The percent proportion is a proportion that sets the ratio of a part of a whole equal to the ratio of a percent out of

100 .

\frac{part}{whole} = \frac{percent}{1 0 0} \Leftrightarrow \frac{a}{b} = \frac{p}{1 0 0}

We can find what number

120

is

30

percent of by thinking about

120

as the part of a whole number

b .

Let's substitute

a = 120

and

p = 30

into the formula and solve for

b

\frac{a}{b} = \frac{p}{1 0 0}

$a = 120$ , $p = 30$

\frac{1 2 0}{b} = \frac{3 0}{1 0 0}

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Solve for

b

$LHS \cdot 100 = RHS \cdot 100$

\frac{1 2 0}{b} \cdot 100 = \frac{3 0}{1 0 0} \cdot 100

$\frac{a}{1 0 0} \cdot 100 = a$

\frac{1 2 0}{b} \cdot 100 = 30

$\frac{a}{c} \cdot b = \frac{a \cdot b}{c}$

\frac{1 2 0 0 0}{b} = 30

$LHS \cdot b = RHS \cdot b$

\frac{1 2 0 0 0}{b} \cdot b = 30 \cdot b

$\frac{a}{b} \cdot b = a$

12000 = 30 \cdot b

$\frac{a}{b} = \frac{a / 3 0}{b / 3 0}$

\frac{1 2 0 0 0}{3 0} = b

Calculate quotient

400 = b

Rearrange equation

b = 400

Knowing the value of

b,

let's look at the completed percent proportion.

\frac{1 2 0}{4 0 0} = \frac{3 0}{1 0 0}

Therefore,

120

is

30 %

of

400 .

Exercise