Start with the sign

Signs give the fastest result in many comparisons. For example, 2/7 > -3/5 because a positive number is greater than a negative number. Likewise, 0 > -1/9. There is no need to convert either value to a decimal.

Compare two negative fractions

When both fractions are negative, compare their distance from zero and reverse the intuitive positive comparison. For example:

-2/5 = -0.4
-3/5 = -0.6
-2/5 > -3/5

The value at negative two-fifths is closer to zero, so it is greater. A number line makes this visible: values increase as you move right, and negative two-fifths is to the right of negative three-fifths.

Compare mixed numbers

1. Compare whole-number parts

For positive mixed numbers, the larger whole-number part is greater. Thus 3 1/8 > 2 7/8 even though the fractional part of the second value is larger.

2. Compare fractional parts when needed

If the whole-number parts match, compare the remaining fractions using a shared denominator, cross multiplication, or an exact calculator result. For 4 2/7 and 4 3/7, the second value is greater because the denominators match and three-sevenths is greater than two-sevenths.

3. Rewrite negative mixed numbers carefully

Read -2 1/3 as the negative of the entire mixed number, not as -2 + 1/3. Converting it gives -7/3. This avoids a sign error before comparison.

Use exact checking for close values

Decimals can help explain a result, but rounding can hide a small difference. When values are close, enter both expressions into the comparator and inspect the exact relationship. Cross multiplication is also useful when denominators are positive; if you multiply an inequality by a negative quantity, its direction changes.

Worked example

Compare -1 1/4 and -1 2/5. Convert the values: negative one and one-quarter is -5/4, while negative one and two-fifths is -7/5. Their decimal values are -1.25 and -1.4, so -1 1/4 > -1 2/5 because it is closer to zero.

Common mistakes

  • Choosing the larger numerator without considering the sign or denominator.
  • Assuming a more negative value is greater because its digits look larger.
  • Reading a negative mixed number as two separate signed terms.
  • Rounding close decimals before the exact comparison is finished.
  • Forgetting to reverse an inequality after multiplying by a negative number.

For the general methods, read four reliable ways to compare fractions. For unlike denominators, see the step-by-step lesson or use the comparison guide.