Question

Simplify: \[35\% \] of \[420\]\[ + \]\[26\% \] of \[150 + \] \[18\% \] of \[350\].

Answer 1

Hint: First of all we need to take the percentage value of each and every part. After doing some simplification, and then we will add them up to get the required result.

Formula used: Percentage of any number is how much part it is out of 100.
\[a\% \] of \[b\] is\[ = \] \[\left( {\dfrac{a}{{100}}} \right) \times b.\]

Complete step-by-step solution:
It is given that \[35\% \] of \[420\]\[ + \]\[26\% \] of \[150 + \] \[18\% \] of \[350\].
First we have to find one by one
Now we have to take first term and we can derive the following forms using the formula:
\[35\% \] of \[420\]\[ = \]\[\left( {\dfrac{{35}}{{100}}} \right) \times 420\].
Multiply the numerator part and the divide it by the denominator part, we get:
\[ \Rightarrow \dfrac{{14700}}{{100}}\]
Let us divide the terms and we get
\[ \Rightarrow 147\]
Similarly, we take second term of the given data,
\[26\% \] of \[150\]\[ = \] \[\left( {\dfrac{{26}}{{100}}} \right) \times 150\].
Multiply the numerator part and the divide it by the denominator part, we get:
\[ \Rightarrow \dfrac{{3900}}{{100}}\]
Let us divide the terms and we get
\[ \Rightarrow 39\]
Again, we take the third term and we get
\[18\% \] of \[350\]\[ = \] \[\left( {\dfrac{{18}}{{100}}} \right) \times 350.\]
Multiply the numerator part and the divide it by the denominator part, we get:
\[ \Rightarrow \dfrac{{6300}}{{100}}\]
On divide the terms we get
\[ \Rightarrow 63\]
So, if we add all these values, then we will get the resultant value of the question.
So,\[35\% \] of \[420\]\[ + \]\[26\% \] of \[150 + \] \[18\% \] of \[350\]
\[ \Rightarrow 147 + 39 + 63\]
\[ \Rightarrow 249\]
\[\therefore \] The answer is \[249\].

Note: Sometimes we can convert the percentage values into decimal forms and then we can use mathematical operations to calculate the values.
Like, \[35\% \] of \[420\]\[ = \left( {\dfrac{{35}}{{100}}} \right) \times 420 = 0.35 \times 420 = 147.\]
Another approach we can use to solve this type of question.
We can convert the whole fraction into a numerator and denominator.
And, then we can factorise the numerator part and also factorise the denominator part.
Then canceling the equal numbers will give us the result.
Like,\[35\% \] of \[420\]
\[ \Rightarrow \left( {\dfrac{{35}}{{100}}} \right) \times 420\]
On rewriting the term we get,
\[ \Rightarrow \dfrac{{35 \times 420}}{{100}}\]
On splitting each value as on multiplication we get
\[ \Rightarrow \dfrac{{(5 \times 7) \times (5 \times 7 \times 4 \times 3)}}{{(5 \times 5 \times 4)}}\]
On cancel the same term and we get
\[ \Rightarrow 7 \times 7 \times 3\]
Let us multiply the term and we get
\[ \Rightarrow 147\]
Like the above way, we can calculate each sub part of the given question and then we can add them up to get the result.
And, always remember that a percentage is a dimensionless number and it has no unit of measurement.