Question

Find the value of the given expression. $\dfrac{-3}{5}-\left( -\dfrac{2}{15} \right)$
$\begin{align}
  & a)\dfrac{-11}{5} \\
 & b)\dfrac{-1}{5} \\
 & c)\dfrac{-7}{15} \\
 & d)\dfrac{7}{15} \\
\end{align}$

Answer 1

Hint: We will solve this by BODMAS rule. Hence fist we will open bracket with the help of property $\left( - \right)\times \left( - \right)=\left( + \right)$ . Now we know that if we want to add two fractions the denominator of the fractions must be same. Hence we will first make the denominators same by taking LCM of the denominator then we know that $\dfrac{a}{b}+\dfrac{c}{b}=\dfrac{a+c}{b}$ . Hence we will now simplify the expression using this and get the final answer.

Complete step-by-step solution:
Now consider the given equation. $\dfrac{-3}{5}-\left( -\dfrac{2}{15} \right)$ .
Now we will use the BODMAS rule. According to BODMAS the order of solving should be
Bracket, Order or Power, Multiplication, Addition, and Subtraction.
Hence first we will open the bracket.
Now we know that $\left( - \right)\times \left( - \right)=\left( + \right)$
Hence we have $-\left( -\dfrac{2}{15} \right)=\dfrac{2}{15}$
Using this we will get $\dfrac{-3}{5}-\left( -\dfrac{2}{15} \right)=\dfrac{-3}{5}+\dfrac{2}{15}$
Now we cannot have any multiplication order, or division hence we will proceed with addition.
Now to add fractions we know that the denominator must be the same. Now the denominators here are 5 and 15. Hence to make it the same we will have to make both denominators equal to LCM of 5 and 15. Now LCM of 5 and 15 is 15.
Hence we will make both the denominators equal to 15.
Now $\dfrac{2}{15}$ already has 15 in its denominator hence no need to change.
But $\dfrac{-3}{5}$ has 5 in its denominator and we have $15\div 5=3$ so we will multiply the numerator and denominator by 3.
Hence we get $\dfrac{-3}{5}=\dfrac{-3\times 3}{5\times 3}=\dfrac{-9}{15}$
Hence now we get
$\dfrac{-3}{5}-\left( -\dfrac{2}{15} \right)=\dfrac{-3}{5}+\dfrac{2}{15}=\dfrac{-9}{15}+\dfrac{2}{15}$
Now since the denominator are same now we can add fractions.
We know that addition of $\dfrac{a}{b}+\dfrac{c}{b}=\dfrac{a+c}{b}$ .
Hence get $\dfrac{-9}{15}+\dfrac{2}{15}=\dfrac{-9+2}{15}$
Now $-9+2=-7$ since the sign is opposite we subtract and give the sing of a larger term. Here 9 > 2. Hence we give a negative sign.
Hence we have
$\dfrac{-9+2}{15}=\dfrac{-7}{15}$
Hence the value of $\dfrac{-3}{5}-\left( -\dfrac{2}{15} \right)=\dfrac{-7}{15}$
Option c is the correct option.

Note:Note that we cannot directly add or subtract fractions $\dfrac{2}{5}+\dfrac{3}{2}\ne \dfrac{5}{7}$ . The denominators must be common. And even after we have common denominators we have $\dfrac{a}{b}+\dfrac{c}{b}=\dfrac{a+c}{b}$
For example $\dfrac{9}{2}+\dfrac{5}{2}=\dfrac{14}{2}$ do not mistaken this as $\dfrac{9}{2}+\dfrac{5}{2}=\dfrac{14}{4}$ .