Problem 38 Which fraction is not equal to \... [FREE SOLUTION] (2024)

Short Answer

The Greatest Common Divisor

The Greatest Common Divisor, or GCD, is crucial in simplifying fractions. The GCD is the highest number that divides both the numerator and the denominator without leaving a remainder.
For example, consider the fraction \(\frac{30}{54}\). The GCD of 30 and 54 is 6 because it is the largest number that can evenly divide both. When you divide both the numerator and the denominator by 6, you get \(\frac{5}{9}\).
Simplifying fractions like this helps us check if two fractions are equal. If simplified versions are the same, the original fractions are equivalent too.

Equivalent Fractions

Equivalent fractions represent the same part of a whole even if they have different numerators and denominators. For example, \(\frac{15}{27}\) and \(\frac{5}{9}\) are equivalent because they simplify to the same fraction.
To find out if fractions like \(\frac{40}{74}\) and \(\frac{5}{9}\) are equivalent, we simplify them. If their simplified versions match, they are equivalent. If not, they are different.
Simplifying \(\frac{40}{74}\) gives us \(\frac{20}{37}\), which is not \(\frac{5}{9}\), so these fractions are not equivalent.

Numerator and Denominator

The numerator and denominator are the two key parts of a fraction. The numerator is the top number, indicating how many parts you have. The denominator is the bottom number, showing how many equal parts the whole is divided into.
For instance, in the fraction \(\frac{5}{9}\), 5 is the numerator and 9 is the denominator. Simplifying fractions involves finding common divisors for both the numerator and the denominator.
This process maintains the balance between the two parts of the fraction, ensuring the fraction represents the same value even after simplification.