Subtract one fraction from another.
Both fractions are put over a common denominator, then the numerators are subtracted.
Difference: a/b − c/d = (a×d − c×b) ÷ (b×d)
A fraction subtraction calculator takes one fraction away from another and gives the difference in lowest terms, with its decimal value. It shows the common denominator, the rewritten fractions and the subtraction of the numerators, and it handles results that come out negative.
Subtraction of fractions answers 'how much is left' and 'how much more is needed'. If 7/10 of a tank was full and 2/5 has been used, what remains? If a project is 3/4 done, what fraction is still pending? These questions appear in Class 6 and 7 textbooks, in time-and-work problems in competitive exams and in everyday measuring. The calculator also helps in algebra, where subtracting rational expressions follows the same pattern.
1. Write the fractions as a/b (the one you start with) and c/d (the one you take away).
2. Choose a common denominator, such as b × d or the LCM of b and d.
3. Rewrite both fractions over that denominator.
4. Subtract the numerators in order: a/b − c/d = (a × d − c × b) ÷ (b × d).
5. Reduce the result by dividing by the HCF of the numerator and denominator.
6. If the numerator is negative, the result is negative; keep the minus sign in front of or on the numerator.
Addition of fractions is commutative, so the order of the two fractions does not matter. Subtraction is not. a/b − c/d and c/d − a/b have the same size but opposite signs. In the formula (a × d − c × b) ÷ (b × d), the first fraction's cross-product comes first. A negative answer simply means you subtracted more than you had. In real contexts, such as fuel left or work remaining, a negative result usually means the inputs were entered the wrong way round.
When one denominator is a multiple of the other, as 10 is of 5, the product denominator contains a repeated factor, so reduction at the end is large. For 7/10 − 2/5 the product method gives 35/50 − 20/50 = 15/50, which reduces by 5 to 3/10. Using the LCM, 10, gives 7/10 − 4/10 = 3/10 directly. Both routes are correct. Spotting that one denominator divides the other saves time in exams.
For mixed numbers such as 3 1/4 − 1 2/3, subtracting the fraction parts alone gives a negative, so you must borrow 1 from the whole part, turning 3 1/4 into 2 5/4. Many errors come from this borrowing step. Converting both to improper fractions first, 13/4 − 5/3, avoids it entirely and is how you would enter the problem here. The result, 19/12, can then be rewritten as 1 7/12.
Vikram's water tank was 7/10 full in the morning, and by evening his family had used water equal to 2/5 of the tank.
Starting point: 7/10 − 2/5
Use a common denominator: 10 × 5 = 50
Rewrite both fractions: 35/50 − 20/50
Subtract the numerators: 35 − 20 = 15
Reduce to lowest terms: Divide both by their GCD of 5 → 3/10
Answer: Result 3/10
Subtracting tops and bottoms separately, as in 7/10 − 2/5 = 5/5.
Swapping the order of the fractions and getting the sign wrong.
Borrowing incorrectly in mixed-number subtraction.
Rewriting only one fraction over the common denominator.
Finding what remains of a tank, packet or budget after a fractional amount is used.
Time-and-work questions where the remaining share of a job is needed.
Measuring how much longer a cut piece must be, in inches and fractions.
Class 6 and 7 fraction exercises and answer checking.
Can the result be negative?
Yes, if the second fraction is bigger than the first. The minus sign then carries into the top number of the answer.