HesapHanem

Subtract Fractions Calculator

Enter the numerators and denominators of two fractions to subtract them.

How it is calculated

The tool subtracts a/b − c/d with cross-multiplication: numerator = a·d − c·b and denominator = b·d. If the denominator comes out negative, the signs are flipped so that it is always positive. The fraction is then reduced by dividing the numerator and the denominator by their greatest common divisor. Three forms of the answer are shown: the reduced fraction, a decimal rounded to four places, and a mixed number such as 1 3/4 when the value is larger than 1 (a proper fraction or a whole number is shown as is, and a result of zero as 0). A negative result keeps its minus sign. Numerators and denominators must be whole numbers: anything after a decimal point is cut off, not rounded, so 1.9 is read as 1. A denominator of 0 returns no result.

Worked example

Subtract 3/8 from 5/6. Step 1: cross-multiply, 5 × 8 − 3 × 6 = 40 − 18 = 22. Step 2: the denominator is 6 × 8 = 48, so the raw answer is 22/48. Step 3: the greatest common divisor of 22 and 48 is 2, so divide both by 2. The reduced result is 11/24. As a decimal, 11 ÷ 24 is 0.4583. Since 11 is smaller than 24, there is no whole part and the mixed form is the same fraction.

Try this example →

Common mistakes

  • Subtracting the numerators and the denominators separately. 5/6 − 3/8 is not 2/(−2); the fractions must first be put over a common denominator, which the cross-multiplication does.
  • Entering a decimal or a mixed number in a field. Each field takes a whole number, so 1 1/2 must be entered as 3/2, and a value like 1.9 would be cut to 1, not rounded.
  • Putting the fractions in the wrong order. The tool calculates the first minus the second, so 1/3 − 1/2 gives −1/6, while 1/2 − 1/3 gives 1/6.
  • Expecting an unreduced answer. 1/2 − 1/4 is shown as 1/4, not 2/8, so reduce your own working to lowest terms before comparing.
  • Entering 0 as a denominator. A fraction with a zero denominator is undefined, and the tool returns no result.

Sources

About this calculator

To subtract one fraction from another, a/b − c/d, this calculator converts both to a common denominator (the least common multiple of b and d), subtracts the numerators, and reduces the result to lowest terms by dividing out the greatest common divisor — equivalent to the cross-multiplication shortcut (ad − bc) ÷ bd.

The result is shown as a simplified fraction, its decimal equivalent, and — when the numerator exceeds the denominator — a mixed number, so the answer is ready to use however you need it. Students checking homework and anyone doing measurements in recipes, woodworking, or sewing that mix fractional units use it to subtract quantities without manually finding a common denominator.

Was this helpful?

You can pick up to 3 reactions.

Comments (1)

  • Editorial team

    Tape-measure work is a natural fit if you turn mixed numbers into improper fractions first, since each field takes whole numbers only. To take 2 3/16 from 6 1/2, enter 13/2 minus 35/16: the tool returns 69/16, which is 4 5/16 in the mixed field, or 4.3125 as a decimal. Writing 16ths as the common denominator by hand is where most slips happen. Which measurements do you subtract most often, inches or recipe cups?

Popular calculators

Loan Calculator

Monthly payment, total interest and full amortization schedule.

Percentage Calculator

Percent change, percent of, and ratio calculations.

Discount Calculator

Calculate final price, savings, and discount amount.

BMI Calculator

Body mass index from height and weight (metric or imperial).

Age Calculator

Compute your exact age in years, months and days from a birth date.

Compound Interest Calculator

Calculate the final amount and interest earned with compounding.

All Calculators