Comparing Fractions

A fraction represents a part of a whole and is written as $$\frac{a}{b}$$ , where 'a' is the numerator (the number of parts) and 'b' is the denominator (the total number of equal parts).

Comparing fractions involves determining which fraction is larger, smaller, or if they are equal by analyzing their numerators and denominators.

To compare fractions with different denominators, convert them to equivalent fractions with a common denominator, then compare the numerators.

An equivalent fraction is a fraction that represents the same value as another fraction, even though the numerator and denominator may be different. For example, $$\frac{1}{2}$$ is equivalent to $$\frac{2}{4}$$ .

A fraction $$\frac{a}{b}$$ is greater than $$\frac{c}{d}$$ if $$a \times d > c \times b$$ .

$$\frac{4}{8}$$ is equivalent to $$\frac{1}{2}$$ because both represent the same value.

Two fractions are equal if they represent the same part of a whole, meaning their cross-products are equal.

To find a fraction greater than $$\frac{2}{3}$$ , you can choose any fraction with a numerator larger than 2 when the denominator is 3 or less, such as $$\frac{3}{3}$$ .

A proper fraction is a fraction where the numerator is less than the denominator, such as $$\frac{3}{4}$$ .

An improper fraction is a fraction where the numerator is greater than or equal to the denominator, such as $$\frac{5}{4}$$ .