Dividing fractions - it's that easy

Dividing fractions is always a challenge. But with a simple trick it becomes very easy. We explain how to solve double fractions using the reciprocal value.

The division of fractions is so easy

• If you have a double fraction or the division of two fractions in front of you (steps 1 and 2 in the graphic), you can convert this division into a product. This is much easier to calculate.
• If you consider a double fraction (a / b) / (c / d), keep the first fraction - i.e. above the large fraction line or before the division sign - (a / b) and multiply it by the reciprocal of the second fraction - ie (d / c).
• You can get the reciprocal of a fraction simply by swapping the numerator and denominator, i.e. the numbers above and below the fraction line. 1/2 becomes 2/1 (which in this case you could even simplify to 2).
• Let us now consider the double fraction (4/3) / (2/9) as an example.
• The first fraction remains unchanged: (4/3) and is multiplied by the reciprocal of (2/9) - i.e. (9/2). For this you can write all numerators and denominators together over or under a large fraction.
• In this example you can also simplify by shortening 9 and 3 or 4 and 2.
• This gives you 2 * 3 in the numerator and 1 * 1 in the denominator. This then simply results in a clean 6. Note that * is often used as a multiplication sign.
• The example is simple, but the method works with all numbers that can be multiplied and divided regularly. In any case, it will make it much easier for you to deal with double fractions and division.