Dividing Fractions

To divide fraction by a fraction multiply numerator of the first fraction by the denominator of the second fraction and denominator of the first fraction by the numerator of the second fraction, i.e. `color(green)(a/b-:c/d=(a/b)/(c/d)=(ad)/(bc))`.

After this you, possibly, need to reduce fraction.

Note! Rules for determining sign of the result are same as when dividing integers.

Example 1 . Divide `5/12` by `11/7`.

`color(blue)(5)/color(red)(12)-:color(red)(11)/color(blue)(7)=(5*7)/(12*11)=35/132`.

Fraction is irreducible.

Answer: `35/132`.

Next example.

Example 2. Divide `16/11` by `8/3`.

`(color(blue)(16)/color(red)(11))/(color(red)(8)/color(blue)(3))=(16*3)/(11*8)=48/88`.

Reduce fraction: `48/88=6/11`.

Answer: `6/11`.

Next example.

Example 3. Divide `39/7` by `5/2` .

`(39/7)/(5/2)=(39*2)/(5*7)=78/35`.

Convert to mixed number if needed: `78/35=2 8/35`.

Answer: `78/35=2 8/35`.

Now, it is time to practice.

Exercise 1. Divide `2/5` by `1/12`.

Answer: `24/5=4 4/5`.

Next exercise.

Exercise 2. Divide 15 by `-5/7` .

Answer: -21. Hint: `15=15/1`.

Last exercise.

Exercise 3. Divide `-21/5` by `-35/4`.

Answer: `12/25`.