An ordinary fraction is a fraction whose upper number is greater than its lower number, such as 5/2. Mixed fractions consist of whole numbers and fractions, such as 21/2. It's usually easier to imagine 21/2 pizza than “five-half” pizza. So, the skill to convert common fractions to mixed fractions is very useful. Division is the fastest way to do it, but there's an easier way if you're having trouble with the first method.
Step
Method 1 of 2: Using Division
Step 1. Start with a common fraction
We will use 15/4 as our example. This is an ordinary fraction because the numerator, 15, is greater than the denominator, 4.
If you're not already comfortable with fractions or division, start with the examples below
Step 2. Rewrite the common fraction as a division problem
Write the fraction as a long division problem. Always write down the numerator divided by the denominator. In our example, 15 ÷ 4.
Step 3. Start solving the division problem
Review long division first if you're not sure what to do. This example will be easier to follow if you write down the long division problem as you read it:
- Divide the first digit, 1 by 4. The number 1 is not divisible by 4. So, we have to enter the next digit.
- Divide the first two digits, 15 by 4. How much is 15 divided by 4? If you're not sure, guess and check if you have the correct answer using multiplication.
- The answer is 3. So, write 3 in the answer line, above the number 5.
Step 4. Find the rest
Unless the numbers are divisible by evenly, there will be a remainder. Here's how to find the remainder of the long division problem:
- Multiply the answer by the divisor (the number on the left). In our example, 3 x 4.
- Write the answer under the number you divide (the number under the divisor). In our example, 3 x 4 = 12. So, write 12 under 15.
-
Subtract the result from the number divided: 15 - 12 =
Step 3.. This is the rest.
Step 5. Write down the mixed number using your result
A mixed number consists of a whole number plus a fraction. Once you've solved your division problem, you've got everything you need to write this mixed number:
-
The whole number is the answer to your division problem. In this problem, the integer is
Step 3..
-
The numerator of the fraction is the remainder of the division. In this case, the numerator is
Step 3..
-
The denominator of the fraction is the same as the denominator of the original fraction. In this case, the denominator is
Step 4..
- Write these values as mixed fractions: 33/4.
Method 2 of 2: No Division
Step 1. Write down the fraction
An ordinary fraction is any fraction that has a top number that is greater than the bottom number. For example, 3/2 is a common fraction because 3 is greater than 2.
- The top number in a fraction is called numerator. The bottom number is called denominator.
- This method takes a long time for large fractions. If the numerator is much larger than the bottom number, the above division method is much faster.
Step 2. Remember the fractions that are equal to one
Did you know that 2 2 = 1 or that 4 4 = 1? In fact, any number divided by itself equals one. Fractions are like that too, like 2/2 = 1, 4/4 = 1, even 397/397 equals 1!
Step 3. Divide the fraction into two parts
It sounds easy to convert a fraction to a whole number. Let's see if we can convert our common fraction:
- To 3/2, the denominator (bottom number) is 2.
- 2/2 is a fraction that is easy to simplify because the top and bottom numbers are the same. We want to get it out of the larger fraction and find out the remainder.
- Write the following: 3/2 = 2/2 + ?/2.
Step 4. Find the second part
How do we turn the question mark into a number? If you don't know how to add and subtract fractions, don't worry. When the denominators (bottom numbers) are the same, we can leave the denominators alone and turn the problem into a regular addition. Here is a step by step guide for our example, 3/2 = 2/2 + ?/2:
- Look at the numerator (top number) only. It says 3 = 2 + "?". What number can we write to replace the question mark so that we can solve this problem? What numbers can you add 2 to get 3?
- The answer is 1 because 3 = 2 + 1.
- When you get the answer, rewrite the equation, including the denominators: 3/2 = 2/2 + 1/2.
Step 5. Simplify the fraction
Now, you know that our common fraction is equal to 2/2 + 1/2. We also know that 2/2 = 1, just like any fraction that has the same top and bottom digits. It means that you can eliminate 2/2 and replace it with 1. Now, we have 1 + 1/2 which is a mixed fraction! For this example, the problem is solved.
- Once you find the answer, you don't have to write down the + symbol again. Just write it down 11/2.
- A mixed number is a whole number plus a fraction.
Step 6. Repeat these instructions if the fraction is still a regular fraction
Sometimes, the fractional part of your answer will still be an ordinary fraction with a larger numerator than the denominator. In this case, you can repeat these instructions by changing the common fraction to another mixed number. Don't forget to re-add the integer “1” when you finish. Here is an example, which is changing 7/3 to a mixed fraction:
- 7/3 = 3/3 + ?/3
- 7 = 3 + ?
- 7 = 3 + 4
- 7/3 = 3/3 + 4/3
- 7/3 = 1 + 4/3
- The fraction is an ordinary fraction. So just leave 1 for now and do the same for the usual fractions: 4/3 = 3/3 + ?/3
- 4 = 3 + ?
- 4 = 3 + 1
- 4/3 = 3/3 + 1/3
- 4/3 = 1 + 1/3
- The fraction is no longer an ordinary fraction, so we're done. Remember to add the 1 we left out earlier: 1 + 1 + 1/3 = 21/3.
