solution: We are told Liam has 3/4 of a cup of chocolate chips. Each batch requires 1/8 of a cup. We want to find how many full batches he can make.
   Full step-by-step solution

   We are told Liam has 3/4 of a cup of chocolate chips. Each batch requires 1/8 of a cup. We want to find how many full batches he can make. Step 1: Set up the division. Number of batches = (total chocolate chips) ÷ (chips per batch) 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. The result is 6, which is a whole number. This means Liam can make exactly 6 full batches with no chips left over. Final answer: 6

2. A construction crew is building a new community garden. They have 5 1/3 cubic yards of soil to distribute evenly among several raised garden beds. Each bed requires 2/3 of a cubic yard of soil to be properly filled. How many complete garden beds can the crew fill with the soil they have? 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 numerators: 16 × 3 = 48 Multiply denominators: 3 × 2 = 6 Simplify the fraction: 48/6 = 8 Since…
   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 numerators: 16 × 3 = 48 Step 5: Multiply denominators: 3 × 2 = 6 Step 6: Simplify the fraction: 48/6 = 8 Step 7: Since the question asks for complete garden beds, and 8 is a whole number, the answer is 8 complete beds. The crew can fill 8 complete garden beds.

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. A rectangular garden is divided into four equal triangular sections by drawing both diagonals from opposite corners. The garden measures 24 3/4 meters by 18 1/2 meters. If a gardener plants flowers in three of the four triangular sections, what fraction of the total garden area is planted with flowers? Answer: 3/4 Solution: Area = length × width = 24 3/4 × 18 1/2 Convert to improper fractions: 24 3/4 = 99/4, 18 1/2 = 37/2 Area = (99/4) × (37/2) = 3663/8 square meters When both diagonals are drawn, they divide the rectangle into 4 equal triangles Each triangle has area = (total area) ÷ 4 = (3663/8) ÷ 4 = 3663/32…
   Full step-by-step solution

   Step 1: Find the total area of the rectangular garden Area = length × width = 24 3/4 × 18 1/2 Convert to improper fractions: 24 3/4 = 99/4, 18 1/2 = 37/2 Area = (99/4) × (37/2) = 3663/8 square meters Step 2: Understand how the diagonals divide the rectangle When both diagonals are drawn, they divide the rectangle into 4 equal triangles Each triangle has area = (total area) ÷ 4 = (3663/8) ÷ 4 = 3663/32 square meters Step 3: Calculate the flower area Flowers are planted in 3 of the 4 triangles Flower area = 3 × (area of one triangle) = 3 × (3663/32) = 10989/32 square meters Step 4: Find the fraction of total area with flowers Fraction = (flower area) ÷ (total area) = (10989/32) ÷ (3663/8) Dividing fractions: (10989/32) × (8/3663) = (10989 × 8) ÷ (32 × 3663) Simplify: 10989/3663 = 3 (since 10989 ÷ 3663 = 3) and 8/32 = 1/4 So fraction = 3 × (1/4) = 3/4 The answer is 3/4.

5. A rectangular garden is divided into 4 equal triangular sections by drawing both diagonals from opposite corners. The garden measures 24 3/4 meters by 18 1/2 meters. If a gardener plants roses in 3 of the 4 triangular sections, what fraction of the total garden area is planted with roses? Answer: 3/4 Solution: The diagonals divide the rectangle into 4 equal triangles. Each triangular section has an area equal to 1/4 of the total garden area. If roses are planted in 3 of the 4 sections, then the fraction is 3 × (1/4) = 3/4.
   Full step-by-step solution

   Step 1: The diagonals divide the rectangle into 4 equal triangles. Step 2: Each triangular section has an area equal to 1/4 of the total garden area. Step 3: If roses are planted in 3 of the 4 sections, then the fraction is 3 × (1/4) = 3/4. Step 4: The answer is 3/4 of the total garden area.

6. 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.

7. Liam is baking cookies and needs 3/4 cup of chocolate chips for each batch. He has 2 1/4 cups of chocolate chips total. How many complete batches of cookies can Liam make? Answer: 3 Solution: Liam uses 3/4 cup of chocolate chips per batch. He has 2 1/4 cups total. We need to find how many complete batches he can make.
   Full step-by-step solution

   Step 1: Understand the problem. Liam uses 3/4 cup of chocolate chips per batch. He has 2 1/4 cups total. We need to find how many complete batches he can make. Step 2: Convert the mixed number to an improper fraction. 2 1/4 cups = 2 + 1/4 = 8/4 + 1/4 = 9/4 cups. Step 3: Set up the division. We divide total chips by chips per batch: (9/4) ÷ (3/4) Step 4: Dividing fractions rule. Dividing by a fraction is the same as multiplying by its reciprocal. So: (9/4) ÷ (3/4) = (9/4) × (4/3) Step 5: Multiply the fractions. Multiply numerators: 9 × 4 = 36 Multiply denominators: 4 × 3 = 12 So we have 36/12. Step 6: Simplify the fraction. 36 ÷ 12 = 3. Step 7: Interpret the result. The answer 3 means Liam can make 3 complete batches. There will be no chocolate chips left over because the division came out exactly to a whole number. Final answer: 3

8. (6/7) ÷ (2/3) = ? Answer: 9/7 Solution: Write the problem: (6/7) ÷ (2/3) Find the reciprocal of the second fraction (2/3). The reciprocal is 3/2.
   Full step-by-step solution

   Step 1: Write the problem: (6/7) ÷ (2/3) Step 2: Find the reciprocal of the second fraction (2/3). The reciprocal is 3/2. Step 3: Change division to multiplication: (6/7) × (3/2) Step 4: Multiply the numerators: 6 × 3 = 18 Step 5: Multiply the denominators: 7 × 2 = 14 Step 6: Write the result as a fraction: 18/14 Step 7: Simplify the fraction. Find the greatest common factor (GCF) of 18 and 14, which is 2. Step 8: Divide numerator and denominator by 2: 18 ÷ 2 = 9, 14 ÷ 2 = 7 Step 9: The simplified fraction is 9/7. The answer is 9/7.