Divide one fraction by another.
The second fraction is flipped (its reciprocal is taken), then the two fractions are multiplied.
Quotient: a/b ÷ c/d = (a×d) ÷ (b×c)
A fraction division calculator divides one fraction by another and gives the quotient in lowest terms, with its decimal value. It flips the second fraction and multiplies, showing each stage, and it refuses to divide by a zero fraction.
Division of fractions answers 'how many of these fit into that' questions. How many 1/8 kg packets can be filled from 3/4 kg of tea? How many 3/4 metre pieces can be cut from 6 1/2 metres of cloth? It also turns up in speed, rate and unit-price problems when the quantities are fractional, and in Class 7 and 8 exercises that test the reciprocal rule.
1. Write the problem as a/b ÷ c/d and check that c is not zero.
2. Find the reciprocal of the divisor: d/c.
3. Multiply the first fraction by that reciprocal: a/b × d/c.
4. Compute (a × d) ÷ (b × c).
5. Reduce by the HCF of the numerator and denominator.
6. Check by multiplying your answer by c/d; you should get back a/b.
Dividing by a number is the same as multiplying by its reciprocal, the number that multiplies with it to give 1. For whole numbers, dividing by 4 is multiplying by 1/4. For a fraction c/d, the reciprocal is d/c, since c/d × d/c = 1. So a/b ÷ c/d = a/b × d/c. Another way to see it: multiply both a/b and c/d by d/c, which leaves the quotient unchanged, and the divisor becomes 1.
3/4 ÷ 1/8 asks how many eighths are in three quarters. Since each quarter holds two eighths, three quarters hold six, and the formula gives (3 × 8) ÷ (4 × 1) = 24/4 = 6. Whenever the divisor is less than 1, the quotient is bigger than the dividend. This is correct, not a mistake, and it is a useful sense check: if you divide by a proper fraction and your answer shrinks, you probably multiplied instead.
A zero fraction such as 0/5 has no reciprocal, because no number multiplied by zero gives 1. So division by a zero fraction is undefined, and the calculator reports it. A zero in the first fraction is fine: 0 divided by anything non-zero is 0. Denominators of zero in either fraction are also rejected, because such a fraction does not represent a number in the first place.
Gopal runs a small tea stall and wants to know how many 1/8 kg packets he can fill from the 3/4 kg of loose tea he has in stock.
Starting point: 3/4 ÷ 1/8
Flip the second fraction and multiply: 3/4 × 8/1
Multiply across: (3 × 8) / (4 × 1) = 24/4
Reduce to lowest terms: Divide both by their GCD of 4 → 6/1
Answer: Result 6/1
Flipping the first fraction instead of the divisor.
Flipping both fractions before multiplying.
Dividing tops and bottoms separately without checking that they divide evenly.
Treating a mixed number such as 2 1/2 as 2 × 1/2 instead of 5/2 before dividing.
Counting how many portions of a fractional size can be made from a stock.
Cutting cloth, pipe or wire into pieces of fractional length.
Finding a unit rate, such as rupees per kilogram when the weight is a fraction.
Speed, time and distance problems with fractional hours.
Class 7 and 8 exercises on reciprocals and division of fractions.
Why does dividing by a fraction make the answer bigger?
Dividing by a number smaller than one always makes the result bigger. Asking how many quarters fit into a whole gives 4, which is bigger than the whole you started with.