You may have come across with fractions often since you are studying the factions. They come in the formulas, algebraic equations, and some practical problems. Algebraic equations contain fractions, so it is an important topic to solve the equations of algebra. You should study about adding fractions that contain algebraic expressions. However, numbers are included in the fractions of arithmetic. You should know all the operations on fractions as they are useful for various problems. You must be capable of solving addition, subtraction, division and multiplication of different fractions. Here, you will study how to add two different fractions that are containing only numbers by an easy method.
Types of fractions
Firstly, you should be aware of the different types of fractions. There are usually two kinds of fractions used that are like or same fractions and unlike fractions for addition. The like fractions are the fractions that have the same number at the denominator place like 2/3 and 4/3. Whereas, the, unlike fractions, has different numbers at the denominators place like 2/3 and 4/11. You should able for adding fractions of both like and unlike fractions.
To add the like fractionsTo add two different fractions having same denominators is simple. You have to add only the numbers at the numerators of both the like fraction. After adding the numerators, check whether it can be simplified further or not. If the fraction can be simplified that is it can be reduced, you should correctly convert it into lowest form. It is explained in the example below.
So, as the both the denominators are same, you can add it as,
It can be reduced further as both 4 and 8 are divisible by a common number that is 4. Thus, the correct answer to this problem will be,
To add the unlike fractions
To add two unlike fractions is little tricky, as the denominators are not same. In this case, you have to make the denominators of the fraction same. So convert the fractions so that they have the same denominator and then simply add them. For adding fractions easily, you must ensure sure that both the bottom numbers that is denominators are same.
Firstly, convert the unlike fractions to like fractions by making both the denominators same.
Then, you have to add only the numerators of both the fractions, as the denominators are made same.
Then, if the fraction obtained after addition can be simply further, you must convert it into lowest or reduced form correctly. it will be your final answer that would be a fraction.
Consider this problem to understand it better, and you can easily add the fractions.
Firstly, you have to make both the denominators same as they are different that are 3 and 6. If we multiply both the numerator and denominator of the first fraction by 1/3 by 2, it can be converted to 2/6. So, you can add this new fraction with the second fraction 5/6 that gives the answer as 7/6.
So, you have studied to add the arithmetic fractions. Adding fractions in the way to add two algebraic fractions is also simple for you.