How to Change Mixed Numbers Into Whole Numbers

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Technically, a mixed number like 2 and 3/4 already contains a whole number – in this case, 2. (Whole numbers are the numbers you learned to count with: zero, one, two, three and so on, and in a mixed number they're always written to the left of the fraction.) Converting a mixed number to a whole number doesn't make much sense, because the whole number is already there. But there are two instances in which you could justify making this conversion: if the fraction part of the mixed number is an improper fraction, you can extract another mixed number from it, or you can convert the mixed number into a whole number with a decimal after it instead of a fraction.

Converting Mixed Numbers to Decimals

When you need to convert a mixed number into a whole number followed by a decimal, simply keep the whole number, then perform the division indicated by the fraction to figure out what goes to the right of the decimal point. Using the example of 2 and 3/4 you'd keep the 2, then divide 3 by 4 to figure out what goes to the right of the decimal point: 0.75, which gives you a final answer of 2.75.

Another Scenario for Finding Whole Numbers in Mixed Numbers

With the previous mixed number used as an example – 2 and 3/4 – the numerator of the fraction, or the number on top, is smaller than the denominator, the number on the bottom of the fraction. That means 3/4 is a proper fraction, or to put it another way, it represents a quantity less than one, and no more whole numbers are in it. But if an improper fraction followed the 2, with a bigger number in the numerator than in the denominator, then sometimes it's possible to extract a whole number from that fraction.

Extracting the Whole Number from an Improper Fraction

Instead of 2 and 3/4, you may find yourself with a number like 2 and 12/4. Because the fraction part of this mixed number is an improper fraction, its value is greater than one, it allows you to extract a mixed number of one (or possibly larger) from it. Simply calculate the division represented by the fraction: 12 ÷ 4 = 3, and you're left with a whole number instead of the fraction 12/4. Because the mixed number 2 and 12/4 means 2 + 12/4, you can rewrite the mixed number as 2 + 3 (substituting 3 for the fraction 12/4) and simplify that to 5 as the final answer.

Improper Fractions with a Remainder

In some cases, the improper fraction won't reduce to a true whole number and instead contains a fractional remainder left over. Consider the mixed number 2 and 13/4. If you perform the division represented by that fraction, 13 ÷ 4, to find you're left with the whole number 3, plus a remainder expressed as the fraction 1/4 or the decimal 0.25. Remember, join each term in a mixed number to the others by addition signs to add all the terms together. 2 + 3 + 1/4 and simplify the result to a new mixed number: 5 and 1/4. Although you're still left with a mixed number as the result, you could say that you've changed part of the fraction into a whole number.


About the Author

Lisa studied mathematics at the University of Alaska, Anchorage, and spent several years tutoring high school and university students through scary -- but fun! -- math subjects like algebra and calculus.