Multiplying Fractions

To multiply fractions, you multiply the numerators together to get the new numerator, and you multiply the denominators together to get the new denominator.
- For example: \frac{a}{b} \times \frac{c}{d} = \frac{a \times c}{b \times d}

Problem: \frac{4}{6} \times \frac{2}{3}
Step 1: Multiply the numerators: 4 \times 2 = 8
Step 2: Multiply the denominators: 6 \times 3 = 18
Initial Solution: \frac{8}{18}
Step 3: Simplify the fraction (if possible).
- Find a common factor for both the numerator and the denominator. In this case, both 8 and 18 are divisible by 2.
- Divide both the numerator and the denominator by the common factor: \frac{8 \div 2}{18 \div 2} = \frac{4}{9}
Simplified Solution: \frac{4}{9}

Sometimes, it’s easier to simplify before multiplying.
Example: \frac{4}{6} \times \frac{2}{3} can be simplified by noticing that 4 and 2 share a common factor with 6 and 3 respectively.
Simplify \frac{4}{6} to \frac{2}{3} by dividing both by 2.
The problem becomes: \frac{2}{3} \times \frac{2}{3}
Multiply the numerators: 2 \times 2 = 4
Multiply the denominators: 3 \times 3 = 9
Solution: \frac{4}{9} (Same as simplifying after multiplying)

The same principle applies when multiplying more than two fractions.
Example: \frac{1}{2} \times \frac{2}{3} \times \frac{3}{4}
Multiply all numerators: 1 \times 2 \times 3 = 6
Multiply all denominators: 2 \times 3 \times 4 = 24
Initial Solution: \frac{6}{24}
Simplify the fraction by dividing both numerator and denominator by their greatest common divisor, which is 6.
Simplified Solution: \frac{6 \div 6}{24 \div 6} = \frac{1}{4}

Always multiply numerators together and denominators together.
Simplify the fraction after multiplying, if possible, to get the answer in its simplest form.
Simplifying before multiplying can make the calculation easier.