5th Grade Area of Rectangles with Fractional Sides Quiz: 10 Questions with Explanations Home 5th Grade Math Worksheets, Lessons and Tests (Free PDF) 5th Grade Area of Rectangles with Fractional Sides Quiz: 10 Questions with Explanations
Answer these 10 multiple-choice questions about the area of rectangles with fractional sides. Each question has one correct answer. Count tiles or multiply the side lengths, then read the explanation after each answer.
Grade 5 · Common Core State Standards: 5.NF.B.4b
Question 1 A unit square is cut into tiles. What is the area of the shaded rectangle?
The unit square has 5 columns and 2 rows. A \(\frac{3}{7}\) square unitB \(\frac{3}{5}\) square unitC \(\frac{3}{10}\) square unitD \(\frac{1}{10}\) square unitThe unit square has 5 x 2 = 10 tiles, and 3 are shaded: 3/10. Counting only the columns gives 3/5.
Question 2 A unit square is cut into 6 columns and 5 rows. What is the area of one tile?
A \(\frac{1}{30}\) square unitB \(\frac{1}{11}\) square unitC \(\frac{1}{6}\) square unitD \(\frac{1}{5}\) square unitThere are 6 x 5 = 30 equal tiles, so each tile is 1/30 of the unit square.
Question 3 Find the area of a rectangle that is \(\frac{2}{5}\) foot by \(\frac{3}{7}\) foot.
A \(\frac{5}{12}\) square footB \(\frac{6}{35}\) square footC \(\frac{6}{12}\) square footD \(\frac{6}{7}\) square footMultiply the numerators and the denominators: 2 x 3 = 6 and 5 x 7 = 35. Adding fractions gives the wrong operation.
Question 4 Find the area of a rectangle that is \(\frac{3}{8}\) yard by \(\frac{4}{9}\) yard.
A \(\frac{7}{17}\) square yardB \(\frac{1}{6}\) square yardC \(\frac{1}{3}\) square yardD \(\frac{12}{17}\) square yard3 x 4 = 12 and 8 x 9 = 72, so the area is 12/72 = 1/6 square yard.
Question 5 Two unit squares are cut into tiles. The shaded rectangle is \(1\frac{1}{2}\) feet by \(\frac{3}{5}\) foot. What is its area?
Two unit squares, each cut into 2 columns and 5 rows. A \(\frac{3}{5}\) square footB \(\frac{9}{7}\) square footC \(1\frac{1}{10}\) square feetD \(\frac{9}{10}\) square footThe shaded rectangle has 3 x 3 = 9 tiles, and each tile is 1/10 square foot. So the area is 9/10.
Question 6 A square patio tile has sides of length \(\frac{4}{5}\) foot. What is its area?
A \(\frac{16}{25}\) square footB \(\frac{8}{5}\) square feetC \(\frac{16}{5}\) square feetD \(\frac{4}{25}\) square footArea = side times side = 4/5 x 4/5 = 16/25. Doubling the side gives 8/5, which is not the area.
Question 7 What is the area of this rectangle?
3 1/2 ft 1 1/2 ft A rectangle. A \(3\frac{1}{4}\) square feetB \(5\frac{1}{4}\) square feetC 5 square feetD \(4\frac{1}{2}\) square feet7/2 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.
Question 8 Maya's patch of grass is \(\frac{5}{6}\) yard by \(\frac{3}{10}\) yard. What is its area?
A \(\frac{1}{4}\) square yardB \(\frac{8}{16}\) square yardC \(\frac{3}{5}\) square yardD \(\frac{1}{6}\) square yard5 x 3 = 15 and 6 x 10 = 60, so the area is 15/60 = 1/4 square yard.
Question 9 Which expression gives the area of a rectangle with sides \(\frac{3}{5}\) unit and \(\frac{7}{8}\) unit?
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.
Question 10 Liam's rug is \(4\frac{1}{2}\) feet by \(\frac{2}{3}\) foot. What is its area?
4 1/2 ft 2/3 ft A rug. A \(5\frac{1}{6}\) square feetB \(4\frac{1}{3}\) square feetC 6 square feetD 3 square feet9/2 x 2/3 = 18/6 = 3. Adding the sides gives 5 1/6, which is not area.
Remember
A unit square has area 1 square unit.
Cutting a unit square into equal tiles gives tiles with a unit fraction area.
Area = length times width, even when the sides are fractions.
Counting tiles and multiplying the side lengths give the same area.
Always write square units, such as square feet, in the answer.
All Grade 5 chapters: Grade 5 math .
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