5th Grade Area of Rectangles with Fractional Sides Test Solutions and Scoring (PDF)

5th Grade math test solutions: Area of Rectangles with Fractional Sides – Maths PDF

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This area fraction sides test answers for 5th Grade covers area of rectangles with fractional sides (Common Core 5.NF.B.4b), with a free PDF to print.

This answer key gives worked solutions and a scoring guide for each of the 9 test questions, worth 20 points in all. Use the scoring notes to award points for correct tile counts or setups even when the final simplification is missing.

Grade 5 · Common Core State Standards: 5.NF.B.4b

Area fraction sides test answers: worked solutions

Question 1 – Tiles in a unit square [2 pts]

The shaded rectangle covers 6 of 15 tiles.

(a) $5 \times 3 = 15$ tiles: each tile is $\frac{1}{15}$ square unit.

(b) $3 \times 2 = 6$ tiles, so $\frac{6}{15} = \frac{2}{5}$: $\frac{2}{5}$ square unit.

Scoring: 1 point for each correct answer.

Question 2 – Multiply the sides [2 pts]

(a)

Multiply the numerators and multiply the denominators: $\frac{3}{5} \times \frac{1}{4} = \frac{3 \times 1}{5 \times 4} = \frac{3}{20}$.

The area is $\frac{3}{20}$ square foot.

(b)

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 yard.

Scoring: 1 point for each correct area in simplest form with square units.

Question 3 – Mixed number sides [2 pts]

(a)

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

Multiply the numerators and multiply the denominators: $\frac{5}{2} \times \frac{1}{3} = \frac{5 \times 1}{2 \times 3} = \frac{5}{6}$.

The area is $\frac{5}{6}$ square foot.

(b)

Write the mixed numbers as improper fractions: $1\frac{1}{2} = \frac{3}{2}$ and $1\frac{3}{4} = \frac{7}{4}$.

Multiply the numerators and multiply the denominators: $\frac{3}{2} \times \frac{7}{4} = \frac{3 \times 7}{2 \times 4} = \frac{21}{8}$.

Write as a mixed number: $\frac{21}{8} = 2\frac{5}{8}$.

The area is $2\frac{5}{8}$ square inches.

Scoring: 1 point for each correct area with square units.

Question 4 – Tiling two squares [3 pts]

Twelve tiles of 1/12 square foot make 1 square foot.

(a) Each unit square has $3 \times 4 = 12$ tiles: $\frac{1}{12}$ square foot.

(b) $4 \times 3 = 12$: 12 tiles.

Scoring: 1 point for each part.

Question 5 – Square tile [2 pts]

(a)

Multiply the numerators and multiply the denominators: $\frac{5}{6} \times \frac{5}{6} = \frac{5 \times 5}{6 \times 6} = \frac{25}{36}$.

The area is $\frac{25}{36}$ square foot.

(b) $\frac{25}{36}$ is less than $\frac{5}{6} = \frac{30}{36}$. Multiplying by a fraction less than 1 gives a smaller number.

Scoring: 1 point for the area; 1 point for the correct comparison with a reason.

Question 6 – Poster board [2 pts]

(a) $\frac{7}{4} \times \frac{5}{2} = \frac{35}{8} = 4\frac{3}{8}$: $4\frac{3}{8}$ square feet.

(b) The second poster has area $2 \times 2 = 4$ square feet. The first poster is greater because $4\frac{3}{8} > 4$.

Scoring: 1 point for each part.

Question 7 – Closet carpet [2 pts]

(a) $\frac{9}{4} \times \frac{4}{3} = \frac{36}{12} = 3$: 3 square feet.

(b) $3 \times 6 = 18$: $18.

Scoring: 1 point for each correct answer.

Question 8 – Area and perimeter [2 pts]

(a) $\frac{2}{3} \times \frac{1}{4} = \frac{2}{12} = \frac{1}{6}$: $\frac{1}{6}$ square yard.

(b) $2 \times \left( \frac{8}{12} + \frac{3}{12} \right) = 2 \times \frac{11}{12} = \frac{22}{12} = 1\frac{5}{6}$: $1\frac{5}{6}$ yards.

Scoring: 1 point for each correct answer with units.

Question 9 – Painted banner [3 pts]

Banner area: 2 sq ft; red part: 1 1/4 sq ft.

(a) $\frac{8}{3} \times \frac{3}{4} = \frac{24}{12} = 2$: 2 square feet.

(b) $\frac{5}{8} \times 2 = \frac{10}{8} = 1\frac{1}{4}$: $1\frac{1}{4}$ square feet.

Scoring: 1 point for each part.

Total score

Total

20 points

Key facts behind this area fraction sides test answers

Key facts

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.

How to use this area fraction sides test answers

Score your test with the point values shown for each question. Then read the worked solution of every question where you lost points and note the method to review.

Download the area fraction sides test answers as a PDF with the button below and keep it with your notes.

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