How To Add And Subtract Fraction With Different Denominators

When the fractions that you want to add have different denominators, there are a few different ways y'all tin can do it.

Add fractions the easy style

At some point in your life, some instructor somewhere told you these golden words of wisdom: "Y'all can't add together two fractions with different denominators." Your teacher was wrong! You tin use the like shooting fish in a barrel way when the numerators and denominators are small (say, 15 or under).

Here'southward the way to do information technology:

Cross-multiply the ii fractions and add the results together to go the numerator of the answer.

Suppose you desire to add the fractions one/three and 2/v. To go the numerator of the reply, cross-multiply. In other words, multiply the numerator of each fraction by the denominator of the other:

ane*5 = 5

2*3 = 6

Add the results to get the numerator of the answer:

5 + 6 = xi
Multiply the ii denominators together to become the denominator of the reply.

To get the denominator, simply multiply the denominators of the two fractions:

3*v = 15

The denominator of the reply is 15.
Write your answer as a fraction.

When you add together fractions, you sometimes need to reduce the respond that y'all become. Here's an instance:

Because the numerator and the denominator are both even numbers, y'all know that the fraction can be reduced. So endeavour dividing both numbers past two:

This fraction tin can't be reduced further, so 37/40 is the final answer.

In some cases, you may accept to add together more i fraction. The method is similar, with one small tweak.

Start out by multiplying the numerator of the start fraction by the denominators of all the other fractions.

(1*5*vii) = 35
Do the same with the second fraction and add this value to the offset.

35 + (3*2*7) = 35 + 42
Exercise the same with the remaining fraction(s).

35 + 42 + (4*2*v) = 35 + 42 + 40 = 117

When you lot're done, you have the numerator of the answer.
To get the denominator, just multiply all the denominators together:

You may need to reduce or modify an improper fraction to a mixed number. In this example, you lot just need to modify to a mixed number:

Add together fractions with the quick trick method

You lot can't always utilise this method, but y'all can apply it when 1 denominator is a multiple of the other. Look at the following trouble:

First, solve it the easy way:

Those are some big numbers, and you're yet not done because the numerator is larger than the denominator. The answer is an improper fraction. Worse nonetheless, the numerator and denominator are both even numbers, so the reply notwithstanding needs to be reduced.

With certain fraction add-on problems, at that place is a smarter style to work. The play a joke on is to plough a problem with different denominators into a much easier problem with the same denominator.

Before you add two fractions with dissimilar denominators, check the denominators to see whether one is a multiple of the other. If information technology is, you can use the quick trick:

Increase the terms of the fraction with the smaller denominator so that it has the larger denominator.

Look at the earlier problem in this new style:

As you lot tin can run into, 12 divides into 24 without a remainder. In this example, you desire to raise the terms of 11/12 so that the denominator is 24:

To fill in the question mark, the trick is to dissever 24 past 12 to find out how the denominators are related; and so multiply the consequence by 11:

? = (24 ÷ 12) 11 = 22
Rewrite the problem, substituting this increased version of the fraction, and add together.

At present you tin rewrite the problem this way:

As you can run into, the numbers in this case are much smaller and easier to work with. The answer here is an improper fraction; changing information technology into a mixed number is easy:

Add together fractions the traditional way

Utilise the traditional mode only when you lot tin't use either of the other methods (or when y'all know the least common multiple [LCM] merely by looking at the denominators).

Here's the traditional way to add fractions with 2 unlike denominators:

Find the LCM of the two denominators.

Suppose you want to add the fractions three/four + vii/10. Showtime find the LCM of the ii denominators, four and 10. Here'southward how to notice the LCM using the multiplication table method:
- Multiples of x: x, 20, thirty, 40
- Multiples of 4: iv, eight, 12, sixteen, 20
So the LCM of 4 and ten is xx.
Increase the terms of each fraction so that the denominator of each equals the LCM.

Increase each fraction to higher terms and then that the denominator of each is twenty.
Substitute these ii new fractions for the original ones and add together.

At this point, y'all have two fractions that have the same denominator:

When the answer is an improper fraction, y'all notwithstanding need to modify it to a mixed number: