Algebra Examples

Solve the following equation: $\frac{3}{5} f = 2 \frac{1}{5}$

Step 1

Simplify the left side.

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Step 1.1

Combine $\frac{3}{5}$ and $f$ .

$\frac{3 f}{5} = 2 \frac{1}{5}$

Step 2

Simplify the right side.

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Step 2.1

Convert $2 \frac{1}{5}$ to an improper fraction.

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Step 2.1.1

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

$\frac{3 f}{5} = 2 + \frac{1}{5}$

Step 2.1.2

Add $2$ and $\frac{1}{5}$ .

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Step 2.1.2.1

To write $2$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{3 f}{5} = 2 \cdot \frac{5}{5} + \frac{1}{5}$

Step 2.1.2.2

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

$\frac{3 f}{5} = \frac{2 \cdot 5}{5} + \frac{1}{5}$

Step 2.1.2.3

Combine the numerators over the common denominator.

$\frac{3 f}{5} = \frac{2 \cdot 5 + 1}{5}$

Step 2.1.2.4

Simplify the numerator.

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Step 2.1.2.4.1

Multiply $2$ by $5$ .

$\frac{3 f}{5} = \frac{10 + 1}{5}$

Step 2.1.2.4.2

Add $10$ and $1$ .

$\frac{3 f}{5} = \frac{11}{5}$

Step 3

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

$3 f = 11$

Step 4

Divide each term in $3 f = 11$ by $3$ and simplify.

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Step 4.1

Divide each term in $3 f = 11$ by $3$ .

$\frac{3 f}{3} = \frac{11}{3}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $3$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{3 f}{3} = \frac{11}{3}$

Step 4.2.1.2

Divide $f$ by $1$ .

$f = \frac{11}{3}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$f = \frac{11}{3}$

Decimal Form:

$f = 3.\overline{6}$

Mixed Number Form:

$f = 3 \frac{2}{3}$