Testinar Grade 5 math

Area with Fractional Side Lengths

Students will find area with fractional side lengths and connect area models to fraction multiplication.

CH05-04 Fraction Multiplication
Name
Date
Score
____ / 8
Directions Solve each problem. Show your reasoning on the page or on separate paper. Check the answer key only after finishing.

  1. An area model can show \(\frac{1}{2} \times \frac{1}{3}\). What is the product?

    Using Area Models to Multiply Fractions visual for G5-C04-T04-Q001
    1. \(\frac{2}{3}\)
    2. \(\frac{1}{5}\)
    3. \(\frac{2}{5}\)
    4. \(\frac{1}{6}\)

  2. The area model below represents a multiplication problem. The rectangle is divided into 3 equal columns and 4 equal rows. The double-shaded region (where blue and red overlap) shows the product. Which multiplication expression matches this model?

    Using Area Models to Multiply Fractions visual for G5-C04-T04-Q002
    1. \(\frac{1}{3} \times \frac{1}{4}\)
    2. \(\frac{1}{3} \times \frac{3}{4}\)
    3. \(\frac{2}{3} \times \frac{1}{4}\)
    4. \(\frac{3}{4} \times \frac{2}{3}\)

  3. Use the area model to find \(\frac{3}{5} \times \frac{2}{4}\). The grid is split into 5 columns and 4 rows. The first factor marks 3 of the 5 columns, and the second factor marks 2 of the 4 rows. The overlap is the part counted for the product. What is the product?

    Using Area Models to Multiply Fractions visual for G5-C04-T04-Q003
    1. \(\frac{3}{10}\)
    2. \(\frac{5}{9}\)
    3. \(\frac{6}{9}\)
    4. \(\frac{7}{20}\)

  4. A rectangular piece of fabric has length \(\frac{2}{3}\) yard and width \(\frac{1}{4}\) yard. The area model below shows the product. What is the area in square yards?

    Using Area Models to Multiply Fractions visual for G5-C04-T04-Q004
    1. \(\frac{3}{7}\)
    2. \(\frac{1}{6}\)
    3. \(\frac{2}{7}\)
    4. \(\frac{3}{12}\)

  5. Below is an area model for \(\frac{2}{5} \times \frac{3}{4}\). Which statement is true?

    Using Area Models to Multiply Fractions visual for G5-C04-T04-Q005
    1. The overlap covers 6 out of 20 squares.
    2. The product is \(\frac{5}{9}\).
    3. The overlap covers 6 out of 12 squares.
    4. The product is \(\frac{2}{4}\).

  6. Find the product: \(\frac{1}{4} \times \frac{2}{5}\)

    Using Area Models to Multiply Fractions visual for G5-C04-T04-Q006
    1. \(\frac{2}{20}\) or \(\frac{1}{10}\)
    2. \(\frac{2}{9}\)
    3. \(\frac{3}{9}\)
    4. \(\frac{1}{9}\)

  7. A garden is \(\frac{3}{4}\) mile long and \(\frac{1}{2}\) mile wide. What is the area of the garden?

    Using Area Models to Multiply Fractions visual for G5-C04-T04-Q007
    1. \(\frac{4}{6}\) square miles
    2. \(\frac{3}{8}\) square miles
    3. \(\frac{1}{2}\) square miles
    4. \(\frac{3}{4}\) square miles

  8. The area model shown represents \(\frac{1}{5} \times \frac{3}{4}\). What is the product?

    Using Area Models to Multiply Fractions visual for G5-C04-T04-Q009
    1. \(\frac{1}{9}\)
    2. \(\frac{3}{20}\)
    3. \(\frac{1}{5}\)
    4. \(\frac{3}{5}\)
Teacher and parent reference

Answer key and explanations

  1. D. \(\frac{1}{6}\)

    In an area model, divide one dimension into 2 equal parts (for \(\frac{1}{2}\)) and the other into 3 equal parts (for \(\frac{1}{3}\)). The overlapping shaded region is 1 out of 6 total squares, so the product is \(\frac{1}{6}\).

  2. A. \(\frac{1}{3} \times \frac{1}{4}\)

    The blue stripe on the left covers 1 out of 3 columns. The red stripe at the top covers 1 out of 4 rows. The overlap is \(\frac{1}{3} \times \frac{1}{4} = \frac{1}{12}\).

  3. A. \(\frac{3}{10}\)

    The model marks 3 of the 5 columns and 2 of the 4 rows. Their overlap covers \(3 \times 2=6\) of the 20 total squares, so \(\frac{3}{5} \times \frac{2}{4} = \frac{6}{20} = \frac{3}{10}\).

  4. B. \(\frac{1}{6}\)

    Area = length \(\times\) width \(= \frac{2}{3} \times \frac{1}{4} = \frac{2}{12} = \frac{1}{6}\) square yard.

  5. A. The overlap covers 6 out of 20 squares.

    The blue region is 2 out of 5. The red region is 3 out of 4. The double-shaded overlap has 6 squares out of a total of 20, so the product is \(\frac{6}{20}\).

  6. A. \(\frac{2}{20}\) or \(\frac{1}{10}\)

    The overlap region has 2 shaded squares out of 20 total squares, giving \(\frac{1}{4} \times \frac{2}{5} = \frac{2}{20}=\frac{1}{10}\).

  7. B. \(\frac{3}{8}\) square miles

    Area = \(\frac{3}{4} \times \frac{1}{2} = \frac{3}{8}\) square miles.

  8. B. \(\frac{3}{20}\)

    The blue region is 1 out of 5. The red region is 3 out of 4. The overlap is 3 out of 20 squares: \(\frac{1}{5} \times \frac{3}{4} = \frac{3}{20}\).

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