Question

How do you simplify \[\left( {\dfrac{5}{{22}}} \right) + 2\] ?

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. As here the denominators of both the numbers are not the same i.e., the denominator of the second term is not given, so we need to multiply and divide the number by 22, and then simplify the terms.

Complete step-by-step answer:
Let us write the given expression:
 \[\left( {\dfrac{5}{{22}}} \right) + 2\]
To simplify the expression, multiply and divide the second term by 22, we get:
 \[ \Rightarrow \dfrac{5}{{22}} + \left( {2 \times \dfrac{{22}}{{22}}} \right)\]
Multiplying the terms, we get:
 \[ \Rightarrow \dfrac{5}{{22}} + \dfrac{{44}}{{22}}\]
Now, keep the denominators as common, and add the numerators of the rational number as: \[ \Rightarrow \dfrac{{5 + 44}}{{22}}\]
Simplify the numerator terms i.e., adding 5 and 44 we get:
 \[ \Rightarrow \dfrac{{49}}{{22}}\]
Therefore,
 \[\left( {\dfrac{5}{{22}}} \right) + 2 = \dfrac{{49}}{{22}}\]
So, the correct answer is “ \[\dfrac{{49}}{{22}} \] ”.

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.
There are four main properties which include commutative property, associative property, distributive property and identity property.
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 add two rational numbers, if the denominators are different, we need to find the L