\( \require{mhchem} \require{enclose} \require{color} \)

You can use the values of the fractions being multiplied together to predict the value of a product. Look at the table below.

• If two proper fractions are multiplied, their product is smaller than either fraction.
• If a proper fraction is multiplied by an improper fraction, mixed number, or whole number other than 0 or 1, then the product is always larger than the proper fraction.
• If an improper fraction is multiplied by another improper fraction, mixed number, or whole number other than 0 or 1, then the product is always larger than the improper fraction.

Read the question on each box. Once you think you know the answer, click the box to check your work.

Is the product of \( \frac{3}{2} \times \frac{5}{4} \) larger or smaller than \( \frac{3}{2} \)?

Larger

The product of improper fractions is larger than the first improper fraction.

\[ \frac{3}{2} \times \frac{5}{4} = \frac{3 \times 5}{2 \times 4} = \frac{15}{8} \]

You can convert the improper fractions to mixed numbers to show this is true.

Is the product of \( \frac{13}{14} \times \frac{1}{2} \) larger or smaller than \( \frac{13}{14} \)?

Smaller

The product of proper fractions is smaller than the factors.

\[ \frac{13}{14} \times \frac{1}{2} = \frac{13 \times 1}{14 \times 2} = \frac{13}{28} \]

The fraction \( \frac{13}{28} \) is smaller than both \( \frac{13}{14} \) and \( \frac{1}{2}. \)

Is the product of \( \frac{7}{5} \times \frac{9}{10} \) larger or smaller than \( \frac{7}{5} \)?

Smaller

The product of an improper and a proper fraction is smaller than the improper factor.

\[ \frac{7}{5} \times \frac{9}{10} = \frac{7 \times 9}{5 \times 10} = \frac{63}{50} \]

You can convert the improper fractions to mixed numbers to show this is true.