Operations With Rational Numbers

							         Operations With Rational Numbers
Operations With Rational Numbers

In mathematics, we generally deal with four types of basic operations called as addition,
subtraction, multiplication, and division. We can easily perform these four kinds of operations
on different type of numbers.

We all know that algebra is an important branch of mathematics and in this we have to tackle
different type of numbers.

Rational numbers are among different types of numbers, and on Rational Numbers we can
easily perform all these different types of operations. Performing operations on rational
numbers is not a big task if you understand the concepts clearly.

A rational number can be expressed as a fraction with an integer on the top and on the
bottom:

Now what happens when you multiply the tops and bottoms of these fractions? Well, the top
multiplication is an integer multiplied by an integer. We know that this will give us another
integer.

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Same with the bottoms – multiplying together two integers will give us an integer as an
answer. So overall, our new number will be:

When is a number a rational number – when it can be written as a fraction with an integer on
the top, and an integer on the bottom.

What do we have here – a rational number! So multiplying together rational numbers gives
you an answer which is itself a rational number.

Dividing rational numbers

When you divide one rational number by another, the answer you get is a rational number as
well. You can show why this is in almost exactly the same way as in the previous section.
The only extra thing you’ll need to remember is that:

Adding and subtracting rational numbers

When you add or subtract rational numbers, the answer you get is always a rational number.
Why is this? Well, take these two rational numbers and add them together:

Before you can add them together, what do you have to do? You need to find a common
denominator. One quick way of doing this is to multiply the two denominators together:

Is this answer a rational number? Yes it is! Why? Because there’s an integer on the top of
the fraction, and an integer on the bottom.

When you add together two rational numbers, you will always be able to find a common
denominator for the two fractions. This means you’ll always be able to add them together,
and your answer will always have an integer on the top and an integer on the bottom, making
it a rational number.

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Sometimes the integers will be large and complicated, like in this case, but that doesn’t matter.
They’re integers, so the number is rational. End of story.

Using a dot instead of a multiplication symbol

Say a question asks you to find the factors of a number, perhaps the number 20. After trying
various numbers you should be able to work out that its factors are 2, 2, and 5. How can you
show that these are the factors of 20? Well, one way you can is by showing that you can get
20 by multiplying them together, like this:

Now obviously this might be a little confusing, because the dot looks just like a decimal point.
There are a few ways to stop getting them mixed up however. There is usually only one
decimal point in a number. In this example, there are two dots, so this tells us they’re
probably not decimal points.

Also, these dots are usually only used to show factors of a number, so if you’re not in a
question dealing with factors the dot is probably a decimal point. The last thing you can do is
to see whether the dot makes sense as a decimal point. For instance, say I had something
like this:




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