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  • Mastering Improper Fractions: How to Add & Subtract with Confidence

    An improper fraction is a fraction in which the numerator is greater than the numerator. To add and subtract improper fractions, make the denominators the same and use equivalent fractions. Then add or subtract in the normal way. Sometimes improper fractions may have the same denominator. Then you just add up the numerators and use the common denominator as the answer denominator.

    To add up improper fractions, make the denominators the same (if they are not, already) and use equivalent fractions.

    Examples: 8/3 + 5/3 + 4/3 = 17/3. Here the denominators are the same so the addition process is straightforward. The numerators were added and then the common denominator was used.

    But this problem could have been: 24/9 + 5/3 + 8/6. In which case you simply find the lowest number that is the multiple of the denominators 9, 6 and 3. This lowest common multiple will be 18 and this will become the common denominator. Each fraction therefore has to increase equivalently.

    24/9 becomes 48/18 (numerator doubled, because denominator 9 doubled to get 18). 5/3 now equals 30/18 (numerator increased six times because denominator 3 had to be increased six times to obtain common denominator 18). And 8/6 is equivalent to 24/18 (numerator increased three times because denominator 6 increased three times to get 18 as common denominator).

    With 18 as the common denominator, 48/18 + 30/18 + 24/18 still = 17/3.

    Subtracting improper fractions is the same process. The denominators should be the same, if they are not already so, and keep the fractions equivalently the same. Then work out the arithmetic ordinarily.

    Sometimes adding and subtracting improper fractions can result in another improper fraction as your answer, where the numerator is again bigger than the denominator. You can report your results this way, as an improper fraction. But sometimes it is advisable to render your answer as a mixed fraction. A mixed fraction is a whole number and a fraction.

    So, if you got 79/8 as your answer, you can present it as such. But to convert to mixed fractions, it is 79 divided by 8 = 9 remainder 7/8. Your answer therefore, will be, 9 7/8.

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