Q&A for How to Add Fractions With Unlike Denominators

Yes, most teachers will want you to show the simplified answer.

Multiply each fraction so that the denominators are the same. Then you can check the numerator to see if the fractions are equal.

A common factor is any prime number that will divide evenly into each number being considered. The greatest common factor is the largest whole number that is a common factor. For example, in Step 9 above, 2 is the greatest common factor of 6 and 8, so they are both divided by 2 to arrive at 3 and 4. In another example, to find the greatest common factor of 42 and 315, first find all the factors of each number: 42 = 2 x 3 x 7, and 315 = 3 x 3 x 5 x 7. The common factors are 3 and 7, so the greatest common factor of 42 and 315 is 7.

Take 1/3 + 1/4 as an example. Find the lowest common denominator (the lowest number that both of the numbers on the bottom of the fraction go into; in this case 12). To get the same denominator, multiply 1/3 by 4 to get 4/12, and 1/4 by 3 to get 3/12. Now you can add them like usual. 4/12 + 3/12 = 7/12.

Then it becomes a mixed fraction and you have whole numbers, e.g 8/5 = 1 3/5.

The numerator does not have to be equal to the denominator for you to add it. Only the denominators must be equal.

If necessary, convert one or both fractions until they have the same denominator, then subtract one numerator from the other.

Convert both to fractions with the same denominator. For example, if you have 2/3 and 3/4, you can multiply the numerator & denominator of the first fraction by 4 and multiply the numerator & denominator of the second fraction by 3 to get 8/12 and 9/12. Then it's clear which is bigger.

Change the mixed numbers to improper fractions, convert one or more fractions until they all have the same denominator, then add them.

Multiply all the numerators together to get the new numerator. Multiply all the denominators together to get the new denominator. For example, multiply these three fractions: (2/5) by (4/7) by (3/8). The new numerator is 2 x 4 x 3 = 24. The new denominator is 5 x 7 x 8 = 280. So the product is 24/280, which reduces to 3/35.

101/70 does not simplify, because there is no integer (other than 1) that will divide evenly into both 101 and 70.

No. Once the denominators are the same, you just add numerators (the denominator remains unchanged).

Simplifying a fraction means to reduce both the numerator and the denominator to the smallest possible numbers while maintaining the same value of the fraction. Do it by dividing both the numerator and denominator by the largest possible whole number that will divide into both evenly.

1¾ = 7/4.

You can always find a common denominator if only by multiplying the original denominators together. It's easier if you can find a lower number to work with, but if you can't, just multiplying the original denominators together will work. For example, if you want to add 4/5 + 3/7 + 8/9, you can find a common denominator by multiplying 5 times 7 times 9, which equals 315. Then choose new numerators to make the new fractions equivalent to the originals.

To multiply one fraction by another fraction, multiply the two numerators to get the new numerator, and multiply the two denominators to get the new denominator.

If you're trying to subtract one mixed number from another mixed number, first convert each to an improper fraction, and, if necessary, change them to equivalent fractions having the same denominator. Then subtract one numerator from the other.

Because there is no whole number that will divide evenly into both the numerator and the denominator, that fraction will not reduce (or simplify).

The first thing to do is always to simplify wherever possible in order to make things easier. So change 7/14 to ½, and change 8/4 to 2. ½ + 2 = 2½, or 5/2. So now it's 5/6 multiplied by 5/2. (5/6)(5/2) = 25/12, which won't reduce but can be expressed as 2 1/12.

It means to change a fraction to an equivalent fraction with a lower numerator and a lower denominator. For example, 8/12 simplifies to 2/3. The value of the fraction doesn't change, but the lower numbers are easier to work with.

Convert the fractions to equivalent fractions with 12 as the denominator of each.

Adding any negative number is the same as subtracting a positive number. For example, to add a negative ½ to ¾ is the equivalent of subtracting ½ from ¾, which is ¼.

If you wind up with an improper fraction as your answer, simplify (reduce) it if possible, and, if you prefer, convert it to a mixed number.

One way to find the LCM is to multiply the denominators together, use that product as the new denominator, or reduce it if you can do so and still have a common multiple. In this case 6 x 14 = 84. That's a common multiple. But if you divide 84 by 2, you get 42, which is also a common multiple of 6 and 14 (and, in fact, the lowest common multiple).

The easiest way to do this is to recognize that 4/4 equals 1. So you're adding 1 to 2/3, which is 1 2/3, or 5/3. Otherwise, you can do it the way the above article demonstrates.

1/4 + 3/16 + 2/8 = 4/16 + 3/16 + 4/16 = 11/16.

Yes. You'll just need to find the lowest common denominator among the three fractions.

38/7 does not reduce, so the simplest form is either 38/7 or 5 3/7.

The quickest way to do this: 12 3/10 + 1/2 = 12 3/10 + 5/10 = 12 8/10 = 12 4/5.

Find the least common multiple for the denominators, and multiply the numerator and denominator by the number of times it takes to get to that least common multiple.