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, $$\frac{3}{8} < \frac{5}{8}$$ because 3 < 5.

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

Equivalent fractions are different fractions that represent the same value. For example, $$\frac{1}{2}$$ is equivalent to $$\frac{2}{4}$$ .

To find an equivalent fraction, multiply or divide both the numerator and the denominator by the same non-zero number. For example, multiplying $$\frac{1}{2}$$ by 3 gives $$\frac{3}{6}$$ .

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

To determine if one fraction is greater than another, compare their values by finding a common denominator or converting them to decimals.

In comparing fractions, if the denominators are the same, compare the numerators. If the numerators are the same, compare the denominators.

To compare $$\frac{6}{12}$$ and $$\frac{3}{4}$$ , convert $$\frac{6}{12}$$ to an equivalent fraction with a denominator of 4: $$\frac{6}{12} = \frac{2}{4}$$ . Then compare: $$\frac{2}{4} < \frac{3}{4}$$ .

A number line model for fractions visually represents fractions on a line, showing their relative sizes and positions. For example, $$\frac{1}{2}$$ is halfway between 0 and 1.