5th Grade Area of Rectangles with Fractional Sides Quiz: 10 Questions with Explanations

A \(\frac{3}{7}\) square unitB \(\frac{3}{5}\) square unitC \(\frac{3}{10}\) square unitD \(\frac{1}{10}\) square unit

The unit square has 5 x 2 = 10 tiles, and 3 are shaded: 3/10. Counting only the columns gives 3/5.

A \(\frac{1}{30}\) square unitB \(\frac{1}{11}\) square unitC \(\frac{1}{6}\) square unitD \(\frac{1}{5}\) square unit

There are 6 x 5 = 30 equal tiles, so each tile is 1/30 of the unit square.

A \(\frac{5}{12}\) square footB \(\frac{6}{35}\) square footC \(\frac{6}{12}\) square footD \(\frac{6}{7}\) square foot

Multiply the numerators and the denominators: 2 x 3 = 6 and 5 x 7 = 35. Adding fractions gives the wrong operation.

A \(\frac{7}{17}\) square yardB \(\frac{1}{6}\) square yardC \(\frac{1}{3}\) square yardD \(\frac{12}{17}\) square yard

3 x 4 = 12 and 8 x 9 = 72, so the area is 12/72 = 1/6 square yard.

A \(\frac{3}{5}\) square footB \(\frac{9}{7}\) square footC \(1\frac{1}{10}\) square feetD \(\frac{9}{10}\) square foot

The shaded rectangle has 3 x 3 = 9 tiles, and each tile is 1/10 square foot. So the area is 9/10.

A \(\frac{16}{25}\) square footB \(\frac{8}{5}\) square feetC \(\frac{16}{5}\) square feetD \(\frac{4}{25}\) square foot

Area = side times side = 4/5 x 4/5 = 16/25. Doubling the side gives 8/5, which is not the area.

A \(3\frac{1}{4}\) square feetB \(5\frac{1}{4}\) square feetC 5 square feetD \(4\frac{1}{2}\) square feet

7/2 x 3/2 = 21/4 = 5 1/4. Multiplying wholes and fractions separately gives 3 1/4, which misses two of the four partial areas.

A \(\frac{1}{4}\) square yardB \(\frac{8}{16}\) square yardC \(\frac{3}{5}\) square yardD \(\frac{1}{6}\) square yard

5 x 3 = 15 and 6 x 10 = 60, so the area is 15/60 = 1/4 square yard.

A \(\frac{3}{5} + \frac{7}{8}\)B \(2 \times \left( \frac{3}{5} + \frac{7}{8} \right)\)C \(\frac{3}{5} \times \frac{7}{8}\)D \(\frac{3}{5} \div \frac{7}{8}\)

Area is length times width. The sum or twice the sum is perimeter work.

A \(5\frac{1}{6}\) square feetB \(4\frac{1}{3}\) square feetC 6 square feetD 3 square feet

9/2 x 2/3 = 18/6 = 3. Adding the sides gives 5 1/6, which is not area.