Question

What should be subtracted from \[\dfrac{{ - 7}}{8}\]so as to get\[\dfrac{5}{{12}}\]?
A. \[\dfrac{{31}}{{24}}\]
B. \[\dfrac{8}{5}\]
C. \[\dfrac{{ - 31}}{{24}}\]
D. \[\dfrac{{ - 6}}{8}\]

Answer 1

Hint: Here we will use arithmetic subtraction. Also, variables will be used for simplification.
In elementary education, the first thing taught to us is addition and subtraction. These two arithmetic operations are pillars of mathematics. Generally, problems given to us are straightaway of direct addition or direct subtraction. For example, if Ram has \[3\] pencils and Raj has \[4\] pencils and he gives 2 pencils to Ram then what will be the new number of the pencils that Ram and Raj have?
It’s very simple to solve this problem, total number of pencils which Ram have is\[3\]and that which Raj have is \[4\], after giving two pencils to Ram, Raj will be left with \[4 - 2 = 2\]pencils, and consequently after gaining two pencils from Raj, Ram will have \[3 + 2 = 5\]pencils.

Complete step by step solution: Now, consider the given question, we are asked to determine a number that should be subtracted from \[\dfrac{{ - 7}}{8}\]so as to get\[\dfrac{5}{{12}}\]. Let the number from which we has to be subtracted be x, so it will be convenient to write this condition mathematically i.e. \[\left( {\dfrac{{ - 7}}{8}} \right) - x = \dfrac{5}{{12}}\].
Simplifying this expression using BODMAS rule, BODMAS stands for,
BO: Bracket open
D: Division
M: Multiplication
A: Addition
S: Subtraction
The above mentioned expressions are used in the same priority as mentioned above. Therefore,
$\left( {\dfrac{{ - 7}}{8}} \right) - x = \dfrac{5}{{12}}$
$\left( {\dfrac{{ - 7}}{8}} \right) - \dfrac{5}{{12}} = x$
$\left( {\dfrac{{ - 7 \times 3 - \left( {5 \times 2} \right)}}{{24}}}\right) = x$
Solving it further we obtain,
$\left( {\dfrac{{ -21 -10}}{{24}}} \right)=x$
$\left( {\dfrac{{-31}}{{24}}} \right)=x$
Hence, option C is correct i.e. \[\dfrac{{ - 31}}{{24}}\]must be subtracted from\[\dfrac{{ - 5}}{8}\]so as to get\[\dfrac{5}{{12}}\].

Note: In such types of problems, basic assumption of the number that is required to be added or subtracted is important. Also, BODMAS rule must be used in solving such expressions.