Fractional Volume

Grade 6 · geometry · 100 practice problems · read aloud

🔊 Listen to this explanation

Fractional Volume: Finding Parts of 3D Shapes

📐 What is Fractional Volume?

Fractional volume helps us find a part of a 3D shape's total volume. It's like figuring out how much juice is in half a juice box or what 1/4 of a swimming pool holds. We use this in real life for cooking, construction, and packing!

🧩 How to Solve Fractional Volume Problems

  1. Step 1: Find the total volume of the rectangular prism. Use the formula: Volume = length × width × height.
  2. Step 2: Identify the fraction of the volume you need to find (like 1/2, 1/3, or 2/5).
  3. Step 3: Multiply the total volume by the fraction.

🔢 Worked Examples

Example 1: A rectangular prism is 8 cm long, 3 cm wide, and 4 cm high. What is 1/2 of its volume?

  1. Total Volume = 8 × 3 × 4 = 96 cm³
  2. Fraction needed = 1/2
  3. Fractional Volume = 96 × (1/2) = 48 cm³

Example 2: A cube has sides of 6 ft. What is 2/3 of its volume?

  1. Total Volume = 6 × 6 × 6 = 216 ft³
  2. Fraction needed = 2/3
  3. Fractional Volume = 216 × (2/3) = 144 ft³

⚠️ Common Mistakes to Avoid

  • Multiplying the fraction first: Don't multiply the side lengths by the fraction first! Always find the total volume first, then multiply by the fraction.
  • Forgetting units: Always include cubic units (like cm³, m³, ft³) in your final answer.
  • Confusing with area: Volume is 3D, so we multiply three dimensions, not two.

💡 Tips & Tricks

  • Order Doesn't Matter: You can multiply the length, width, and height in any order.
  • Simplify First: When multiplying by a fraction, see if you can simplify before calculating. For 96 × (1/2), think "half of 96" instead of doing the multiplication.
  • Visualize: Draw the shape and shade the part you're finding. It helps to see the problem!

🎯 How to Practice

Try these ideas to master fractional volume:

  • Use building blocks or LEGOs to build rectangular prisms and calculate fractional parts.
  • Find boxes at home, measure their dimensions, and calculate what 1/4 or 3/4 of their volume would be.
  • Create your own word problems: "If a fish tank holds 120 gallons, how much water is in it when it's 3/4 full?"

Practice problems

6 of the 100, worked through step by step — try them before opening the answer.

1 6.5 × 8.4 × 10.2 = ?

Hint: Multiply the three decimal numbers together. You can ignore the decimal points at first, multiply as whole numbers, then place the decimal point in the product by counting the total number of decimal places in all three factors.

Show the answer

Answer: 556.92

  1. Write the problem: 6.5 × 8.4 × 10.2
  2. Multiply 6.5 and 8.4 first. Ignore decimals: 65 × 84 = 5460. Since 6.5 has 1 decimal place and 8.4 has 1 decimal place, the product has 2 decimal places: 54.60.
  3. Multiply 54.60 by 10.2. Ignore decimals: 5460 × 102 = 5460 × (100 + 2) = 546000 + 10920 = 556920. Since 54.60 has 2 decimal places and 10.2 has 1 decimal place, the final product has 3 decimal places: 556.920.
  4. Remove the trailing zero: 556.92.

The answer is 556.92.

2 7.5 × 9.25 × 11.75 = ?

Hint: Multiply the three decimal dimensions together. You can convert each decimal to a fraction (like 7.5 = 15/2) to make multiplication easier, then convert back to a decimal at the end.

Show the answer

Answer: 815.15625

  1. Write the dimensions: 7.5, 9.25, 11.75.
  2. Convert each decimal to a fraction: 7.5 = 75/10 = 15/2, 9.25 = 925/100 = 37/4, 11.75 = 1175/100 = 47/4.
  3. Multiply the fractions: (15/2) × (37/4) × (47/4) = (15 × 37 × 47) / (2 × 4 × 4).
  4. Multiply the numerators: 15 × 37 = 555, 555 × 47 = 555 × (50 - 3) = 27750 - 1665 = 26085.
  5. Multiply the denominators: 2 × 4 = 8, 8 × 4 = 32.
  6. The fraction is 26085/32.
  7. Convert to a decimal: 26085 ÷ 32 = 815.15625.

The answer is 815.15625.

3 (3/4 × 2/3) ÷ (1/6) = ?

Hint: Remember to multiply fractions first, then divide by the third fraction. When dividing fractions, multiply by the reciprocal.

Show the answer

Answer: 3

  1. Multiply the first two fractions: 3/4 × 2/3 = (3×2)/(4×3) = 6/12 = 1/2
  2. Now we have 1/2 ÷ 1/6
  3. When dividing fractions, multiply by the reciprocal: 1/2 × 6/1 = (1×6)/(2×1) = 6/2 = 3
  4. The final answer is 3

4 (2/3 × 0.75) ÷ (1/4) = ?

Hint: Convert the decimal to a fraction first, then follow the order of operations for multiplication and division of fractions.

Show the answer

Answer: 2

  1. Simplify 2/3 × 0.75 0.75 is the same as 3/4. So we have: 2/3 × 3/4
  2. Multiply the fractions Multiply numerators: 2 × 3 = 6 Multiply denominators: 3 × 4 = 12 So 2/3 × 3/4 = 6/12
  3. Simplify 6/12 6/12 = 1/2
  4. Now the expression is (1/2) ÷ (1/4) Dividing by 1/4 is the same as multiplying by 4/1. So (1/2) × (4/1) = 4/2
  5. Simplify 4/2 4/2 = 2 Final answer: 2

Let's solve step-by-step.

5 (3/4) × (2/3) ÷ (1/2) = ?

Hint: When multiplying fractions, multiply the numerators together and the denominators together. Dividing by a fraction is the same as multiplying by its reciprocal.

Show the answer

Answer: 1

  1. Understand the division by a fraction** Dividing by a fraction is the same as multiplying by its reciprocal. So, ÷ (1/2) is the same as × (2/1). The expression becomes: (3/4) × (2/3) × (2/1) --- **
  2. Multiply the fractions** When multiplying fractions, multiply the numerators together and the denominators together. Numerator: 3 × 2 × 2 = 12 Denominator: 4 × 3 × 1 = 12 So we have: 12/12 --- **
  3. Simplify** 12/12 = 1 --- **Final Answer:** 1

Let's solve step-by-step. We have: (3/4) × (2/3) ÷ (1/2) --- **

6 (2/3) × (3/4) ÷ (1/2) = ?

Hint: When working with fractions, remember to multiply across numerators and denominators, then simplify before dividing by multiplying by the reciprocal.

Show the answer

Answer: 1

  1. Write the problem as given. (2/3) × (3/4) ÷ (1/2)
  2. Recall that dividing by a fraction is the same as multiplying by its reciprocal. So, ÷ (1/2) = × (2/1). Now the expression becomes: (2/3) × (3/4) × (2/1)
  3. Multiply the fractions by multiplying all numerators together and all denominators together. Numerator: 2 × 3 × 2 = 12 Denominator: 3 × 4 × 1 = 12
  4. Write the result as a fraction: 12/12
  5. Simplify 12/12 = 1. Final answer: 1

Let's solve step-by-step.

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