Question

How do u simplify \[\dfrac{3}{{10}} - \dfrac{{11}}{{15}}\] ?

Answer 1

Hint: The given expression are rational numbers, hence to simplify the given numbers we need to perform arithmetic functions, i.e., Addition, Subtraction, Multiplication and Division. Here the denominators of both the numbers are not same, hence to simplify the given rational numbers, we need to find the LCM of both the numbers and then evaluate the terms.

Complete step-by-step answer:
Let us write the given expression:
 \[\dfrac{3}{{10}} - \dfrac{{11}}{{15}}\]
To simplify the expression, we need to find the LCM of both the numbers i.e., in order to add fractions, the denominators need to be the same. The multiples of 15 are 15, 30, 45... etc. We can see that 30 is divisible by 10, so this will be the lowest common denominator.
 \[\dfrac{3}{{10}} - \dfrac{{11}}{{15}}\]
As, we got the LCM as 30, hence we have:
 \[ = \dfrac{{\left( {3 \times 3} \right) - \left( {11 \times 2} \right)}}{{30}}\]
Evaluating the terms, we get:
 \[ = \dfrac{{9 - 22}}{{30}}\]
 \[ = \dfrac{{ - 13}}{{30}}\]
Hence, we get:
 \[ = - \dfrac{13}{{30}}\]
Therefore,
 \[\dfrac{3}{{10}} - \dfrac{{11}}{{15}} = \dfrac{{ - 13}}{{30}}\] .
So, the correct answer is “ \[\dfrac{{ - 13}}{{30}}\] ”.

Note: Real numbers can be defined as the union of both the rational and irrational numbers. They can be both positive or negative and are denoted by the symbol “R”. All the natural numbers, decimals and fractions come under this category. The set of real numbers consist of different categories, such as natural and whole numbers, integers, rational and irrational numbers.
We know that the algebraic expression should be any one of the forms such as addition, subtraction, multiplication and division, hence main key point is that to subtract the two rational numbers, if the denominators are different, we need to find the LCM of both the denominator terms and then simplify the given expression.