Question

The approximate value of $\dfrac{4}{9} + 99\dfrac{{48}}{{49}} \times 245$ is?
A. $99\dfrac{1}{5}$
B. $2,450$
C. $24,499$
D. $245$

Answer 1

Hint: Simplification is the process of writing the given algebraic expression effectively and most comfortably to understand without affecting the original expression. Moreover, various steps are involved to simplify an expression.
Here, we need to apply the BODMAS rule to this question.
That is, we need to calculate the brackets first and then orders, then division or multiplication, and finally we need to add or subtract.
Also, if $a\dfrac{b}{c}$ is given, then we can write it as $\dfrac{{ac + b}}{c}$ . That is, we are converting mixed fractions into improper fractions.

Complete step by step answer:
  The given expression is $\dfrac{4}{9} + 99\dfrac{{48}}{{49}} \times 245$
First, we shall convert the mixed fraction into an improper fraction.
$99\dfrac{{48}}{{49}} = \dfrac{{99 \times 49 + 48}}{{49}}$
$ = \dfrac{{4899}}{{49}}$
Hence the given expression is rewritten as follows.
$\dfrac{4}{9} + 99\dfrac{{48}}{{49}} \times 245 = \dfrac{4}{9} + \dfrac{{4899}}{{49}} \times 245$
$ = \dfrac{4}{9} + 4899 \times 5$
 \[
   = \dfrac{4}{9} + 24495 \\
   = \dfrac{{4 + 9 \times 24495}}{9} \\
 \]
$
   = \dfrac{{4 + 220455}}{9} \\
   = \dfrac{{220459}}{9} \\
 $
$ = 24,499$ (approximately)
Hence, the approximate value of $\dfrac{4}{9} + 99\dfrac{{48}}{{49}} \times 245$ is$24,499$

So, the correct answer is “Option C”.

Note: Simplification of an expression is the process of changing the expression effectively without changing the meaning of an expression.
Here, we need to apply the BODMAS rule in this question.
 That is, we need to calculate the brackets first and then orders, then division or multiplication, and finally we need to add or subtract.
Moreover, various steps are involved to simplify an algebraic expression. Some of the steps are listed below:
If the given expression contains like terms, we need to combine them.
Example: $3x + 2x + 4 = 5x + 4$
We need to split an expression into factors (i.e) the process of finding the factors for the given expression.
Example: ${x^2} + 4x + 3 = (x + 3)(x + 1)$
We need to expand an algebraic expression (i.e) we have to remove the respective brackets of an expression.
Example: $3(a + b) = 3a + 3b$.
We need to cancel out the common terms in an expression.
Example: $\dfrac{{{x^2} + 4x + 3}}{{x + 1}} = \dfrac{{(x + 3)(x + 1)}}{{x + 1}}$
                                        $ = x + 3$