Fraction ÷ Fraction

lessonbunny.com

Answer Key & Explanations

Fraction ÷ Fraction · Grade 6 · Worksheet 2

1. Liam is making a special salad dressing for a family dinner. The recipe calls for 3/4 cup of olive oil, but he only has a 1/8 cup measuring cup. How many times will Liam need to fill his 1/8 cup measuring cup to get the required amount of olive oil? Answer: 6 Solution: We need to find how many 1/8 cups fit into 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 cups fit into 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 the numerators: 3 × 8 = 24 Multiply the 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 to fill the 1/8 cup measuring cup 6 times to get 3/4 cup of olive oil. Answer: 6

2. A construction crew is paving a road that is 2 1/4 miles long. Each day they can pave exactly 3/8 of a mile. How many complete days will it take them to finish paving the entire road? Answer: 6 Solution: Convert the mixed number to an improper fraction: 2 1/4 = (2 × 4 + 1)/4 = 9/4 Set up the division problem: total road length ÷ daily paving amount = 9/4 ÷ 3/8 To divide fractions, multiply by the reciprocal: 9/4 × 8/3 Multiply numerators: 9 × 8 = 72 Multiply denominators: 4 × 3 = 12 Simplify the…
   Full step-by-step solution

   Step 1: Convert the mixed number to an improper fraction: 2 1/4 = (2 × 4 + 1)/4 = 9/4 Step 2: Set up the division problem: total road length ÷ daily paving amount = 9/4 ÷ 3/8 Step 3: To divide fractions, multiply by the reciprocal: 9/4 × 8/3 Step 4: Multiply numerators: 9 × 8 = 72 Step 5: Multiply denominators: 4 × 3 = 12 Step 6: Simplify the fraction: 72/12 = 6 Step 7: Since the question asks for complete days, and 6 is a whole number, the answer is 6 complete days. The construction crew will take 6 complete days to pave the road.

3. A rectangular garden is divided into two sections by a diagonal path. The garden measures 12 meters by 8 meters. The path divides the garden into two triangular flower beds of equal area. If a gardener plants 5 flowers per square meter in one triangular bed, how many flowers are planted in that section? Answer: 240 Solution: Find the area of the entire rectangular garden. The garden is a rectangle with length 12 m and width 8 m. Area of rectangle = length × width = 12 × 8 = 96 square meters.
   Full step-by-step solution

   Step 1: Find the area of the entire rectangular garden. The garden is a rectangle with length 12 m and width 8 m. Area of rectangle = length × width = 12 × 8 = 96 square meters. Step 2: Determine the area of one triangular flower bed. The diagonal divides the rectangle into two triangles of equal area. So, area of one triangle = total area ÷ 2 = 96 ÷ 2 = 48 square meters. Step 3: Calculate the number of flowers in one triangular bed. The gardener plants 5 flowers per square meter in one triangular bed. Number of flowers = area of one triangle × flowers per square meter = 48 × 5. Step 4: Perform the multiplication. 48 × 5 = 240. Step 5: State the final answer. The number of flowers planted in that section is 240.

4. A construction company is building a new community center and needs to calculate how many support beams they can cut from a long steel beam. The original beam is 7 1/2 meters long, and each support beam needs to be exactly 5/8 of a meter. How many complete support beams can be cut from the original steel beam? Answer: 12 Solution: Convert the mixed number to an improper fraction: 7 1/2 = (7 × 2 + 1)/2 = 15/2 Set up the division problem: (15/2) ÷ (5/8) When dividing fractions, multiply by the reciprocal: (15/2) × (8/5) Multiply numerators: 15 × 8 = 120 Multiply denominators: 2 × 5 = 10 Simplify the fraction: 120/10 = 12…
   Full step-by-step solution

   Step 1: Convert the mixed number to an improper fraction: 7 1/2 = (7 × 2 + 1)/2 = 15/2 Step 2: Set up the division problem: (15/2) ÷ (5/8) Step 3: When dividing fractions, multiply by the reciprocal: (15/2) × (8/5) Step 4: Multiply numerators: 15 × 8 = 120 Step 5: Multiply denominators: 2 × 5 = 10 Step 6: Simplify the fraction: 120/10 = 12 Step 7: Since the problem asks for complete beams, and we got exactly 12, that's our answer. The construction company can cut 12 complete support beams from the original steel beam.

5. A rectangular garden is divided into two triangular sections by a diagonal path. The garden measures 15 1/2 meters by 12 3/4 meters. One triangular section is planted with roses, and the other with tulips. If the rose section occupies 5/8 of the total garden area, what fraction of the garden is planted with tulips? Answer: 3/8 Solution: The entire garden represents 1 whole (or 8/8) The rose section occupies 5/8 of the total garden To find the tulip section, subtract the rose fraction from the whole: 8/8 - 5/8 8/8 - 5/8 = 3/8 Therefore, the tulip section occupies 3/8 of the total garden area 3/8
   Full step-by-step solution

   Step 1: The entire garden represents 1 whole (or 8/8) Step 2: The rose section occupies 5/8 of the total garden Step 3: To find the tulip section, subtract the rose fraction from the whole: 8/8 - 5/8 Step 4: 8/8 - 5/8 = 3/8 Step 5: Therefore, the tulip section occupies 3/8 of the total garden area Answer: 3/8

6. A rectangular garden is divided into two triangular sections by a diagonal path. The garden measures 18 3/4 meters by 14 2/5 meters. One triangular section is planted with sunflowers, and the other with daisies. If the sunflower section occupies 7/12 of the total garden area, what fraction of the garden is planted with daisies? Answer: 5/12 Solution: The entire garden represents 1 whole The sunflower section occupies 7/12 of the garden Since the two triangular sections together make up the entire garden, the daisy section must be the remaining portion Calculate the remaining fraction: 1 - 7/12 = 12/12 - 7/12 = 5/12 Therefore, the daisy…
   Full step-by-step solution

   Step 1: The entire garden represents 1 whole Step 2: The sunflower section occupies 7/12 of the garden Step 3: Since the two triangular sections together make up the entire garden, the daisy section must be the remaining portion Step 4: Calculate the remaining fraction: 1 - 7/12 = 12/12 - 7/12 = 5/12 Step 5: Therefore, the daisy section occupies 5/12 of the garden The answer is 5/12.