Bringing fractions together

Most fraction problems involve finding a common denominator for the fractions. There are basically three ways to do this. The essence of each is the same, but there are advantages and disadvantages that you should consider. Let's look at what they are!

When do you need to bring fractions together?

First, let's clarify what the denominator is. To do this, you need to know the parts of the fractures, but for now it may be enough to number below the fractional linewe are talking about.

But still when to apply to bring fractions together?

• when the fractions are added together,
• when they are extracted,
• for fractional equations,
• for tasks that require a common denominator (for example, if you need to represent fractions in such a way that it is better to bring them to a common denominator).

Bringing fractions together step by step

As I mentioned above, there are basically two ways to bring fractions into common denominators. You need to know both, how to expand fractions.

Finding common denominators of fractions by simple multiplication

The simplest method is to multiply the denominator of the fractions. In this case, make sure that you must also multiply the counter with the number in the denominator of the other fraction! I will show you an example:

First, you multiply the numerator and denominator of the first fraction by the number in the denominator of the second fraction, and then do the same in reverse:

This is what it will look like:

Then you just need to multiply:

The method Advantagesthat it can be done very quickly. Disadvantage, that for some fractions, a large number can enter into the denominator and can be difficult to calculate.

Bringing fractions together by extending only one fraction

Sometimes the denominator of one fraction is just a multiple of the denominator of the other fraction. In this case, it is useless to multiply the two together, because you get larger numbers, and they are not so good to calculate with.

Instead, the solution is to expand one fraction to the denominator of the other fraction.

Let's look at an example, so it's clearer:

As you can see, the two denominators are 2 and 4. 4 is a multiple of 2, because you can divide 4 by 2.

To do this, multiply both the numerator and the denominator by 2:

You have already brought the two fractions together:

The method Advantagesthat it's very simple and you don't have to do big numbers. Disadvantagethat you can use it relatively rarely.

Finding common denominators of fractions by finding the least common multiple

You might get a very large number by multiplying the two denominators (method 1) and not want to count with it. In this case, it may be easier to you find the two denominators the smallest common multiple of.

Let's look at an example:

If you multiply 25 by 35, you get 875. As you can see, fractions with a denominator of 875 are not very good to calculate.

The first step is to find the least common multiple of the two denominators. I will not go into this in detail here, I have linked to an understandable article above.

The point is that the smallest common multiple of 25 and 35 is 175, which is not a small number, but it is still more friendly than 875.

The question is: what to do about it?

See how many times in 175 you have 25 and 35!

You have the result:

This method is used to Advantages, so that you can avoid extra large numbers when adding fractions to a common denominator. A downsidethat you should consider whether it is worth the effort to calculate the least common multiple.

Whichever method you use to get the fractions to a common denominator, the main thing is to get a good result. Use whichever is more comfortable and sympathetic to you, because they all give a good solution.