Q&A for How to Reduce Fractions

If either the numerator or the denominator -- or both -- is odd, you will have to find some low, odd number that will divide evenly into both numbers. If you can't do so, the fraction may be irreducible.

The fact that a fraction's denominator is larger than its numerator means it's a proper fraction. It has no bearing on whether the fraction can be reduced. A reducible fraction is one whose numerator and denominator are both divisible by the same number.

8/12 reduces only to 4/6 and 2/3.

Find a small number (in this case 2) that will divide evenly into both numerator and denominator, and do that as many times as possible. Here 10/8 = 5/4. 5/4 is irreducible, because no number (other than 1) will divide evenly into both 5 and 4.

First round 68.75 up to 70, and round 78 up to 80. Then multiply 70 by 80 in your head by multiplying 7 by 8 (which is 56) and adding two zeroes to the right: 5,600. That could be your estimate, or you could choose to reduce the number a little to offset the rounding up you did earlier. You could reduce 5,600 by about 2% to perhaps 5,500 (a slightly more accurate estimate).

If you divide both numerator and denominator by 125, you get 3/100.

No.

The only "calculating" you can do is to divide 12 into 5 and get a decimal number that is less than 1.

Mathematicians have been studying fractions for many centuries, and the best and fastest way to learn about fractions is the way they're taught in school, since mathematicians are the ones who designed the schools' math curricula.

Find the largest possible number that will divide evenly into both the numerator and the denominator. As it happens, 161 will divide evenly into both 161 and 483, so that the fraction reduces to 1/3.

If you're wondering whether or not one ratio is equal to another ratio, look for some number that will divide evenly into the larger numerator to yield the smaller numerator and will also divide evenly into the larger denominator to yield the smaller denominator. If you can find such a number, the ratios are equal. For example, compare the ratio 15:18 (or the fraction 15/18) to the ratio 5:6 (or 5/6). You can divide both 15 and 18 by 3, yielding 5 and 6. Therefore, 15/18 is equal to 5/6.

That fraction is not reducible.

37,944 / 41,616 reduces to 527 / 578. (7¾)(6/51) = (31/4)(6/51) = 186/204 = 31/34.

3/2 + (-6/5) = 3/2 - 6/5 = 15/10 - 12/10 = 3/10.

(3/4)(36) = 108/4 = 27.

Because 5/10 equals 1/2, all the other fractions in the series must equal 1/2. So the series is 5/10, 1/2, 3/6, 15/30, 3/6, 1/2, 5/10.

First find the lowest (least) common denominator, which is 3 x 8 = 24. Then the problem becomes 4 12/24 + 3 6/24 + 6 16/24 + 5 15/24 = 108/24 + 78/24 + 144/24 + 135/24 = 465/24. Perform that division, which yields 19 9/24 or 19 3/8.

4/8 is the same as a half. You can figure this out by finding a number both the numerator and denominator can be divided by, in this case 4. And divide both numbers by that to get ½. Say you didn't know you could divide both numbers by 4, you could divide both numbers by 2 to get 2/4. From there you could divide it by 2 again to get ½.

The same way as reducing proper fractions. Divide the numerator and the denominator by the greatest common factor, and if desired, turn it into a mixed number by dividing the numerator by the denominator.

See Understand Math and related articles.