Algebra Examples

$\frac{2}{5} s = 4 \frac{1}{5}$

Step 1

Simplify the left side.

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Step 1.1

Combine $\frac{2}{5}$ and $s$ .

$\frac{2 s}{5} = 4 \frac{1}{5}$

Step 2

Simplify the right side.

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Step 2.1

Convert $4 \frac{1}{5}$ to an improper fraction.

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Step 2.1.1

A mixed number is an addition of its whole and fractional parts.

$\frac{2 s}{5} = 4 + \frac{1}{5}$

Step 2.1.2

Add $4$ and $\frac{1}{5}$ .

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Step 2.1.2.1

To write $4$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{2 s}{5} = 4 \cdot \frac{5}{5} + \frac{1}{5}$

Step 2.1.2.2

Combine $4$ and $\frac{5}{5}$ .

$\frac{2 s}{5} = \frac{4 \cdot 5}{5} + \frac{1}{5}$

Step 2.1.2.3

Combine the numerators over the common denominator.

$\frac{2 s}{5} = \frac{4 \cdot 5 + 1}{5}$

Step 2.1.2.4

Simplify the numerator.

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Step 2.1.2.4.1

Multiply $4$ by $5$ .

$\frac{2 s}{5} = \frac{20 + 1}{5}$

Step 2.1.2.4.2

Add $20$ and $1$ .

$\frac{2 s}{5} = \frac{21}{5}$

Step 3

Since the expression on each side of the equation has the same denominator, the numerators must be equal.

$2 s = 21$

Step 4

Divide each term in $2 s = 21$ by $2$ and simplify.

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Step 4.1

Divide each term in $2 s = 21$ by $2$ .

$\frac{2 s}{2} = \frac{21}{2}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $2$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{2 s}{2} = \frac{21}{2}$

Step 4.2.1.2

Divide $s$ by $1$ .

$s = \frac{21}{2}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$s = \frac{21}{2}$

Decimal Form:

$s = 10.5$

Mixed Number Form:

$s = 10 \frac{1}{2}$