In mathematics, improper fractions are those in which the numerator (the number above the dash) is greater than or equal to the denominator (the number below the dash). To convert one to a mixed number (a number consisting of an integer and a fraction, such as 2 3/4), you must divide the numerator by the denominator. Write the integer part of the quotient next to the fraction that is composed of the remainder, as the numerator, and the denominator of the original fraction; at this point, you have found the mixed number!
Steps
Part 1 of 2: Converting an Improper Fraction
Step 1. Divide the numerator by the denominator
Write the improper fraction and then perform the division; in other words, you have to solve the operation that is already proposed by the fraction itself. Don't forget to write the rest.
- Consider this example. Suppose you need to transform the fraction 7/5 into a mixed number. To start divide 7 by 5:
- 7/5 → 7 ÷ 5 = 1 R2.
Step 2. Write the whole number of the solution
This corresponds to the integer part of the mixed number (the one to the left of the fractional part); in other words, you just have to write the quotient of the division leaving out the remainder for the moment.
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In the above example, since the answer is "1 with the remainder of 2", you have to ignore the remainder and just write
Step 1..
Step 3. Build the fraction with the original remainder and denominator
You have to find the fractional portion of the mixed number; then proceed to put the remainder in place of the nominator and use the denominator of the original improper fraction. Write this fraction to the left of the whole part and you have found the mixed number you were looking for.
- Considering the example described in the previous steps, the remainder is "2". Then put it in the place of the numerator, use "5" as the denominator and you get "2/5". This fraction is associated with the whole number to obtain the result:
- 1 2/5.
Step 4. To return to the improper fraction add the whole number to the fractional portion
Mixed numbers are easy to read, but they are not always the best choice. For example, if you are multiplying a fraction by a mixed number, it is much easier to convert it to an improper fraction first. To do this, multiply the integer portion by the denominator and add the product to the numerator.
- If you want to use the example number (1 2/5) to find the improper fraction, you should proceed as follows:
- 1 × 5 = 5 → (2 + 5)/5 = 7/5.
Part 2 of 2: Troubleshoot
Step 1. Convert 11/4 to a mixed number
This is a simple problem to solve, just follow the instructions described above. The step-by-step procedure is described below.
- Starting with the fraction 11/4, divide the numerator by the denominator;
- 11 ÷ 4 = 2 R3. At this point you have to "construct" the fractional part using the remainder and the original denominator.
- 11/4 = 2 3/4.
Step 2. Convert 99/5
In this case, the numerator is a big value, but you don't have to be intimidated; the process does not change! Here's how to do it:
- Consider the fraction 99/5, how many times does 5 go into 99? Since 5 is exactly 20 times in 100, you can say that 5 is 19 times in 99.
- 99 ÷ 5 = 19 R4; now you can "assemble" the mixed number just like you did before.
- 99/5 = 19 4/5.
Step 3. Convert 6/6 to a mixed number
Up until now you have used improper fractions where the numerator is greater than the denominator. But what happens when the two numbers are the same? Read on to find out.
- Starting with 6/6, you can say that 6 goes into 6 once with no remainder.
- 6 ÷ 6 = 1 R0; since a fraction with a null numerator is zero, the mixed number has no fractional portion, only the whole number.
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6/6 =
Step 1..
Step 4. Convert 18/6
If the numerator is a multiple of the denominator, you don't have to worry about the rest; you just have to solve the division to get the answer. Here is the procedure:
- Consider 18/6; since 18 equals 6 × 3, you know the remainder is zero, so you don't have to worry about the fractional portion of the mixed number.
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18/6 =
Step 3..
Step 5. Turn -10/3 into a mixed number
The procedure for negative numbers is the same as for positive numbers:
- -10/3;
- -10 ÷ 3 = -3 R1;
- -10/3 = - 3 1/3.
Advice
- The presence of improper fractions is not necessarily negative; in some cases, they are in fact more useful than mixed numbers. For example, if you are multiplying two fractions together, it is better to use improper fractions that allow you to calculate the product of the numerators and denominators: 1/6 × 7/2 = 7/12; if you try instead to carry out this multiplication: 1/6 × 3 1/2 you realize that it is not so simple.
- Mixed numbers are more effective for expressing real-life quantities. For example, a recipe has 4 1/2 pounds of flour among the ingredients, but you would never see "9/2 pounds of flour".
