Fraction ÷ Whole

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Answer Key & Explanations

Fraction ÷ Whole · Grade 5 · Worksheet 2

1. A baker has 3/4 of a cup of chocolate chips and wants to divide them equally among 6 batches of cookies. What fraction of a cup of chocolate chips will be used in each batch? Answer: 1/8 Solution: The baker has 3/4 of a cup of chocolate chips and wants to divide them equally among 6 batches. This means we need to divide the total amount (3/4) by the number of batches (6).
   Full step-by-step solution

   The baker has 3/4 of a cup of chocolate chips and wants to divide them equally among 6 batches. This means we need to divide the total amount (3/4) by the number of batches (6). So the calculation is: 3/4 divided by 6. When you divide a fraction by a whole number, it is the same as multiplying the fraction by the reciprocal of the whole number. The reciprocal of 6 is 1/6. Therefore, the problem becomes: 3/4 multiplied by 1/6. To multiply fractions, multiply the numerators together and multiply the denominators together. Numerators: 3 multiplied by 1 equals 3. Denominators: 4 multiplied by 6 equals 24. This gives us the new fraction: 3/24. Now we simplify 3/24. The greatest common factor of 3 and 24 is 3. Divide both the numerator and the denominator by 3: 3 divided by 3 equals 1. 24 divided by 3 equals 8. So, 3/24 simplifies to 1/8. Therefore, each batch of cookies will use 1/8 of a cup of chocolate chips.

2. Liam is making a large batch of soup for a community dinner. The recipe calls for 3/4 cup of chopped onions, but he needs to divide this amount equally among 6 pots of soup. What fraction of a cup of onions should Liam put in each pot? Answer: 1/8 Solution: We start with the total amount of onions: 3/4 cup. This total must be divided equally among 6 pots. Write the division as a fraction.
   Full step-by-step solution

   We start with the total amount of onions: 3/4 cup. This total must be divided equally among 6 pots. Step 1: Write the division as a fraction. We have 3/4 divided by 6. That is: (3/4) ÷ 6. Step 2: Dividing by 6 is the same as multiplying by 1/6. So: (3/4) × (1/6). Step 3: Multiply the numerators: 3 × 1 = 3. Multiply the denominators: 4 × 6 = 24. So we get 3/24. Step 4: Simplify 3/24. Both numerator and denominator can be divided by 3: 3 ÷ 3 = 1, and 24 ÷ 3 = 8. So 3/24 = 1/8. Step 5: Conclusion. Liam should put 1/8 cup of onions in each pot.

3. A construction crew needs to divide 3/4 of a ton of gravel equally among 5 different sections of a pathway. What fraction of a ton of gravel will each section receive? Answer: 3/20 Solution: We start with the problem: We have 3/4 of a ton of gravel to divide equally among 5 sections. Dividing 3/4 ton equally among 5 sections means we need to perform: (3/4) ÷ 5 Write 5 as a fraction. 5 is the same as 5/1.
   Full step-by-step solution

   We start with the problem: We have 3/4 of a ton of gravel to divide equally among 5 sections. Step 1: Understand the operation. Dividing 3/4 ton equally among 5 sections means we need to perform: (3/4) ÷ 5 Step 2: Write 5 as a fraction. 5 is the same as 5/1. So (3/4) ÷ (5/1) Step 3: Dividing by a fraction is the same as multiplying by its reciprocal. The reciprocal of 5/1 is 1/5. So (3/4) ÷ (5/1) = (3/4) × (1/5) Step 4: Multiply the fractions. Multiply the numerators: 3 × 1 = 3 Multiply the denominators: 4 × 5 = 20 So the result is 3/20 Step 5: Interpret the result. Each section receives 3/20 of a ton of gravel. Final answer: 3/20

4. 5/7 ÷ 4 = ? Answer: 5/28 Solution: Write the problem: 5/7 ÷ 4 Write the whole number as a fraction: 5/7 ÷ 4/1 Change division to multiplication by the reciprocal: 5/7 × 1/4 Multiply the numerators: 5 × 1 = 5 Multiply the denominators: 7 × 4 = 28 Write the result: 5/28 The answer is 5/28.
   Full step-by-step solution

   Step 1: Write the problem: 5/7 ÷ 4 Step 2: Write the whole number as a fraction: 5/7 ÷ 4/1 Step 3: Change division to multiplication by the reciprocal: 5/7 × 1/4 Step 4: Multiply the numerators: 5 × 1 = 5 Step 5: Multiply the denominators: 7 × 4 = 28 Step 6: Write the result: 5/28 The answer is 5/28.

