Area and volume with fractional lengths

Three quick questions from earlier lessons.

A rectangle is $\tfrac{1}{2}$ m by $\tfrac{1}{3}$ m. Its area is what part of a square meter?

Area and volume formulas work with fractions too.

Area of a rectangle

= \ell \cdot w

and volume of a box

= \ell \cdot w \cdot h

also for fractional lengths: multiply numerators and denominators. A unit cube holds

k^3

cubes of edge

\tfrac{1}{k}

.

A box $\tfrac{1}{2}$ by 3 by $\tfrac{2}{3}$ .

\tfrac{1}{2} \cdot 3 \cdot \tfrac{2}{3} = 1

cubic unit

Multiply.

Your turn: a square with side $\tfrac{3}{4}$ . Its area.

\tfrac{9}{16}

3/4 · 3/4.

A rectangle is $\tfrac{ 1 }{ 5 }$ m by $\tfrac{ 2 }{ 5 }$ m. What is its area (m²)?
A rectangle is $\tfrac{ 4 }{ 5 }$ m by $\tfrac{ 5 }{ 6 }$ m. What is its area (m²)?

A box is $\tfrac{ 1 }{ 2 }$ ft by 7 ft by $\tfrac{ 1 }{ 3 }$ ft. What is its volume (ft³)?

Three questions to check you have got it.

A rectangle is $\tfrac{ 1 }{ 5 }$ m by $\tfrac{ 2 }{ 5 }$ m. What is its area (m²)?
A rectangle is $\tfrac{ 4 }{ 5 }$ m by $\tfrac{ 5 }{ 6 }$ m. What is its area (m²)?
A rectangle is $\tfrac{ 1 }{ 6 }$ m by $\tfrac{ 2 }{ 3 }$ m. What is its area (m²)?

Fractional lengths

Multiply lengths for areas and volumes, fractions included.

Watch out: a 1/k cube is 1/k³ of a unit cube.

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