# Basic Steps of Dividing Fractions

The proper method for dividing fractions uses the idea of reciprocals. We talked about those once before. A reciprocal is a flipped fraction. The reciprocal of 2/3 is 3/2. The reciprocals of most fractions are improper. Dividing is just like division, but you need to create the reciprocal of your divisor (the second value). After you have the reciprocal, you just multiply. Here's a quick example...

1/3 ÷ 1/2 = ?
• Reciprocal of divisor: 2/1
• Rewrite as multiplication problem: 1/3 * 2/1 = ?
• Multiply numerators: 1*2 = 2
• Multiply denominators: 3*1=3
• Write out new fraction: 2/3
• Simplify: None needed.
Answer: 1/3 ÷ 1/2 = 2/3

If you want the short way, remember to flip the second term and then multiply.

# Dividing Simple Fractions

Let's try an example with simple numbers. It works just like the example above. This example will have you converting an improper fraction, since the answer will be greater than one.

4/5 ÷ 3/7 = ?
• Reciprocal of divisor: 7/3
• Rewrite as multiplication problem: 4/5 * 7/3 = ?
• Multiply numerators: 4*7=28
• Multiply denominators: 5*3=15
• Write out new fraction: 28/15
• Convert the improper fraction to a mixed number:
28/15 = 28÷15 = 1r13 = 1 13/15
• Simplify: None needed.
Answer: 4/5 ÷ 3/7 = 1 13/15

How did we get an answer bigger than 1? As with many of your early division problems, your dividend can go into the divisor more than one time. For example, 45 ÷ 9 = 5. The same thing works with fractions. You can have a really big fraction divided by a little one. There will be a whole bunch of little pieces that go into the bigger value. Try the example below where 9/10 is close to one and 1/20 is close to zero. 1/20 should go into 9/10 a bunch of times, since it is so small.

9/10 ÷ 1/20 = ?
• Reciprocal of divisor: 20/1
• Rewrite as multiplication problem: 9/10 * 20/1 = ?
• Multiply numerators: 9*20=180
• Multiply denominators: 10*1=10
• Write out new fraction: 180/10
• Convert the improper fraction to a mixed number:
180/10 = 180÷10 = 18
• Simplify: None needed.
Answer: 9/10 ÷ 1/20 = 18

That answer means that it takes 18 pieces of 1/20 to fill up one space the size of 9/10.

# Dividing Mixed Numbers

Time for some mixed numbers before we go. We're going to go ahead and make some improper fractions as we did with multiplication. You'll start by converting everything into improper fractions, do your flip, and then multiply. Finish it off with a little simplification if you need it.

5 1/3 ÷ 2 4/9 = ?
• Convert dividend and divisor into improper fractions:
5 1/3 = 5 + 1/3 = 15/3 + 1/3 = 16/3
2 4/9 = 2 + 4/9 = 18/9 + 4/9 = 22/9
• Rewrite the problem: 16/3 ÷ 22/9 = ?
• Reciprocal of the divisor: 9/22
• Rewrite as a multiplication problem: 16/3 * 9/22 = ?
• Multiply the numerators: 16*9=144
• Multiply the denominators: 3*22=66
• Write out new fraction: 144/66
• Convert the improper fraction to a mixed number:
144/66 = 144÷66 = 2r12 = 2 12/66
• Simplify the fraction: You've got 12 and 66. When you work it out, you can see that they have the common factor of 6. Divide the top and bottom by six to get 2/11.
Answer: 5 1/3 ÷ 2 4/9 = 2 2/11

There's an extra step in the process and the numbers can get big. Usually, you will have easier values in your examples. We like to challenge you. If you can make it this far, you can handle three digit division problems. Remember to take your time and do all of the steps. Sometimes you won't have to do anything for a step, but you still have to check. You won't always have to simplify your fractions but you always have to check.

► NEXT PAGE ON FRACTIONS & DECIMALS

► Or search the sites...