5. A rectangular garden is divided into 8 equal sections. If 3/4 of the garden is planted with vegetables, how many sections contain vegetables? Answer: 6 Solution: The garden is divided into 8 equal sections. We know that 3/4 of the garden is planted with vegetables. We need to find how many sections contain vegetables.
   Full step-by-step solution

   Step 1: Understand the problem. The garden is divided into 8 equal sections. We know that 3/4 of the garden is planted with vegetables. We need to find how many sections contain vegetables. Step 2: Relate the fraction of the garden to the number of sections. If the whole garden is 8 sections, then 3/4 of the garden means 3/4 of 8 sections. Step 3: Calculate 3/4 of 8. "Of" means multiplication in this context. So we compute: 3/4 × 8 = (3 × 8) / 4 Step 4: Perform the multiplication. 3 × 8 = 24 Step 5: Divide by 4. 24 / 4 = 6 Step 6: Interpret the result. 6 sections contain vegetables. Final Answer: 6

6. 2/3 ÷ 4 = ? Answer: 1/6 Solution: Write the problem as a fraction division: 2/3 ÷ 4 Write the whole number as a fraction: 2/3 ÷ 4/1 Change division to multiplication by the reciprocal: 2/3 × 1/4 Multiply the numerators: 2 × 1 = 2 Multiply the denominators: 3 × 4 = 12 Simplify the fraction: 2/12 = 1/6 The answer is 1/6.
   Full step-by-step solution

   Step 1: Write the problem as a fraction division: 2/3 ÷ 4 Step 2: Write the whole number as a fraction: 2/3 ÷ 4/1 Step 3: Change division to multiplication by the reciprocal: 2/3 × 1/4 Step 4: Multiply the numerators: 2 × 1 = 2 Step 5: Multiply the denominators: 3 × 4 = 12 Step 6: Simplify the fraction: 2/12 = 1/6 The answer is 1/6.

7. 5/8 ÷ 6 = ? Answer: 5/48 Solution: Write the division problem: 5/8 ÷ 6 Rewrite the whole number as a fraction: 5/8 ÷ 6/1 Change division to multiplication by the reciprocal: 5/8 × 1/6 Multiply the numerators: 5 × 1 = 5 Multiply the denominators: 8 × 6 = 48 Write the result: 5/48 The answer is 5/48.
   Full step-by-step solution

   Step 1: Write the division problem: 5/8 ÷ 6 Step 2: Rewrite the whole number as a fraction: 5/8 ÷ 6/1 Step 3: Change division to multiplication by the reciprocal: 5/8 × 1/6 Step 4: Multiply the numerators: 5 × 1 = 5 Step 5: Multiply the denominators: 8 × 6 = 48 Step 6: Write the result: 5/48 The answer is 5/48.

8. A rectangular prism-shaped fish tank has a length of 3/4 meter, a width of 1/2 meter, and a height of 2/3 meter. What is the volume of the fish tank in cubic meters? Answer: 1/4 Solution: Volume of a rectangular prism = length × width × height Volume = (3/4) × (1/2) × (2/3) Multiply the numerators: 3 × 1 × 2 = 6 Multiply the denominators: 4 × 2 × 3 = 24 Simplify the fraction: 6/24 = 1/4 The volume is 1/4 cubic meter.
   Full step-by-step solution

   Step 1: Volume of a rectangular prism = length × width × height Step 2: Volume = (3/4) × (1/2) × (2/3) Step 3: Multiply the numerators: 3 × 1 × 2 = 6 Step 4: Multiply the denominators: 4 × 2 × 3 = 24 Step 5: Simplify the fraction: 6/24 = 1/4 Step 6: The volume is 1/4 cubic meter.

9. Emma is preparing trail mix for her hiking club. She has 2/3 of a pound of almonds and needs to divide them equally among 8 small snack bags. What fraction of a pound of almonds should she put in each bag? Answer: 1/12 Solution: Emma has 2/3 pound of almonds to divide among 8 bags Dividing a fraction by a whole number means we multiply the fraction by the reciprocal of the whole number 2/3 ÷ 8 = 2/3 × 1/8 Multiply the numerators: 2 × 1 = 2 Multiply the denominators: 3 × 8 = 24 The fraction is 2/24 Simplify by dividing…
   Full step-by-step solution

   Step 1: Emma has 2/3 pound of almonds to divide among 8 bags Step 2: Dividing a fraction by a whole number means we multiply the fraction by the reciprocal of the whole number Step 3: 2/3 ÷ 8 = 2/3 × 1/8 Step 4: Multiply the numerators: 2 × 1 = 2 Step 5: Multiply the denominators: 3 × 8 = 24 Step 6: The fraction is 2/24 Step 7: Simplify by dividing numerator and denominator by 2: 2÷2/24÷2 = 1/12 Step 8: Each bag gets 1/12 pound of almonds