5th Grade Area of Rectangles with Fractional Sides Worksheet Solutions (PDF)

The unit square has \(3 \times 2 = 6\) equal tiles.

Each tile is \(\frac{1}{6}\) of the unit square.

Number of tiles: \(4 \times 4 = 16\).

Area of one tile: \(\frac{1}{4} \times \frac{1}{4} = \frac{1}{16}\) square unit.

There are 16 tiles, and each has area \(\frac{1}{16}\) square unit.

The unit square has \(6 \times 4 = 24\) tiles, so each tile is \(\frac{1}{24}\) square unit.

The shaded rectangle is 5 tiles wide and 3 tiles tall: \(5 \times 3 = 15\) tiles.

\(\frac{15}{24} = \frac{5}{8}\)

The area is \(\frac{5}{8}\) square unit.

Multiply the numerators and multiply the denominators: \(\frac{1}{2} \times \frac{1}{5} = \frac{1 \times 1}{2 \times 5} = \frac{1}{10}\).

The area is \(\frac{1}{10}\) square foot.

Multiply the numerators and multiply the denominators: \(\frac{2}{3} \times \frac{3}{7} = \frac{2 \times 3}{3 \times 7} = \frac{6}{21}\).

Simplify: \(\frac{6}{21} = \frac{2}{7}\).

The area is \(\frac{2}{7}\) square foot.

Multiply the numerators and multiply the denominators: \(\frac{3}{4} \times \frac{5}{6} = \frac{3 \times 5}{4 \times 6} = \frac{15}{24}\).

Simplify: \(\frac{15}{24} = \frac{5}{8}\).

The area is \(\frac{5}{8}\) square inch.

Multiply the numerators and multiply the denominators: \(\frac{4}{5} \times \frac{5}{8} = \frac{4 \times 5}{5 \times 8} = \frac{20}{40}\).

Simplify: \(\frac{20}{40} = \frac{1}{2}\).

The area is \(\frac{1}{2}\) square yard.

Each unit square is cut into 12 tiles, so each tile is \(\frac{1}{12}\) square inch. The rectangle is 5 tiles wide and 2 tiles tall: 10 tiles.

\(\frac{10}{12} = \frac{5}{6}\)

Write the mixed number as improper fraction: \(1\frac{1}{4} = \frac{5}{4}\).

Multiply the numerators and multiply the denominators: \(\frac{5}{4} \times \frac{2}{3} = \frac{5 \times 2}{4 \times 3} = \frac{10}{12}\).

Simplify: \(\frac{10}{12} = \frac{5}{6}\).

The area is \(\frac{5}{6}\) square inch.

Write the mixed number as improper fraction: \(2\frac{1}{2} = \frac{5}{2}\).

Multiply the numerators and multiply the denominators: \(\frac{5}{2} \times \frac{3}{5} = \frac{5 \times 3}{2 \times 5} = \frac{15}{10}\).

Simplify: \(\frac{15}{10} = \frac{3}{2}\).

Write as a mixed number: \(\frac{3}{2} = 1\frac{1}{2}\).

The area is \(1\frac{1}{2}\) square yards.

Write the mixed numbers as improper fractions: \(1\frac{3}{4} = \frac{7}{4}\) and \(1\frac{1}{3} = \frac{4}{3}\).

Multiply the numerators and multiply the denominators: \(\frac{7}{4} \times \frac{4}{3} = \frac{7 \times 4}{4 \times 3} = \frac{28}{12}\).

Simplify: \(\frac{28}{12} = \frac{7}{3}\).

Write as a mixed number: \(\frac{7}{3} = 2\frac{1}{3}\).

The area is \(2\frac{1}{3}\) square feet.

Area of A: \(\frac{3}{4} \times \frac{4}{5} = \frac{12}{20} = \frac{3}{5}\) square foot.

Area of B: \(\frac{2}{3} \times \frac{7}{8} = \frac{14}{24} = \frac{7}{12}\) square foot.

Common denominator 60: \(\frac{3}{5} = \frac{36}{60}\) and \(\frac{7}{12} = \frac{35}{60}\).

Rectangle A has the greater area.

Multiply the numerators and multiply the denominators: \(\frac{2}{5} \times \frac{2}{5} = \frac{2 \times 2}{5 \times 5} = \frac{4}{25}\).

The area is \(\frac{4}{25}\) square foot.

