Usually, people use fractions to represent numbers smaller than one: 3/4, 2/5 and the like. But if the number on top of the fraction (the numerator) is bigger than the number on the bottom of the fraction (the denominator), the fraction represents a number bigger than one, and you can write it either as a whole number or as a combination of a whole number and a decimal or a fraction remainder.
Calculating Whole Numbers From Fractions
To find the whole number hidden in an improper fraction, remember that the fraction represents division. So, if you have a fraction like:
There is no whole number in that fraction, because the numerator was smaller than the denominator, which means the result will always be less than one. But if the numerator and denominator were the same, you'd get a whole number. For example:
If the numerator of a fraction is a multiple of the denominator, the result will always be a whole number: For example,
Calculating Mixed Fractions
What if the numerator of your fraction is bigger than the denominator – so you know there's a whole number in there somewhere – but it's not an exact multiple of the denominator. You still use the same technique: Do the division that the fraction represents. So, if your fraction is
Depending on the purpose behind your calculations, you might be able to leave the answer in decimal form, or you might need to express the result as a mixed number, which is a combination of the whole number (in this case, 2) and the fractional remainder.
Calculating the Fractional Remainder: Method 1
If you need to put the result of the above example, 11 ÷ 5 = 2.2, into mixed number form, there are two ways of going about it. If you already have the decimal result, just write the decimal part of the number as a fraction. The numerator of the fraction is whichever digits are to the right of the decimal point – in this case, 2 – and the denominator of the fraction is the place value of the digit that's furthest to the right of the decimal. The "2" is in the tenths spot, so the denominator of the fraction is 10, giving us 2/10. You can simplify that fraction to 1/5, so your complete result in mixed number form is:
Calculating the Fractional Remainder: Method 2
You can also calculate the fractional reminder of a mixed number without converting it to a decimal first. In that case, once you work out the whole number, simply write that number as a fraction with the same denominator as your initial fraction, then subtract the result from the initial fraction. The result is your fractional reminder. This makes a lot more sense once you see an example so, again, let's consider the example of 11/5. Even if you work out the division longhand, you'll see quickly that the answer is two-something. Writing the 2 as a fraction with the same denominator gives you 10/5. Subtracting that from the original fraction gives you
So 1/5 is your fractional remainder. When you write your final answer, don't forget to give the whole number, too:
As you progress in math, you'll see that fractions can also represent negative values. In that case you can still use this technique to find the "whole numbers" hidden in the fraction. But the very specific math term "whole numbers" only applies to zero and positive numbers. So, if the result is ultimately a negative number, you can't call it a whole number. Instead, you must use the proper math term for both positive and negative whole numbers: integers.
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.