DIVIDING FRACTIONS

Dividing fractions can be fun once you get to know the game.

To divide a fraction by a fraction you have to turn the second fraction upside down. For instance, ½ divided by ¼ = ½ divided by 4/1. After you turn the fraction upside down then you multiply both numerators together and both of the denominators together. Like this: ½ x 4/1 = 4/2 = 2. Simple, huh?

Another example is ¾ divided by 1/3.
¾ divided by 1/3 = ¾ divided 3/1 = ¾ x 3/1 = 9/4 = 2 ¼.

Every once in a while you may come across a whole number divided by a fraction. In this case, you turn the whole number into a proper fraction before dividing, then invert and multiply across. It is almost like a multiplication problem in disguise.

2 divided by 1/3 = 2/1 divided by 1/3 = 2/1 divided by 3/1 = 2/1 x 3/1 = 6/1 = 6

Another example is 3 divided by ¼ = 3/1 divided by ¼ = 3/1 divided by 4/1 =
3/1 x 4/1 = 12/1 = 12


Also, occasionally you will come across a fraction divided by a whole number.
When this happens it’s just like flipping a whole number divided by a fraction around.
½ divided by 2 = ½ divided by 2/1 = ½ divided by ½ = ½ x ½ = ¼.

2/7 divided by 3 = 2/7 divided by 3/1 = 2/7 divided by 1/3 = 2/7 x 1/3 = 2/21.


If you have a mixed number divided by a mixed number, you just have to change the mixed numbers into improper fractions before starting the equations. If you had
4 ½ divided by 2 1/3 = 9/2 divided by 7/3 = 9/2 divided by 3/7 = 9/2 x 3/7 =
27/ 14 = 1 13/14.

Another example is 7 6/8 divided by 6 1/3=
62/8 divided by 19/3 = 62/8 divided by 3/19 – 62/8 divided by 19/3 = 186/152 =
1/34/52 = 1 17/76. By the way, that was a challenge problem!

Algorithm:
Step 1: Make improper fractions if necessary out of whole and mixed numbers
Step 2: Invert second fraction
Step 3: Multiply across
Step 4: Simplify (if necessary)



DIVIDING FRACTIONS

Here are some more examples of dividing fractions.

1. 2/3 divided by 5/8 =
2. 4/9 divided by 3/5 =
3. 2 divided by 1/7 =
4. 2 divided by 1/8 =
5. ½ divided by 3 =
6. 2/3 divided by 4 =
7. 2 3/8 divided by 1 1/5 =
8. 1 ½ divided by 2 1/3 =







Answers:

1. 2/3 divided by 5/8 = 2/3 divided by 8/5 = 2/3 x 8/5 = 16/15 = 1 1/15
2. 4/9 divided by 3/5 = 4/9 divided by 5/3 = 4/9 x 5/3 = 20/27
3. 2 divided by 1/7 = 2/1 divided 1/7 = 2/1 divided 7/1 =
2/1 x 7/1 = 14/1 = 14
4. 2 divided by 1/8 = 2/1 divided by 8/1 = 2/1 x 8/1 = 16/1 = 16
5. ½ divided by 3 = ½ divided by 3/1 = ½ divided by 1/3 =
½ x 1/3 = 1/6
6. 2/3 divided by 4 = 2/3 divided by 4/1 = 2/3 divided by ¼ =
2/3 x ¼ = 2/12 = 1/6
7. 2 3/8 divided by 1 1/5 = 19/8 divided by 6/5 = 19/8 divided by 5/6 =
19/8 x 5/6 = 95/48 = 1 47/48
8. 1 1/2 divided by 2 1/3 = 3/2 divided by 7/3 = 3/2 divided by 3/7 =
3/2 x 3/7 = 9/14

Congratulations, you can now divide fractions!