Question

What is the value of 35% of 240?

Answer 1

Hint: To find the value of 35% of 240, we have to express this in mathematical form by changing the ‘of’ into a multiplication sign. Then we have to convert 35% into numbers and simplify by cancelling the common factors.

Complete step by step solution:
We have to find the value of 35% of 240. Let us denote it in mathematical form.
$35\%\times 240$
Let us convert 35% into numbers. We have to divide 35 by 100.
$\dfrac{35}{100}\times 240$
Now, we have to simplify this. Let us cancel 0 from the denominator and 240.
$\Rightarrow \dfrac{35}{10\require{cancel}\cancel{0}}\times 24\require{cancel}\cancel{0}$
The result of above simplification is
$\Rightarrow \dfrac{35}{10}\times 24$
We can further cancel the common factor in the numerator (35) and denominator. Let us cancel the common factor 5.
\[\begin{align}
&\Rightarrow\dfrac{{{\require{cancel}\cancel{35}}^{7}}}{{{\require{cancel}\cancel{10}}^{2}}}\times 24 \\
 & =\dfrac{7}{2}\times 24 \\
\end{align}\]
Let us cancel the common factor 2 from 24 and the denominator.
\[\begin{align}
&\Rightarrow\dfrac{7}{\require{cancel}\cancel{2}}\times {{\require{cancel}\cancel{24}}^{12}} \\
 & =7\times 12 \\
\end{align}\]
Let us multiply 7 and 12.
\[\Rightarrow 7\times 12=84\]
Hence, 35% of 240 is 84.

Note: Students must know that ‘of’ these types of problems means multiplication. They must also know how a percentage is converted into its number. They must divide the percentage number by 100 to convert it into its number form. Similarly, to convert a number into percentage, we have to multiply the number by 100. Students must simplify the expressions by first cancelling the common terms and factors. We can also simplify $\dfrac{35}{100}\times 240$ in an alternate method.
Instead of cancelling the common terms, let us divide 35 by 100.
$\Rightarrow 0.35\times 240$
Now, we have to multiply 0.35 with 240. This procedure will be time consuming.
$\Rightarrow 0.35\times 240=84$