Dividing fractions by fractions
Online calculator — enter the values and get the result instantly, with the formula and a worked example.
a, c, e = numerator
b, d, f = denominator
-- = fraction line
Dividing fractions means finding how many times one fraction fits into another, or splitting a fractional quantity into equal parts. The key idea is that dividing by a fraction is the same as multiplying by its reciprocal, which is the fraction turned upside down, so a division problem quickly becomes a familiar multiplication. Because of this trick, the result can be larger than either starting fraction, which surprises many people the first time they see it. The operation works for proper fractions, improper fractions, and mixed numbers, as long as you never divide by zero. After multiplying, you usually simplify the answer to its lowest terms so the result is as clean as possible. Fraction division shows up everywhere in daily life, from scaling a recipe down to figuring out how many half-metre pieces you can cut from a longer board. It is also a foundation for algebra, ratios, and rates, where dividing quantities that are not whole numbers is completely routine. Mastering it gives you confidence with all the other fraction operations.
Quotient of fractions
–
Change the fractions — the bars show their size and the quotient
Worked example
numeratorA is 1
denominatorA is 4
numeratorB is 1
denominatorB is 2
| 1 | ||
| -- | ||
| 4 | 1 | |
| --- | = | --- |
| 1 | 2 | |
| -- | ||
| 2 |
We divide fractions as follows.
numeratorA is divided by numeratorB in our case
1/1=1
and denominatorA by denominatorB in our case
4/2=2
