Grade 6 Math · Topic 63

Volume with Fractional Edges

The same volume formula V = ℓ w h works when edges are fractions or mixed numbers. Convert mixed numbers to improper fractions, multiply, then convert back if you like.

Lesson alignment: 6.G.A.2 · Take your time. You can return to this lesson whenever you need it.

Explore visually

Count fractional unit cubes in a prism

Each edge is divided into half-unit lengths. The small prisms build the full volume.

Think first: How many half-unit segments fit along each edge, and what does one small prism measure?

Ready? Reveal the model and try your prediction

Swipe horizontally to see the full diagram.

Turn on JavaScript to adjust this model. The examples and practice below work without it.

Follow the worked examples

Read each step, then cover the explanation and see if you can explain why it works.

Worked example 1

Find V: ℓ = 3/2, w = 5/4, h = 4/5.

Use the volume formula and substitute the given numbers: V = 3/2 · 5/4 · 4/5 = (3 · 5 · 4)/(2 · 4 · 5) = 60/40 = 3/2 unit³.

Answer: 3/2 unit³

Worked example 2

ℓ = 2 1/2, w = 3, h = 1 1/2.

First convert to a form that is easier to calculate: 5/2 · 3 · 3/2 = 45/4 = 11 1/4 unit³.

Answer: 11 1/4 unit³

Try a few on your own

Work these on paper first. Open “Check” when you are ready to compare your answer.

  1. ℓ=1/2, w=1/2, h=1/2
    Check

    1/8

  2. ℓ=3/4, w=2/3, h=1
    Check

    1/2

  3. ℓ=2, w=3/2, h=4/5
    Check

    2 2/5

  4. ℓ=1 1/2, w=2, h=3
    Check

    9

  5. ℓ=5/2, w=4/3, h=3/2
    Check

    5

  6. ℓ=3, w=5/6, h=1/2
    Check

    1 1/4

  7. ℓ=2 1/2, w=1 1/2, h=2
    Check

    7 1/2

  8. ℓ=7/4, w=3/2, h=2/3
    Check

    1 3/4

Try this situation 1

A box is 3/2 ft by 2/3 ft by 1/2 ft. Find its volume.

Show a worked solution

Answer: 1/2 ft³.

Start by writing the calculation clearly: 3/2 · 2/3 · 1/2 = 6/12 = 1/2.

Try this situation 2

A planter is 2 1/2 ft long, 1 1/2 ft wide, and 1 ft tall. Find its volume.

Show a worked solution

Answer: 3 3/4 ft³.

Start by writing the calculation clearly: 5/2 · 3/2 · 1 = 15/4 = 3 3/4.

Fresh questions · saved on this device

Practice this skill

13 question pool

Try a fresh set each time. Answer one question, check your thinking, and read the explanation. If you miss one, return to the visual model and try another round.

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Check what you learned

Answer these five questions on your own. You can review the explanations after you submit and try again whenever you like. This short check is for practice, not a grade.

1. An aquarium is shaped like a rectangular prism with a length of 3 1/2 inches, a width of 2 inches, and a height of 1 1/2 inches. What is the volume of the aquarium in cubic inches?

2. A rectangular box has length 1 2/3 feet, width 3/4 foot, and height 2 feet. What is the volume?

3. A small plastic cube has edges of 1/2 foot each. What is the volume?

4. A decorative box has a volume of 5/6 cubic inches. If the length is 5/2 inches and the width is 1/3 inch, what is the height?

5. A rectangular box has dimensions of 3/2 feet long, 4/3 feet wide, and 2 feet tall. What is the volume of the box in cubic feet?

Practice and finish

Try the linked topic quiz for more practice. If something is tricky, return to the example and look for the step that changes the numbers or representation.

Open the practice quiz

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More Grade 6 resources

Use these free materials if you want another explanation, extra paper practice, or a broader review.

Browse free Grade 6 topic lessons ↗Print Grade 6 worksheets ↗Review Grade 6 flashcards ↗Open the formula review ↗Try the Geometry: Area, Surface Area & Volume quiz ↗Try a full practice test ↗