How to Estimate With Fractions

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Students who have mastered fractions may struggle with using them to arrive at estimates, for fractions are very precise and seem to go against the idea of estimating a number. However, for certain kinds of problems, such as multiple-choice questions, estimating fractions can be a simple way to arrive at the correct answer. Whether you are adding, subtracting, multiplying or dividing fractions, learning how to estimate fractions can be a valuable skill for your math studies later on.

    Refresh your understanding of fraction sizes. Keep in mind that the larger the numerator, or top part, of a fraction, the larger it will be (2/4 is bigger than 1/4, for example). On the other hand, the larger the denominator, or bottom part, of a fraction, the smaller it will be (1/4 is smaller than 1/3).

    Study the problem at hand and evaluate which fraction is easier to work with. When estimating with fractions you will have to combine two fractions in some way (usually addition, subtraction, multiplication or division). Fractions with smaller numerators, like 1/2, are usually easier to work with than fractions with larger numerators, like 1/8.

    Start with the fraction that is easiest to work with, putting in terms of the harder fraction's denominator. To do this, multiply the top and the bottom by the same number until the bottom number matches the other fraction's denominator. For example, if you have 1/2 + 1/8, as in the previous step, you could change 1/2 to 4/8.

    Change hard-to-visualize fractions, such as 1/27, into the closest number that's easier to work with, like 1/26. For estimating purposes, it's okay to overlook the difference. In this case, 26 is a better denominator because it's easier to convert when you're working with more than one fraction. For example, 1/2 is the same as 13/26.

    Perform the required operation on the numbers. If adding the previous terms, for example, you would have 1/26+13/26. Adding them together, you arrive at 14/26.

    Estimate the size of the fraction in relationship to 1 (one whole). You know that 1, in terms of 26, would be 26/26; therefore, you know that 14/26 is less than 1.

    Estimate the size of the fraction in relationship to 1/2. In this case, 13/26 is 1/2, so 14/26 is slightly bigger than 1/2.

    Reduce the fraction, dividing both the numerator and the denominator by the same number, in order to check your work. Here, 14 and 26 both have factors of 2; when divided by 2, you arrive at 7/13, which makes it easy to see that it's slightly more than 1/2.

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