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:**

If **\(60\text{%}\) **of a number is \(42\), find the number.

Here, the number which is to be found out, represents the whole.

**To solve the above problem, consider the following steps:**

**Step 1 : **Assume the number as a variable.

Let the number be \(x\).

**Step 2: **Write the problem as an equation.

\(60\text{%}\) of \(x \) is \(42\)

\(\Rightarrow60\text{%}\) of \(x=42\)

**Step 3: **Solve the equation.

\(60\text{%}\) of \(x=42\) ( 'of' means multiply)

\(60\text{%}×x=42\)

\(\dfrac {60}{100}×x=42\) (converting \(60\text{%}\) into a fraction)

\(\dfrac {60}{100}×\dfrac {x}{1}=42\) (converting \(x\) into a fraction by putting it over \(1\))

\(\dfrac {60×x}{100}=42\) (multiplying both the fractions)

\(\dfrac {60x}{100}=\dfrac {42}{1}\) ( converting \(42\) into a fraction by putting it over \(1\))

Applying cross-multiplication method.

\(60x×1=42×100\)

\(60x=4200\)

Dividing both sides by \(60\) to calculate \(x\).

\(\dfrac {60x}{60}=\dfrac {4200}{60}\)

\(x=70\)

**Step 4: **Write the answer.

\(x=70\)

Thus, \(60\text {% of } 70\) is \(42\).

- Since percents, decimals and fractions are all parts of the whole, so we can easily compare and arrange them in the required order.
**To understand it more clearly, let's consider the following example:**- Mrs.Thomson prepares her household budget in the first week of each month.
- In January, she decides to spend \($1255\).
- She would spend \($62.77\) on groceries, \(35\text {%}\) on rent, and three-fifths on miscellaneous bills.
- On which of the items listed above would she spend the most?

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.

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 \(36\text{%}\)