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 equal if they represent the same part of a whole. For example, $$\frac{1}{2} = \frac{2}{4}$$ .

To find a common denominator, identify the least common multiple (LCM) of the denominators of the fractions you want to compare.

You can tell if one fraction is greater than another by comparing their values after converting them to a common denominator or decimals.

Fractions can be interpreted as division. For example, $$\frac{a}{b}$$ means 'a divided by b'.

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.