Operations with Rational Numbers Math Example 2

Follow the full solution, then compare it with the other examples linked below.

Example 2

medium
Calculate \(\frac{5}{6} \times \frac{3}{10}\) and simplify.

Solution

  1. 1
    Multiply numerators: \(5 \times 3 = 15\).
  2. 2
    Multiply denominators: \(6 \times 10 = 60\).
  3. 3
    Result: \(\frac{15}{60}\).
  4. 4
    Simplify: GCF(15,60)=15, so \(\frac{15}{60} = \frac{1}{4}\).
  5. 5
    Or cancel before multiplying: \(\frac{5}{6} \times \frac{3}{10} = \frac{\cancel{5}}{\cancel{6}_2} \times \frac{\cancel{3}}{\cancel{10}_2} = \frac{1}{4}\).

Answer

\(\dfrac{1}{4}\)
Multiply across, then simplify (GCF=15). Cross-cancelling before multiplying is often easier: \(5/10 = 1/2\) and \(3/6 = 1/2\), giving \(\frac{1}{2} \times \frac{1}{2} = \frac{1}{4}\).

About Operations with Rational Numbers

Extending addition, subtraction, multiplication, and division to the full set of rational numbers—including fractions, decimals, mixed numbers, and their negative counterparts.

Learn more about Operations with Rational Numbers →

More Operations with Rational Numbers Examples

Example 1 easy

Calculate (frac{2}{3} + frac{1}{4}).

Example 3 easy

Calculate (frac{3}{4} - frac{1}{6}).

Example 4 medium

Calculate (frac{7}{8} div frac{3}{4}).

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