We will now learn to calculate the amount in numbers, expressed in terms of percent by replacing the keyword 'of', with the multiplication operation and then solving it.
Let's solve the following example:
What is \(20\text{%}\) of \(12\) ?
Here, the word 'of' is a keyword for multiplication operation,
= \(20\text {%}×12\)
Follow the given steps:
Step 1: Convert the percent to a decimal.
\(20\text {%}=0.20=0.2\)
Step 2: Write the problem again.
\(20\text {%}\) of \(12=0.2\) of \(12=0.2×12\)
\( \begin{array}[b]{r} 12 \\ ×0.2 \\ \hline 24 \\ \hline \end{array}\)
Since, we have a tenth place decimal,
\(\therefore\) \(0.2×12=2.4\)
Thus, \(20\text{%}\) of \(12\) is \(2.4\).
A \(24\)
B \(84\)
C \(120\)
D \(100\)
A percent is a part of a whole, where whole is the total quantity.
Let's consider the following example:
\(12\) is what percent of \(60?\)
Here, \(60\) represents the whole and \(12\) represents a part of \(60\).
To solve the above problem, consider the following steps:
Step 1 : Assume the percent as a variable.
Let's assume that \(12\) is \(x\text{%}\) of \(60\).
Step 2: Write the problem as an equation.
\(x\text{%}\) of \(60=12\)
Step 3: Solve the problem.
\(x\text{%}\) of \(60=12\)
\(\Rightarrow\,\dfrac {x}{100}×60=12\) (Converting \(x\text{%}\) into a fraction and 'of' means multiply)
\(\Rightarrow\,\dfrac {x}{100}×\dfrac {60}{1}=12 \) (Converting \(60\) into a fraction by putting it over \(1\))
\(\Rightarrow\,\dfrac {x×60}{100×1}=12\) (Multiplying both the fractions)
\(\Rightarrow\,\dfrac {60x}{100}=12\)
\(\Rightarrow\,\dfrac {60x}{100}=\dfrac {12}{1}\) ( Converting \(12\) into a fraction by putting it over \(1\))
Applying cross-multiplication method:
\(60x×1=12×100\)
\(60x=1200\)
Dividing both sides of the equation by \(60\) to calculate \(x\).
\(\dfrac {60x}{60}=\dfrac {1200}{60}\)
\(\Rightarrow x=\dfrac {1200}{60}\)
\(x=20\)
Step 4: Write the answer in the required form.
\(x=20\)
Thus, \(12\) is \(20\text {%}\) of \(60\).
A \(35\text{%}\)
B \(30\text{%}\)
C \(84\text{%}\)
D \(36\text{%}\)
Case I: When the number of figures are given
Five figures are given, out of which two are shaded.
Now the question is,
"What percent of the figures are shaded?"
Here,
Total number of figures \(=5\)
Number of shaded figures \(=2\)
We can say that \(2\) out of \(5\) figures are shaded.
\(=2\) out of \(5\)
\(=\dfrac {2}{5}\)
To calculate the percent, we should follow the given steps:
\(\dfrac {2}{5}=\dfrac {?}{100}\)
To make the denominator \(100\) , \(2\) and \(5\), both should be multiplied with \(20\).
\(\dfrac {2×20}{5×20}=\dfrac {40}{100}\)
\(\dfrac {2}{5}=\dfrac {40}{100}=40\text{%}\)
Thus, \(40\text{%}\) figures are shaded.
Case II: When only one figure is given (Grid)
What percent of the grid is shaded?
Here,
Total number of cells \(=100\)
Number of cells shaded \(=40\)
There are \(40\) cells out of \(100\) which are shaded.
\(\therefore\) Shaded cells \(=\dfrac {40}{100}=40\text{%}\)
Here, we observe that
\(40\) shaded cells represent \(40\text{%}\).
Case II: When only one figure is given (Grid)
What percent of the grid is shaded?
Here,
Total number of cells \(=100\)
Number of cells shaded \(=40\)
\(\because\) There are \(40\) cells out of \(100\) which are shaded.
\(\therefore\) Shaded cells \(=\dfrac {40}{100}=40\text{%}\)
Here, we observe that
\(40\) shaded cells represent \(40\text{%}\).
To determine this answer, we should compare these expenditures.
The amount she would spend on:
Groceries = \($62.77\)
Rent \(=35\text {%}\) of \($1255\)
\(=\dfrac {35}{100}×1255\)
\(=\dfrac {7}{20}×1255\)
\(=\dfrac {7}{4}×251\) \(=\dfrac {1757}{4}=$439.25\)
Miscellaneous bills = Three - fifth of \(1255\)
\(=\dfrac {3}{5}×1255=$753.00\)
Now, on comparing \($62.77,\;$439.25\) and \($753.00\), we get that
\($753.00>$439.25>$62.77\)
\(\therefore\) She would spend maximum on her bills.
A Kara is the most efficient.
B Larry is the most efficient.
C Cooper is more efficient than Larry.
D Cooper is the most efficient.
Let us consider the following example:
Here, the circle represents the percentage of students that play different sports, at a school.
The total number of students is \(200\).
Now the question is....... "How many students play baseball, cricket and basketball?"
We can calculate it by using the concept of "Percent of a number".
Thus, the number of students who play
Baseball = \(50\text {% of }200\)
\(=.50×200=100\)
Cricket = \(20\text {% of }200\)
\(=.20×200=40\)
Basketball = \(30\text {% of }200\)
\(=.30×200=60\)
This means, \(100\) students play Baseball, \(40\) students play Cricket, and \(60\) students play Basketball.
We will now learn to calculate the amount in numbers, expressed in terms of percent by using proportion.
For example: \(13\text{% of }30\)
Step 1: Write the percent as a fraction.
\(13\text{%}=\dfrac {13}{100}\)
Step 2: Write the problem as a proportion.
(Let \(13\text{% of }30\) is \(x\))
\(\dfrac {13}{100}=\dfrac {x}{30}\)
Step 3: Apply cross-multiplication method.
\(13×30=x×100\)
\(390=100x\)
Divide both sides by \(100\) to calculate \(x\).
\(\dfrac {390}{100}=x\)
\(\Rightarrow x=3.9\)
Thus, \(13\text{% of } 30\) is \(3.9\).
\(13×30=x×100\)
\(390=100x\)
Divide both the sides by \(100\) to calculate \(x\).
\(\dfrac {390}{100}=x\)
\(\Rightarrow x=3.9\)
Thus, \(13\text{% of } 30\) is \(3.9\)
A \(32\)
B \(21\)
C \(8\)
D \(18\)