Write the mixed numbers as improper fractions: \(1\frac{1}{2} = \frac{3}{2}\) and \(1\frac{1}{2} = \frac{3}{2}\).

Multiply the numerators and multiply the denominators: \(\frac{3}{2} \times \frac{3}{2} = \frac{3 \times 3}{2 \times 2} = \frac{9}{4}\).

Write as a mixed number: \(\frac{9}{4} = 2\frac{1}{4}\).

The area is \(2\frac{1}{4}\) square inches.

Multiply the numerators and multiply the denominators: \(\frac{3}{4} \times \frac{1}{2} = \frac{3 \times 1}{4 \times 2} = \frac{3}{8}\).

The area is \(\frac{3}{8}\) square foot.

Perimeter: \(2 \times \left( \frac{3}{4} + \frac{1}{2} \right) = 2 \times \left( \frac{3}{4} + \frac{2}{4} \right) = 2 \times \frac{5}{4} = \frac{10}{4} = 2\frac{1}{2}\) feet.

The area is \(\frac{3}{8}\) square foot and the perimeter is \(2\frac{1}{2}\) feet.

Multiply the numerators and multiply the denominators: \(\frac{7}{8} \times \frac{2}{3} = \frac{7 \times 2}{8 \times 3} = \frac{14}{24}\).

Simplify: \(\frac{14}{24} = \frac{7}{12}\).

The area is \(\frac{7}{12}\) square foot.

Area:

Write the mixed numbers as improper fractions: \(2\frac{1}{2} = \frac{5}{2}\) and \(1\frac{1}{2} = \frac{3}{2}\).

Multiply the numerators and multiply the denominators: \(\frac{5}{2} \times \frac{3}{2} = \frac{5 \times 3}{2 \times 2} = \frac{15}{4}\).

Write as a mixed number: \(\frac{15}{4} = 3\frac{3}{4}\).

\(3\frac{3}{4}\)

Cost: \(3\frac{3}{4} \times 4 = \frac{15}{4} \times 4 = 15\) dollars.

The poster has an area of \(3\frac{3}{4}\) square feet, and the paint costs $15.

Write the mixed numbers as improper fractions: \(2\frac{1}{3} = \frac{7}{3}\) and \(1\frac{1}{2} = \frac{3}{2}\).

Multiply the numerators and multiply the denominators: \(\frac{7}{3} \times \frac{3}{2} = \frac{7 \times 3}{3 \times 2} = \frac{21}{6}\).

Simplify: \(\frac{21}{6} = \frac{7}{2}\).

Write as a mixed number: \(\frac{7}{2} = 3\frac{1}{2}\).

The area is \(3\frac{1}{2}\) square yards.

Area of the board:

Write the mixed numbers as improper fractions: \(4\frac{1}{2} = \frac{9}{2}\) and \(2\frac{2}{3} = \frac{8}{3}\).

Multiply the numerators and multiply the denominators: \(\frac{9}{2} \times \frac{8}{3} = \frac{9 \times 8}{2 \times 3} = \frac{72}{6}\).

Simplify: \(\frac{72}{6} = 12\).

\(12\)

Blue paper: \(\frac{3}{4} \times 12 = 9\).

Ethan covers 9 square feet with blue paper.

Bed A: \(\frac{3}{4} \times \frac{1}{2} = \frac{3}{8}\) square yard.

Bed B: \(\frac{5}{6} \times \frac{3}{4} = \frac{15}{24} = \frac{5}{8}\) square yard.

Total: \(\frac{3}{8} + \frac{5}{8} = \frac{8}{8} = 1\).

The total area is 1 square yard.

One decal:

Write the mixed number as improper fraction: \(1\frac{2}{3} = \frac{5}{3}\).

Multiply the numerators and multiply the denominators: \(\frac{5}{3} \times \frac{3}{4} = \frac{5 \times 3}{3 \times 4} = \frac{15}{12}\).

Simplify: \(\frac{15}{12} = \frac{5}{4}\).

Write as a mixed number: \(\frac{5}{4} = 1\frac{1}{4}\).

The area is \(1\frac{1}{4}\) square feet.

Six decals: \(6 \times 1\frac{1}{4} = 6 \times \frac{5}{4} = \frac{30}{4} = 7\frac{1}{2}\).

One decal has area \(1\frac{1}{4}\) square feet, and 6 decals have a total area of \(7\frac{1}{2}\) square feet.