You want to know how to do operations with fractions? The difference between operations with numbers and operations with fractions is that in the latter, we have the denominator, which in many cases is a big problem.
We must be very clear about how the denominators will affect the different operations and what to do with them in each case.
Next, we will see how to solve operations with fractions step by step.
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Sum and Subtraction of Fractions
Fractions can only be added and subtracted when they have the same denominator. Therefore, if we have to add or subtract fractions with different denominator, we must carry out a previous step, which is to reduce the fractions to common denominator.
Sum and Subtraction of Fractions with the Same Denominator
This is the simplest case within fraction operations, because it is done in exactly the same way as adding or subtracting numbers, but adding the denominator.
For example, we have the following operation:
The first thing we have to do is to see if they have the same denominator, which they do. Now, it’s very easy, in just three steps, we perform the operation:
1 – Leave the denominator of all fractions
2 – Now we place the numerators, taking into account the sign in front of the fraction:
3 – Add and subtract the numerators:
All that remains to be seen now is whether we need to simplify the fraction, which in this case is already simplified, and so we have now finished.
In the next section we will see what happens when the denominators are not equal.
Sum and Subtraction of Fractions with Different Denominator
As we have indicated before, only fractions with the same denominator can be added and subtracted. When we find ourselves in this case, we have to reduce the fractions to a common denominator and we will be with fractions with the same denominator. For example:
1 – We reduce the fractions to common denominator (you can see how it is done step by step in the link) and transform them to their equivalent fractions:
2 – We now have the same denominator, so we operate as in the previous case:
To multiply fractions, they do not need to have the same denominator, so we do not have to worry about that.
Fractions are multiplied in-line, i. e. numerator with numerator and denominator with denominator:
Never forget to simplify fractions.
In order to make the division of fractions, it is not necessary to have the same denominator.
Fractions are divided by multiplying in the cross, that is to say:
- The numerator of the 1st, by the denominator of the 2nd, in the final numerator
- The denominator of the 1st, by the numerator of the 2nd, in the final denominator.
If instead of being placed next to each other, they are in the form of a fraction, a good way to remember is to resemble the fraction to a 4-storey building and then. the 1st goes up to the 4th and the 2nd goes up to the 3rd:
Powers in fractions
When we have a fraction elevated to a power, it is the same as if the numerator and denominator were elevated to that exponent separately. For example:
If the exponent is negative, first of all we have to pass the exponent to positive, turning the fraction around and then we can raise the numerator and the denominator separately. For example: