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).

When comparing fractions with the same denominator, the fraction with the larger numerator is greater. For example, $$\frac{3}{5} > \frac{2}{5}$$ because 3 > 2.

To compare fractions with different denominators, convert them to equivalent fractions with a common denominator or convert them to decimals.

Two fractions are equivalent if they represent the same part of a whole, even if they have different numerators and denominators. For example, $$\frac{1}{2}$$ is equivalent to $$\frac{2}{4}$$ .

The first step in comparing fractions is to find a common denominator or convert them to decimals.

$$\frac{3}{4} > \frac{1}{2}$$ because when both are converted to a common denominator (4), $$\frac{1}{2} = \frac{2}{4}$$ .

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 $$\frac{5}{4}$$ .

A mixed number is a whole number combined with a proper fraction, such as $$1 \frac{1}{2}$$ .

To convert an improper fraction to a mixed number, divide the numerator by the denominator. The quotient is the whole number, and the remainder is the new numerator.