Question

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

Answer 1

Hint: We are given two term which are being added up we are asked to simplify our equation, to answer this we first learn about type of terms, then we learn how to add those term, in fraction we first simplify our terms and then make their denominator same and then when denominator is same, we add the numerator.

Complete step-by-step solution:
We are given two terms as $\dfrac{3}{5}$ and $\dfrac{6}{10}$ .
We are asked to add them.
We can see that our given terms are in fraction ($\dfrac{p}{q}$) form , so we are asked to add two fractions.
To do our problem we will learn how to add the fraction (rational).
If we have two fractions say $\dfrac{a}{b}$ and $\dfrac{c}{d}$ , then we first make their denominator equal by multiplying numerator and denominator by appropriate numbers.
Now in our case, we have fractions as $\dfrac{3}{5}$ and $\dfrac{6}{10}$ , where denominators are 5 and 10, we first have to make their equation.
The common multiple of 5 and 10 is 10.
So, we make the denominator as 10.
So, we multiply the first fraction $\dfrac{3}{5}$ by 2.
So, we get
$\dfrac{3}{5}=\dfrac{3\times 2}{5\times 2}=\dfrac{6}{10}$ .
For the second term, it remains the same as the denominator is already 10.
So, our fraction $\dfrac{3}{5}+\dfrac{6}{10}$ becomes $\dfrac{6}{10}+\dfrac{6}{10}$ .
Now as denominator is same, so we add numerator directly, so we get –
$\Rightarrow \dfrac{6}{10}+\dfrac{6}{10}=\dfrac{6+6}{10}=\dfrac{12}{10}$ .
Hence, we get
$\Rightarrow \dfrac{3}{5}+\dfrac{6}{10}=\dfrac{12}{10}$ .
By simplifying our terms, we get
$\dfrac{3}{5}+\dfrac{6}{10}=\dfrac{6}{5} = 1\dfrac{1}{5}$

Note: When we add fraction, we made the denominator equal first, if we add $\dfrac{2}{3}+\dfrac{4}{5}$ as $\dfrac{6}{8}$ then it is not correct because firstly denominator are not equal and we do not add terms in denominator also when we subtract the term we follow same methodology .
$\dfrac{2}{3}-\dfrac{4}{6}=\dfrac{2\times 2}{3\times 2}-\dfrac{4}{6}=\dfrac{4}{6}-\dfrac{4}{6}=\dfrac{4-4}{6}=\dfrac{0}{6}=0$ .