How do you simplify fractions?

To simplify fractions, divide the numerator and the denominator by their greatest common divisor (GCD).

Simplifying fractions makes them easier to work with and understand. The first step is to find the greatest common divisor (GCD) of the numerator (the top number) and the denominator (the bottom number). The GCD is the largest number that divides both the numerator and the denominator without leaving a remainder.

For example, let's simplify the fraction 18/24. First, list the factors of both numbers. The factors of 18 are 1, 2, 3, 6, 9, and 18. The factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24. The largest common factor is 6, so the GCD of 18 and 24 is 6.

Next, divide both the numerator and the denominator by the GCD. For 18/24, divide both 18 and 24 by 6:
\[ \frac{18 \div 6}{24 \div 6} = \frac{3}{4} \]

So, 18/24 simplifies to 3/4.

If you struggle to find the GCD, you can use the Euclidean algorithm, which involves repeated division. Alternatively, prime factorisation can help: break both numbers into their prime factors and multiply the common factors.

Remember, a fraction is fully simplified when the numerator and the denominator have no common factors other than 1. Simplifying fractions is a useful skill for solving problems in algebra, geometry, and everyday life.