Fractions with different denominators are different kinds of fractions. To add fractions with mixed numbers, there are simple techniques one needs to follow to add fractions with mixed numbers. Let’s look at the steps in Adding fractions with mixed numbers.
How to add fractions with mixed numbers
step1: find the Equivalent fractions of the given fractions with common denominators. The best common denominator is to find the LCM of the denominators
Step2: After finding the common denominator of the given fractions and all the fractions are written over one particular denominator, add the numerators (top) numbers and take them over the common denominator.
There are two ways to add fractions with mixed numbers,
Let’s look at them one after the other.
• the first method, is to convert the mixed numbers to improper fractions and then find the common denominator of the fractions. Then proceed to add the numerators and take them over the common denominator. Let’s look at the example below.
\text{Example 1: add} \space3\frac{1}{2}+2\frac{2}{3}\\
Answer: \text{first convert the given fractions to improper fractions}\space=\frac{(3×2)+1}{2}+\frac{(2×3)+2}{3}=\frac{6+1}{2}+\frac{6+2}{3}=\frac{7}{3}+\frac{8}{3}\\
\text{find the LCM of 2 and 3. The LCM of 2 and 3 is 6}=\frac{7}{2}+\frac{8}{3}=\frac{21+16}{6}=\frac{37}{6}=6\frac{1}{6}
• the Second method of adding fractions with mixed numbers is to add the whole number part separately and then add the fraction part by writing them over the common denominator. Let’s look at this example below
\text{Example 1: add 3}\frac{1}{2}+2\frac{2}{3}\\
Answer: \text{simply add the whole number part and then fractions part}\space3\frac{1}{2}+2\frac{2}{3}=(3+2)[\frac{1}{2}+\frac{2}{3}]\\
\text{we know that the LCM of 2 and 3 is 6}=\space(5)\frac{3+4}{6}=5\frac{7}{6}=6\frac{1}{6}On how to multiply fractions click here