Author:
Marcus Baldwin
Date Of Creation:
14 June 2021
Update Date:
12 May 2024
Content
An irregular fraction is a fraction whose numerator (top number) is greater than or equal to the denominator (bottom number). A mixed fraction (mixed number) includes an integer and a regular fraction, for example, 2 3/4. To convert an improper number to a mixed number, divide the numerator by the denominator; write down the integer result of division as the whole part of the mixed number, write the remainder in the numerator of the fractional part, and write down the original denominator in the denominator.
Steps
Method 1 of 2: Converting an improper fraction
1 Divide the numerator by the denominator. First, write down the improper fraction. Then divide the numerator by the denominator, that is, perform the division operation. Don't forget the rest. - For example, you are given an improper fraction 7/5 that needs to be converted to a mixed fraction. First divide 7 by 5:
- 7/5 → 7 ÷ 5 = 1 rest 2
2 Write down the integer division result. The integer (whole part) of the mixed fraction is equal to the integer result of dividing the numerator by the denominator. For now, just write down the integer division result (no remainder). - In our example, the result of division is 1 remain. 2, that is, the integer result of division is 1. For now, just write 1.
3 Convert the remainder and the original denominator to a correct fraction. Now you need to find the fractional part of the mixed number. To do this, write the remainder in the numerator of the new fraction, and write the original denominator in its denominator. Write down the resulting fraction next to (on the right) with an integer to get a mixed fraction. - In our example, the remainder is 2. Write it down in the numerator of the new fraction, and in its denominator, write down the original denominator, which is 5. You will get the correct fraction 2/5. Write this fraction next to an integer (1) to get a mixed fraction:
- 1 2/5.
4 Convert the mixed fraction to an improper one, if necessary. Mixed fractions look good on paper or screen, but sometimes they are difficult to work with. For example, if you need to multiply a fraction and a mixed number, it is easier to do this if you convert the mixed fraction to an improper one and multiply the two fractions. To convert a mixed fraction to an improper one, multiply the whole number by the denominator and add the numerator to the resulting value. - For example, you can convert a mixed fraction 1 2/5 to an incorrect one like this:
- 1 × 5 = 5 → (2 + 5)/5 = 7/5
Method 2 of 2: Problem Solving
1 Convert the irregular fraction 11/4 to a mixed number. This is a simple task; to solve it, follow the steps in the previous section. Below is the solution to this problem. - 11/4. First, divide the numerator by the denominator.
- 11 ÷ 4 = 2 rest 3. Now create a correct fraction from the remainder and the original denominator.
- 11/4 = 2 3/4
2 Convert the improper fraction 99/5 to a mixed number. Here we are dealing with a large numerator, but don't worry - you need to follow the same steps. - 99/5. 100 divided by 5 is 20, so 99 divided by 5 is 19 with a remainder.
- 99 ÷ 5 = 19 rest 4; now just write down the mixed number.
- 99/5 = 19 4/5
3 Convert the improper 6/6 to a mixed number. So far, we've looked at improper fractions with a larger numerator than the denominator. Now let's work with a fraction with the numerator equal to the denominator. - 6/6. Obviously, 6 is divisible by 6 without a remainder.
- 6 ÷ 6 = 1 rest 0. Since the fraction with 0 in the numerator is zero, you do not need to write anything next (to the right) with the integer.
- 6/6 = 1
4 Convert the improper fraction 18/6 to a mixed number. If the numerator is a multiple of the denominator, there will be no remainder; just divide the numerator by the denominator to get your answer. - 18/6. 18 divided by 6 is 3, so there is no remainder. In this case, the mixed number will not have a fractional part.
- 18/6 = 3
5 Convert the improper fraction -10/3 to a mixed number. Work with negative fractions in the same way as with positive ones. - -10/3
- -10 ÷ 3 = -3 rest 1
- -10/3 = -3 1/3
Tips
- Incorrect fractions do not need to be converted to mixed numbers. In most cases, improper fractions are easier to work with than mixed numbers. For example, if you need to multiply two fractions, it is better to work with an improper fraction, because in this case, you simply multiply the numerators and denominators of the two fractions. For example: 1/6 × 7/2 = 7/12. Now try to multiply 1/6 × 3 1/2; you will understand that it is not so easy.
- It is more convenient to use mixed numbers in everyday life. For example, the recipe says to take 4 1/2 cups flour, not 9/2 cups flour.
