Multiply & Divide Rational Numbers Quick Check

Answer 1

Sure! Here’s a quick check covering multiplication and division of rational numbers with examples.

Multiplying Rational Numbers

To multiply two rational numbers, simply multiply the numerators together and the denominators together.

Example:

Multiply \( \frac{2}{3} \) and \( \frac{4}{5} \).

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

Dividing Rational Numbers

To divide by a rational number, multiply by its reciprocal.

Example:

Divide \( \frac{3}{4} \) by \( \frac{2}{3} \).

\[ \frac{3}{4} \div \frac{2}{3} = \frac{3}{4} \times \frac{3}{2} = \frac{3 \times 3}{4 \times 2} = \frac{9}{8} \]

Quick Check Questions:

1. Multiply \( \frac{5}{6} \) and \( \frac{2}{3} \).
2. Divide \( \frac{7}{8} \) by \( \frac{1}{4} \).
3. Multiply \( -\frac{3}{5} \) and \( \frac{4}{7} \).
4. Divide \( -\frac{6}{11} \) by \( -\frac{2}{3} \).

Answers:

1. \( \frac{5}{6} \times \frac{2}{3} = \frac{10}{18} = \frac{5}{9} \)
2. \( \frac{7}{8} \div \frac{1}{4} = \frac{7}{8} \times 4 = \frac{28}{8} = 3.5 \) or \( \frac{7}{2} \)
3. \( -\frac{3}{5} \times \frac{4}{7} = -\frac{12}{35} \)
4. \( -\frac{6}{11} \div -\frac{2}{3} = -\frac{6}{11} \times -\frac{3}{2} = \frac{18}{22} = \frac{9}{11} \)

Feel free to ask for clarification on any step or concept!