Question

How do you write in simplest form given $-\dfrac{7}{8}-\left( -\dfrac{3}{16} \right)$ ?

Answer 1

Hint: Firstly, By the rule of BODMAS, in any given mathematical expression the contents in the brackets have the highest priority. Hence solve the value in the brackets first and then perform the mathematical expression between those two terms which is subtraction. If the denominators are the same, then directly subtract the numerator. If they are not, then Find the LCM of the denominators and then evaluate.

Complete step by step solution:
The given expression is, $-\dfrac{7}{8}-\left( -\dfrac{3}{16} \right)$
According to the BODMAS rule, we always solve the contents in the brackets first because it is of higher priority than the other mathematical operations.
On opening the brackets firstly, we get,
$\Rightarrow -\dfrac{7}{8}+\dfrac{3}{16}$
Now we have two terms.
To perform any mathematical operation between any two fractions, we must first ensure that they have the same denominators.
But here in our case, the denominators are different.
To make the denominator common we find the least common multiple (LCM) of both the denominators.
The list of multiples for the denominator $16\;$ is $16,32,48...\;$
The list of multiples for the denominator $8\;$ is $8,16,24,32,40,48...\;$
Here the least common multiple is $16\;$
Hence the common denominator will be $16\;$
Now to make the denominator we try to multiply the numerator and denominator with the same number.
$\Rightarrow \left( -\dfrac{7}{8}\times \dfrac{2}{2} \right)+\left( \dfrac{3}{16}\times \dfrac{1}{1} \right)$
Now evaluate the terms.
$\Rightarrow \left( -\dfrac{14}{16} \right)+\left( \dfrac{3}{16} \right)$
Since our denominators are common now, we can directly add the numerators.
$\Rightarrow \dfrac{-14+3}{16}$
$\Rightarrow \dfrac{-11}{16}$
Hence, the simplest form given $-\dfrac{7}{8}-\left( -\dfrac{3}{16} \right)$ is $-\dfrac{11}{16}$.

Note: According to the BODMAS rule, the priority order of operators in solving any mathematical expression is,
B- Bracket
O- Order or power
D- Division
M- Multiplication
A- Addition
S- Subtraction
Use this to solve any mathematical expression to avoid any errors.