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Comparing Fractions Calculator

Compare two fractions to see which is larger, smaller, or if they are equal, with the working shown over a common denominator.

What this tool does

Compare two fractions to see which is larger, smaller, or if they are equal, with the working shown over a common denominator. You fill in these fields: First numerator, First denominator, Second numerator, and Second denominator. It shows comparison, first fraction, second fraction, common denominator, first fraction over it, and second fraction over it.

Inputs

  • First numerator: A whole number.
  • First denominator: A whole number. Cannot be 0.
  • Second numerator: A whole number.
  • Second denominator: A whole number. Cannot be 0.

How to use

  1. Enter the first numerator.
  2. Enter the first denominator.
  3. Enter the second numerator.
  4. Enter the second denominator.
  5. Read the result: comparison, first fraction, second fraction, common denominator, first fraction over it, and second fraction over it. It appears once every required field has a valid value.

Worked examples

Example 1. Inputs:

  • First numerator: 3
  • First denominator: 4
  • Second numerator: 2
  • Second denominator: 3

Results:

  • Comparison: 3/4 > 2/3
  • First fraction: 3/4 (as a decimal: 0.75)
  • Second fraction: 2/3 (as a decimal: 0.666667)
  • Common denominator: 12
  • First fraction over it: 9/12
  • Second fraction over it: 8/12
  • Both fractions are reduced to lowest terms and rewritten with the same denominator, 12. Comparing their numerators, 9 and 8, gives the result.

How this is worked out: Both fractions are already in lowest terms. lcm(4, 3) = 12. 3/4 = 9/12 and 2/3 = 8/12. Since 9 > 8 the first is larger. 3 / 4 = 0.75 and 2 / 3 = 0.666666...

Example 2. Inputs:

  • First numerator: 1
  • First denominator: 2
  • Second numerator: 2
  • Second denominator: 4

Results:

  • Comparison: 1/2 = 2/4
  • First fraction: 1/2 (as a decimal: 0.5)
  • Second fraction: 1/2 (as a decimal: 0.5)
  • Common denominator: 2
  • First fraction over it: 1/2
  • Second fraction over it: 1/2
  • Both fractions are reduced to lowest terms and rewritten with the same denominator, 2. Comparing their numerators, 1 and 1, gives the result.

How this is worked out: 2/4 divides by the common factor 2 to give 1/2, so both fractions are 1/2. lcm(2, 2) = 2, and 1/2 = 1/2. Cross products agree too: 1 * 4 = 4 and 2 * 2 = 4.

Example 3. Inputs:

  • First numerator: 6
  • First denominator: -8
  • Second numerator: -9
  • Second denominator: -12

Results:

  • Comparison: 6/-8 < -9/-12
  • First fraction: -3/4 (as a decimal: -0.75)
  • Second fraction: 3/4 (as a decimal: 0.75)
  • Common denominator: 4
  • First fraction over it: -3/4
  • Second fraction over it: 3/4
  • Both fractions are reduced to lowest terms and rewritten with the same denominator, 4. Comparing their numerators, -3 and 3, gives the result.

How this is worked out: 6/-8 = -6/8 = -3/4 (sign moved to the numerator, common factor 2 removed). -9/-12 = 9/12 = 3/4 (two minus signs cancel, common factor 3 removed). Both already have denominator 4, so compare -3 with 3: -3 < 3, the first is smaller.

Example 4. Inputs:

  • First numerator: 0
  • First denominator: 5
  • Second numerator: -1
  • Second denominator: 7

Results:

  • Comparison: 0/5 > -1/7
  • First fraction: 0 (as a decimal: 0)
  • Second fraction: -1/7 (as a decimal: -0.142857)
  • Common denominator: 7
  • First fraction over it: 0/7
  • Second fraction over it: -1/7
  • Both fractions are reduced to lowest terms and rewritten with the same denominator, 7. Comparing their numerators, 0 and -1, gives the result.

How this is worked out: 0/5 = 0, which in lowest terms is 0/1. lcm(1, 7) = 7. 0 = 0/7 and -1/7 stays -1/7. Since 0 > -1 the first is larger: zero is greater than any negative fraction.

Limitations

  • Takes whole numbers only; mixed numbers and decimals must be converted to fractions first.
  • Values so large that the common denominator cannot be held exactly are refused rather than approximated.
  • The decimal values shown are for reference. The comparison itself is exact and does not use them.

FAQs

Q: How does the calculator decide which fraction is larger?
A: It reduces both fractions to lowest terms, rewrites them over their least common denominator, and compares the two numerators. The page shows that working so you can check it.
Q: Can I compare negative fractions?
A: Yes. Put the minus sign on the numerator or the denominator. A fraction such as 1/-2 is treated as -1/2, so -1/2 is correctly smaller than 1/3.
Q: What if the two fractions are equal?
A: The result shows an equals sign and both fractions reduce to the same lowest terms, for example 1/2 and 2/4.
Q: Can I enter mixed numbers or decimals?
A: No. Each field takes a whole number. Turn a mixed number into an improper fraction first, for example 1 1/2 becomes 3/2.
Q: Why can't the denominator be 0?
A: Division by zero has no answer, so a fraction with a denominator of 0 has no value to compare. The tool asks for a different denominator.

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