Lesson 4: Fractions in Lengths, Areas, and Volumes

Property

To find how many times as large one quantity is compared to another, you use division. This involves comparing a specific quantity to a reference quantity.

Property

The order of division depends on the question being asked. These two questions produce reciprocal answers:

• "How many times as large is $A$ than $B$?" $\rightarrow$ Divide $A \div B$.
• "What fraction of $A$ is $B$?" $\rightarrow$ Divide $B \div A$.

Examples

Property

To divide quantities given as mixed numbers, you must standardise the format first:

1. Convert mixed numbers to improper fractions ($a\frac{b}{c} = \frac{ac + b}{c}$).
2. Multiply by the reciprocal of the divisor.
3. Simplify or convert back to a mixed number if needed.

Examples

Property

Division is used to find a missing dimension (Length, Width, or Height) when the Area or Volume is known.
This relies on the inverse relationship between multiplication and division.

• Area: If $Area = Length \times Width$, then $Width = Area \div Length$.
• Volume: If $Volume = Base \times Height$, then $Height = Volume \div Base$.

Examples