Compare Fractions Calculator

How to compare fractions

It is not always clear that fractions are equal. There are a number of rules for comparing fractions.

To compare fractions:

1. If the fractions are mixed (there is an integer part) convert them to improper.
2. Make the denominators of fractions the same.
3. Use the rule: Of two fractions with the same denominators, the one with the larger numerator is greater and the one with the smaller numerator is smaller. Of two fractions with the same numerator, the one with the smaller denominator is greater.

Example for comparing fractions

Compare fractions ${\displaystyle 5⁤\frac{39}{7}}$$and$${\displaystyle 6⁤\frac{1}{3}}$

1. Convert the mixed fraction ${\displaystyle 5⁤\frac{39}{7}}$ to improper:

${\displaystyle 5⁤\frac{39}{7}}$$=$${\displaystyle \mathrm{}⁤\frac{\mathrm{(5\; ·\; 7)\; +\; 39}}{7}}$$=$${\displaystyle \mathrm{}⁤\frac{74}{7}}$

2. Convert the mixed fraction ${\displaystyle 6⁤\frac{1}{3}}$ to improper:

${\displaystyle 6⁤\frac{1}{3}}$$=$${\displaystyle \mathrm{}⁤\frac{\mathrm{(6\; ·\; 3)\; +\; 1}}{3}}$$=$${\displaystyle \mathrm{}⁤\frac{19}{3}}$

3. Let's make the denominators the same, for this we multiply the numerator of the first fraction by the denominator of the second fraction, and the numerator of the second fraction by the denominator of the first. The new common denominator will be the product of the denominators of the first and second fractions.

${\displaystyle \mathrm{}⁤\frac{74}{7}}$${\displaystyle \mathrm{=}⁤\frac{\mathrm{74\; \cdot \; 3}}{\mathrm{7\; \cdot \; 3}}}$${\displaystyle \mathrm{=}⁤\frac{222}{21}}$

${\displaystyle \mathrm{}⁤\frac{19}{3}}$${\displaystyle \mathrm{=}⁤\frac{\mathrm{19\; \cdot \; 7}}{\mathrm{7\; \cdot \; 3}}}$${\displaystyle \mathrm{=}⁤\frac{133}{21}}$

4. Of two fractions with the same denominator, the one with the larger numerator is larger.

${\displaystyle \mathrm{}⁤\frac{222}{21}}$$>$${\displaystyle \mathrm{}⁤\frac{133}{21}}$

${\displaystyle 5⁤\frac{39}{7}}$$>$${\displaystyle 6⁤\frac{1}{3}}$