How To Add Fraction With The Same Denominator

When the fractions that you want to add together have different denominators, there are a few different ways you can practise it.

Add fractions the like shooting fish in a barrel way

At some point in your life, some instructor somewhere told you these golden words of wisdom: "Y'all can't add two fractions with unlike denominators." Your teacher was wrong! You can employ the piece of cake manner when the numerators and denominators are small (say, 15 or nether).

Here'south the way to practise it:

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

Suppose yous want to add together the fractions 1/iii and 2/5. To go the numerator of the answer, cantankerous-multiply. In other words, multiply the numerator of each fraction by the denominator of the other:

1*five = five

two*three = 6

Add the results to get the numerator of the answer:

5 + six = 11
Multiply the ii denominators together to get the denominator of the answer.

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

3*5 = 15

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

When you lot add fractions, yous sometimes need to reduce the answer that you get. Here's an example:

Because the numerator and the denominator are both even numbers, you know that the fraction can be reduced. So try dividing both numbers past ii:

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

In some cases, y'all may have to add together more than 1 fraction. The method is similar, with one pocket-size tweak.

Get-go out by multiplying the numerator of the beginning fraction by the denominators of all the other fractions.

(i*v*7) = 35
Do the same with the second fraction and add together this value to the start.

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

35 + 42 + (4*2*5) = 35 + 42 + twoscore = 117

When you're washed, you have the numerator of the answer.
To become the denominator, but multiply all the denominators together:

You may need to reduce or change an improper fraction to a mixed number. In this example, you simply need to alter to a mixed number:

Add together fractions with the quick trick method

Yous can't e'er utilise this method, simply yous can use it when one denominator is a multiple of the other. Expect at the following problem:

Kickoff, solve information technology the like shooting fish in a barrel fashion:

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

With certain fraction addition bug, there is a smarter fashion to work. The trick is to turn a trouble with unlike denominators into a much easier problem with the same denominator.

Earlier you add together two fractions with different denominators, check the denominators to see whether ane is a multiple of the other. If it is, yous tin use the quick play a joke on:

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

Look at the earlier problem in this new way:

As you can see, 12 divides into 24 without a remainder. In this case, you want to enhance the terms of eleven/12 then that the denominator is 24:

To fill in the question marking, the trick is to divide 24 by 12 to find out how the denominators are related; then multiply the upshot by 11:

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

Now you can rewrite the problem this way:

As you lot tin can see, the numbers in this example are much smaller and easier to work with. The answer here is an improper fraction; changing it into a mixed number is easy:

Add fractions the traditional fashion

Utilize the traditional fashion only when y'all can't use either of the other methods (or when you know the to the lowest degree common multiple [LCM] just by looking at the denominators).

Hither's the traditional way to add fractions with two different denominators:

Find the LCM of the ii denominators.

Suppose you desire to add the fractions 3/iv + 7/10. Offset observe the LCM of the ii denominators, 4 and 10. Here's how to find the LCM using the multiplication table method:
- Multiples of 10: x, xx, thirty, twoscore
- Multiples of 4: iv, 8, 12, 16, 20
So the LCM of four and 10 is xx.
Increase the terms of each fraction so that the denominator of each equals the LCM.

Increase each fraction to college terms so that the denominator of each is twenty.
Substitute these two new fractions for the original ones and add.

At this point, you have two fractions that have the same denominator:

When the answer is an improper fraction, you even so demand to change it to a mixed number: