A fraction is a number that tells us how many parts we are talking about of a whole that has been divided into certain equal parts. The clearest example is when we divide a cake into 8 equal parts, for example, we have already had 1, in this case we would be talking about an eighth part or 1/8.
Taking into account how these numbers are written, operating with them may seem complicated to us, and the truth is that it is not, but it does require certain knowledge, and of course practice to be good with this ability to operate with fractions.
Add and subtract if the fractions have the same denominator
Adding and subtracting fractions with the same denominator is the easiest addition and subtraction case we can find. In this case we will only have to keep the same denominator and add the numerators. And in the case of subtraction we are also going to keep the same denominator and then we will subtract the denominators.
Example:
A / B + C / B = A + C / B
2/5 + 4/5= 2+ 4/5 = 6/5
Addition and subtraction with different denominators
In the event that the fractions have a different denominator, the addition and subtraction can take a little more time, since to carry out the operation we must calculate the common denominator.
This common denominator will be determined by calculating the least common multiple of the denominators.
The least common multiple is calculated by dividing the denominators into their divisors, and then we will take the common and uncommon ones with the greatest exponent and multiply them. The result of the multiplication is the least common multiple.
For example:
Least Common Multiple of 4 and 6
4= 2²
6 = 2, 3
lcm (4.6)= 2² * 3 = 12
The next step is to change all the denominators and put the lcm in its place. And the numerator will also change. We will have to divide the lcm by the denominator from before and then, the quotient will be multiplied by the numerator, turning this result into the new numerator. We will have to do this with each fraction.
Then we will perform the addition or subtraction as we explained in the previous case of fractions with the same denominator.
Example:
3 / 4 + 2 / 6 =
lcm (4, 6)= 12
3/4 + 2/6 = 9/12 + 4/12 = 13/12
Another way to calculate the addition or subtraction of a fraction with different denominators, and perhaps the easiest way to do it is through this formula:
We will multiply the two denominators, this will be our common denominator. Later, the change of the numerator will consist of multiplying the numerator of a fraction with the denominator of the fraction next to it.
The final fraction will be a multiple of the original result, therefore we must divide both the numerator and the denominator by the greatest common divisor that both numbers have.
Example:
A / b + c / d = a*d +b*c / b*d
3/4 +2/6= 3*6+2*4 / 4*6 = 18+8 / 24 = 26 / 24 which is a multiple of the actual result, so we must then divide it by the greatest common divisor that have. In this case, 2.
26:2 / 24:2 = 13/12
Fraction multiplication
Although the contrary is believed, the multiplication of fractions is much easier than addition and subtraction, since you do not have to look for a common denominator. In this case we will only have to multiply numerator with numerator, being the result of the numerator of the multiplication and we will also multiply the denominator by the denominator, being the final denominator.
Example:
A / b * c/d = a*c / b*d
3/4 * 2/6 = 3*2 / 4*6 = 6 / 24
As you can see, the final result is another fraction, whose numerator is the result of multiplying the numerators of the operation, while the denominator is the result of multiplying the denominators of the operation.
Division of fractions
We must bear in mind that to do a division of fractions we will not have to “divide” as it really should be done. Performing an operation on fractions involves multiplying several parts according to a pattern. It is known as:
The final numerator is the result of multiplying the extremes, while the final denominator will be the result of multiplying the means. Now we will see an example with letters so that you understand it better.
Example:
A / b : c /d= a*d / b*c
3/4 : 2/6= 3*6 / 4*2 = 18 / 8
In operations with fractions it is common for the result to be simplified as much as possible, hence we must divide the numerator and denominator of the final fraction by the greatest common divisor of both commons and continue dividing between the common divisors until we reach the least and Finally, obtain a fraction that cannot be further simplified since both numbers do not have more common divisors.
Operations with fractions on the calculator
If you want to solve your operations with fractions with the help of the calculator, it’s quite simple, and you don’t have to resort to special buttons. You just have to put each fraction in parentheses, leaving the symbol of the operation outside, between closed parentheses and open parentheses. The fraction bar will be represented by the division symbol. The problem with doing this with the calculator is that it will give you the result in whole numbers or with decimals, and not as a fraction.
If you want to input fractions proper into your calculator you will need a scientific calculator. In this case, the button with the symbol of an improper fraction will be important: ab/c.
In this case we must press this button to then enter the numerator number, press that button again and enter the denominator number.
For example: if we want to enter 3/4, it would be like this: 3 ab/c button 4
In the event that we work with improper fractions, we first introduce the whole number and then the fraction as we have done in the previous paragraph.
Example: if we want to enter 5 ¾, it would be like this: 5 ab/c button 3 ab/c button 4
Next we are going to see an example of how we would introduce an operation with fractions in the calculator. All operations are entered in the same way, except that we change the symbol of the operation to the one that corresponds in each case.
Example: 5 3/4 + 2/6
In this case the buttons are like this: 5 ab/c button 3 ab/c button 4 ab/c button symbol (+, -, *, /) 2 ab/c button 6
We hope that with this explanation and these examples we have been able to solve your doubts about how to do operations with fractions. Remember that this is not as complicated as you might think, but it is important that you practice a lot to get it right without having to resort to an explanation every time you try it. To do this, you only have to remember the basic points that we have explained to you in each operation. In addition, practice will lead you to solve operations with fractions not take so much time, which is ideal especially in the case of solving exams.