Fractions with the Same Numerators Added

Fractions with the Same Numerators Added

Fractions with the Same Numerators Added

When two fractions have the same denominator, adding them is simple. We simply add the numerators of each fraction together with the same denominator.


Add frac 2 3 to frac 5 3 to get frac 2 + 5 3 to get frac 7 3.

Fractions with Unlike Denominators Added

Let’s say we want to add frac1 to frac1 to get frac1+frac1

Because the denominators of the two fractions are not equal, we cannot simply add the numerators and denominators to obtain the answer.

Finding a common (same) denominator for both fractions that will allow us to add them correctly is the trick.

What number can we pick where 2 and 4 will split equally?

Since we always want to choose the smallest such number, our best option would be 4.

Any number that can be divided by both 2 and 4 is acceptable, such as 8, 12, or 16, and it will work. We simply save time by selecting the smallest one, as we will see in a moment.

Our task is to convert frac12 into an equivalent fraction with a 4 in the denominator because frac14 already has a 4 in the denominator.

With a 4 in the denominator, frac12 becomes frac24, which is the equivalent fraction.

We can now combine them by adding them together.


Multiplication by 1 and Common Denominators equal a/a

A common denominator for both fractions—preferably the Least Common Denominator—and equivalent fraction conversion are required to add two fractions correctly.

The last example's common denominator was relatively simple to find because 4 is a multiple of 2.

Here, we'll go over how we can actually find a common denominator.

For instance, add "frac 2 3 " and "frac 3 "

To solve this problem, multiply each fraction by a form of 1 that has an equivalent value and will give all the fractions a common denominator.

What is the first integer into which the numerators 3 and 4 divide equally?

In this instance, it is simply 3 x 4 = 12.

How can we convert each fraction to its equivalent form with a 12 as the denominator?

So to speak, we multiply each fraction by 1.

\frac{4}{4}\times\frac{2}{3}=\frac{8}{12} \sand


Take note that frac 3 3 and frac 4 4 both equal 1.

Now that we've prepared ourselves, we can add these fractions.






In order to find a common denominator, we multiplied both fractions by a form of 1: 1=fracaa for the first and 1=fracbb for the second.

Example \sAdd


The first number that 6 and 8 divide evenly into is: \frac{24}{6}=4 and frac 24 8 = 3.

Divide each fraction by the equivalent form of 1 to get the denominator, which is 24. For frac5-6, 1=frac4-4, and for frac3-8, 1=frac3-3.





\frac{2}{5}+\frac{1}{6} \s\frac{2}{5}+\frac{1}{6}=(\frac{6}{6})


3 or more fractions added

The same procedure is used to add three or more fractions, but there are now three or more denominators to take into consideration when determining a common denominator.

Example \sAdd


2, 3, 4, and 6 all have a common denominator. It is 12.

\frac{7}{6}+\frac{4}{3}+\frac{5}{4}+\frac{3}{2}= \s(\frac{2}{2})





= \s\frac{14}{12}+\frac{16}{12}+\frac{15}{12}+\frac{18}{12}=\frac{63}{12}=\frac{21}{4}

Quick and simple Formula \s\frac{a}{b}+\frac{c}{d}=\frac{ad+bc}{bd}

Shahid Lakha
Shahid Lakha

Shahid Lakha is a seasoned educational consultant with a rich history in the independent education sector and EdTech. With a solid background in Physics, Shahid has cultivated a career that spans tutoring, consulting, and entrepreneurship. As an Educational Consultant at Spires Online Tutoring since October 2016, he has been instrumental in fostering educational excellence in the online tutoring space. Shahid is also the founder and director of Specialist Science Tutors, a tutoring agency based in West London, where he has successfully managed various facets of the business, including marketing, web design, and client relationships. His dedication to education is further evidenced by his role as a self-employed tutor, where he has been teaching Maths, Physics, and Engineering to students up to university level since September 2011. Shahid holds a Master of Science in Photon Science from the University of Manchester and a Bachelor of Science in Physics from the University of Bath.