Question

How do you simplify \[\dfrac{3}{5} + \dfrac{6}{{10}}\]?

Answer 1

Hint: If the denominators are not the same, then you have to use equivalent fractions which do have a common denominator. To do this, you need to find the least common multiple (LCM) of the two denominators. To add fractions with unlike denominators, rename the fractions with a common denominator. Then add and simplify. Unlike fractions as denominators are different, to perform addition, subtraction with unlike fractions first we have to convert unlike fractions into like fractions.

Complete step-by-step solution:
If a whole thing is divided into equal parts then each part is said to be a fraction. In other words a fraction is a part of the whole. Fractions represent equal parts of a whole or a collection.
Fraction of a whole: When we divide a whole into equal parts, each part is a fraction of the whole.
A fraction has two parts. The number on the top of the line is called the numerator. It tells how many equal parts of the whole or collection are taken. The number below the line is called the denominator. It shows the total divisible number of equal parts the whole into or the total number of equal parts which are there in a collection.
Fraction can be represented by \[\dfrac{{{\text{numerator}}}}{{{\text{denominator}}}}\],
Now given expression is \[\dfrac{3}{5} + \dfrac{6}{{10}}\],
So, here denominators are not equal, so we have to take the least common multiple of the both the denominators.
Here denominators are 5 and 10,
Taking LCM of both the denominators and making the denominators equal, we get,
LCM \[\left( {5,10} \right) = 1 \times 2 \times 5 = 10\],
Now multiply the given fractions to get the denominators equal to 10, we get,
\[ \Rightarrow \dfrac{3}{5} \times \dfrac{2}{2} + \dfrac{6}{{10}} \times \dfrac{1}{1}\],
Now the given expression becomes,
\[ \Rightarrow \dfrac{6}{{10}} + \dfrac{6}{{10}}\],
Now denominators are equal so we can perform addition then we get,
\[ \Rightarrow \dfrac{{6 + 6}}{{10}}\],
Now multiplying the numerators we get,
\[ \Rightarrow \dfrac{{12}}{{10}} = \dfrac{6}{5}\],
So,\[\dfrac{3}{5} + \dfrac{6}{{10}} = \dfrac{6}{5}\],

\[\therefore \]The simplified form of \[\dfrac{3}{5} + \dfrac{6}{{10}}\] is \[\dfrac{6}{5}\].

Note: To perform mathematical operations like addition and subtraction we need to convert unlike fractions to like fractions, we can convert them by finding the Least common multiple i.e., LCM , and calculate the fractions to make the denominators same.