Fraction ÷ Fraction

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Fraction ÷ Fraction · Grade 6 · Worksheet 2

1. Emma is creating a mosaic art project using small colored tiles. She has 2 1/4 square feet of space to cover on her canvas. Each tile covers 3/8 of a square foot. How many complete tiles can Emma fit in her mosaic? Answer: 6 Solution: To find how many times one quantity fits into another, we use division. When dividing fractions, we multiply by the reciprocal of the divisor.
   Full step-by-step solution

   To find how many times one quantity fits into another, we use division. When dividing fractions, we multiply by the reciprocal of the divisor. For example, if you had 3 cups of flour and each recipe needed 1/2 cup, you would calculate 3 ÷ 1/2 = 3 × 2/1 = 6 recipes.

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 that are each 2/3 of a foot long for 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 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 problem asks for complete sections, and we got exactly 8, that's our answer. The construction crew can cut 8 complete sections from the beam.

3. 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. 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 olive oil Liam needs. Each bottle contains 1/8 cup, and the recipe requires 3/4 cup. Write the problem as a division.
   Full step-by-step solution

   We need to find how many bottles of olive oil Liam needs. Each bottle contains 1/8 cup, and the recipe requires 3/4 cup. Step 1: Write the problem as a division. We want to know how many 1/8 cups fit into 3/4 cup. So we divide: (3/4) ÷ (1/8) Step 2: Dividing by a fraction is the same as multiplying by its reciprocal. The reciprocal of 1/8 is 8/1. So: (3/4) × (8/1) Step 3: Multiply the numerators and denominators. Numerator: 3 × 8 = 24 Denominator: 4 × 1 = 4 So we have 24/4. Step 4: Simplify 24/4. 24 divided by 4 equals 6. Step 5: Interpret the result. Liam needs 6 bottles of olive oil to get 3/4 cup. Final answer: 6

4. A construction crew is building a new community garden that requires dividing a large rectangular plot of land into smaller sections. The original plot measures 3 1/2 acres total. If each individual garden section needs to be exactly 2/5 of an acre, how many complete garden sections can the crew create from the original plot? Answer: 8 Solution: Convert the mixed number to an improper fraction: 3 1/2 = (3 × 2 + 1)/2 = 7/2 acres Set up the division problem: (7/2) ÷ (2/5) To divide fractions, multiply by the reciprocal: (7/2) × (5/2) Multiply the numerators: 7 × 5 = 35 Multiply the denominators: 2 × 2 = 4 Simplify the fraction: 35/4 = 8…
   Full step-by-step solution

   Step 1: Convert the mixed number to an improper fraction: 3 1/2 = (3 × 2 + 1)/2 = 7/2 acres Step 2: Set up the division problem: (7/2) ÷ (2/5) Step 3: To divide fractions, multiply by the reciprocal: (7/2) × (5/2) Step 4: Multiply the numerators: 7 × 5 = 35 Step 5: Multiply the denominators: 2 × 2 = 4 Step 6: Simplify the fraction: 35/4 = 8 3/4 Step 7: Since we need complete garden sections, we take the whole number part: 8 Step 8: The 3/4 represents a partial section that cannot be used, so the answer is 8 complete garden sections.

5. 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.

6. 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.