Like fractions are fractions that have the same denominators. To add these types of fractions, we have to write the fractions in a single denominator. Then, we add the numerators, and we will obtain the result. Lastly, we can simplify the final fraction if possible.
Here, we will learn to how to add like fractions step by step. In addition, we will solve several practice problems to learn the concepts.
Steps to add like fractions
When we have an addition of two or more fractions with the same denominators (homogeneous fractions), we can follow the following steps:
Step 1: Make sure the denominator of the fractions is the same.
Let's recall that the denominator is the number at the bottom of the fraction and the numerator is the number at the top of the fraction.
Step 2: Write the fractions with only one denominator. Since the fractions have the same denominator, we can combine them to form a single fraction.
Step 3: Add the numerators of the fraction obtained in step 2.
Step 4: Simplify the final fraction if possible.
These steps apply to any number of fractions. Look at the following examples to fully understand these steps.
Adding like fractions - Examples with answers
These examples are solved using the steps for adding like fractions seen above. Try to solve the problems yourself before looking at the solution.
EXAMPLE 1
Find the result of the addition $latex \frac{1}{3}+\frac{1}{3}$.
Solution
Step 1: The fractions are homogeneous since the numerators of both fractions are 3.
Step 2: Combining the fractions, we have:
$$\frac{1}{3}+\frac{1}{3}$$
$$=\frac{1+1}{3}$$
Step 3: Now we add the numerators, and we have:
$$=\frac{1+1}{3}$$
$$=\frac{2}{3}$$
Step 4: The fraction is now simplified.
EXAMPLE 2
Find the result of the addition of fractions $latex \frac{2}{5}+\frac{3}{5}$.
Solution
Step 1: We can see that both denominators are equal to 5, so the fractions are homogeneous.
Step 2: Combining the fractions, we have:
$$\frac{2}{5}+\frac{3}{5}$$
$$=\frac{2+3}{5}$$
Step 3: Adding the numerators, we have:
$$=\frac{2+3}{5}$$
$$=\frac{5}{5}$$
Step 4: Simplifying, we have:
$latex =1$
EXAMPLE 3
Solve the addition of fractions $latex \frac{1}{5}+\frac{2}{5}+\frac{1}{5}$.
Solution
Step 1: The denominators of the three fractions are equal to 5, so the fractions are homogeneous.
Step 2: Writing the fractions with a single denominator, we have:
$$\frac{1}{5}+\frac{2}{5}+\frac{1}{5}$$
$$=\frac{1+2+1}{5}$$
Step 3: Adding the numerators, we have:
$$=\frac{1+2+1}{5}$$
$$=\frac{4}{5}$$
Step 4: The fraction is now simplified.
EXAMPLE 4
Find the result of the addition $latex \frac{2}{9}+\frac{4}{9}+\frac{7}{9}$.
Solution
Step 1: The three fractions are homogeneous since they all have the same denominator, equal to 9.
Step 2: Combining the fractions, we have:
$$\frac{2}{9}+\frac{4}{9}+\frac{7}{9}$$
$$=\frac{2+4+7}{9}$$
Step 3: Now we add the numerators, and we have:
$$=\frac{2+4+7}{9}$$
$$=\frac{13}{9}$$
Step 4: We can write the fraction as a mixed number:
$$=1\frac{4}{9}$$
EXAMPLE 5
Find the result of the addition $latex \frac{2}{5}+\frac{2}{10}+\frac{3}{5}$.
Solution
Step 1: The fractions have denominators 5, 10, and 5. These fractions do not appear to be homogeneous at first glance. However, we can simplify the second fraction as follows:
$$\frac{2}{5}+\frac{2}{10}+\frac{3}{5}$$
$$=\frac{2}{5}+\frac{1}{5}+\frac{3}{5}$$
Step 2: Writing the fractions in a single denominator, we have:
$$\frac{2}{5}+\frac{1}{5}+\frac{3}{5}$$
$$=\frac{2+1+3}{5}$$
Step 3: Now we add the numerators, and we have:
$$=\frac{2+1+3}{5}$$
$$=\frac{6}{5}$$
Step 4: We can write the fraction as a mixed number:
$$=1\frac{1}{5}$$
EXAMPLE 6
Find the result of $latex \frac{3}{11}+\frac{9}{33}+\frac{4}{11}$.
Solution
Step 1: Similar to the previous example, we can simplify the second fraction as follows to obtain like denominators:
$$\frac{3}{11}+\frac{9}{33}+\frac{4}{11}$$
$$=\frac{3}{11}+\frac{3}{11}+\frac{4}{11}$$
Step 2: Combining the fractions, we have:
$$\frac{3}{11}+\frac{3}{11}+\frac{4}{11}$$
$$=\frac{3+3+4}{11}$$
Step 3: Now we add the numerators, and we have:
$$=\frac{3+3+4}{11}$$
$$=\frac{10}{11}$$
Step 4: The fraction is already simplified
Adding like fractions - Practice problems
Solve the following problems by applying the process used to solve an addition of like fractions.
See also
Interested in learning more about adding fractions? You can take a look at these pages:
