The lesson
This lesson teaches Volume with Fractions. Read each section in order, work through every example on paper, then use the practice problems and quick check at the bottom.
The volume formula still works
Volume of a rectangular prism is always length × width × height. When edges are mixed numbers, turn each into an improper fraction (or a decimal) first, then multiply.
The denominator tells you how many equal parts the whole is split into. The numerator tells you how many of those parts you have.
Always ask: "What is the whole?" In 3/4 of a pizza, the whole is one pizza. In 3/4 of 20 students, the whole is 20 students.
Find the volume of a box that is 1½ ft × 2 ft × 4 ft.
- 1Write 1½ as 1.5 (or 3/2).
- 21.5 × 2 × 4 = 12.
- 3Volume = 12 cubic feet.
Why this matters
Volume with Fractions shows up constantly in same length × width × height - even when the edges are fractions. It also connects to what you will see on homework, quizzes, and the next unit in this grade.
Teachers often move fast in class. This page is here so you can pause, re-read, and practice until the idea feels familiar, not just until you have memorized a rule for one day.
Common mistakes to avoid
Rushing to the answer without writing steps. Middle-school math rewards clear work, and you catch errors earlier when steps are visible.
Mixing up similar ideas from the same topic. If two terms feel alike, make a two-column note: what is the same, what is different, and one example of each.
Key ideas from this lesson
- The volume formula still works
Video walkthrough
Volume of Rectangular Prisms
Length × width × height for box-shaped objects.
Watch on YouTubePractice
For each problem: write your work in the box, type your answer, and check it. If you are stuck, reveal the solution one step at a time. Do not skip straight to the final answer.
Exercise 1
Try it yourselfFind the volume of a box 2 ft × 3 ft × 5 ft.
Step-by-step solution
- 1V = 2 × 3 × 5 = 30 ft³.
Exercise 2
Try it yourselfFind the volume of a prism 1½ in × 4 in × 2 in.
Step-by-step solution
- 11.5 × 4 × 2 = 12 in³.
Exercise 3
Try it yourselfA fish tank is 2½ ft long, 1 ft wide, and 1½ ft tall. How many cubic feet of water does it hold?
Step-by-step solution
- 12.5 × 1 × 1.5 = 3.75 ft³.
Exercise 4
Try it yourselfA prism has volume 45 m³. The base is 7½ m². Find the height.
Step-by-step solution
- 145 = 7.5 × h.
- 2h = 45 ÷ 7.5 = 6 m.
Exercise 5
Try it yourselfA storage crate is 3¼ ft × 2 ft × 1⅖ ft. Round to the nearest tenth and find the volume in cubic feet.
Step-by-step solution
- 13.25 × 2 × 1.4 = 9.1 ft³ (nearest tenth).
Worksheet - Applied geometry
End-of-year mixed practice across area, surface area, and volume.
Quick check
Answer all questions. Retake the quiz until you feel confident before moving on.
Volume with Fractions
Question 1 of 5
A box has dimensions 2 ft × 3 ft × 5 ft. What is its volume?