Basic Math Examples

$\frac{3}{5} c = 6 \frac{1}{4}$

Step 1

Simplify the left side.

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Step 1.1

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

$\frac{3 c}{5} = 6 \frac{1}{4}$

Step 2

Simplify the right side.

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Step 2.1

Convert $6 \frac{1}{4}$ to an improper fraction.

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Step 2.1.1

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

$\frac{3 c}{5} = 6 + \frac{1}{4}$

Step 2.1.2

Add $6$ and $\frac{1}{4}$ .

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Step 2.1.2.1

To write $6$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{3 c}{5} = 6 \cdot \frac{4}{4} + \frac{1}{4}$

Step 2.1.2.2

Combine $6$ and $\frac{4}{4}$ .

$\frac{3 c}{5} = \frac{6 \cdot 4}{4} + \frac{1}{4}$

Step 2.1.2.3

Combine the numerators over the common denominator.

$\frac{3 c}{5} = \frac{6 \cdot 4 + 1}{4}$

Step 2.1.2.4

Simplify the numerator.

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Step 2.1.2.4.1

Multiply $6$ by $4$ .

$\frac{3 c}{5} = \frac{24 + 1}{4}$

Step 2.1.2.4.2

Add $24$ and $1$ .

$\frac{3 c}{5} = \frac{25}{4}$

Step 3

Multiply both sides of the equation by $\frac{5}{3}$ .

$\frac{5}{3} \cdot \frac{3 c}{5} = \frac{5}{3} \cdot \frac{25}{4}$

Step 4

Simplify both sides of the equation.

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Step 4.1

Simplify the left side.

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Step 4.1.1

Simplify $\frac{5}{3} \cdot \frac{3 c}{5}$ .

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Step 4.1.1.1

Cancel the common factor of $5$ .

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Step 4.1.1.1.1

Cancel the common factor.

$\frac{5}{3} \cdot \frac{3 c}{5} = \frac{5}{3} \cdot \frac{25}{4}$

Step 4.1.1.1.2

Rewrite the expression.

$\frac{1}{3} (3 c) = \frac{5}{3} \cdot \frac{25}{4}$

Step 4.1.1.2

Cancel the common factor of $3$ .

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Step 4.1.1.2.1

Factor $3$ out of $3 c$ .

$\frac{1}{3} (3 (c)) = \frac{5}{3} \cdot \frac{25}{4}$

Step 4.1.1.2.2

Cancel the common factor.

$\frac{1}{3} (3 c) = \frac{5}{3} \cdot \frac{25}{4}$

Step 4.1.1.2.3

Rewrite the expression.

$c = \frac{5}{3} \cdot \frac{25}{4}$

Step 4.2

Simplify the right side.

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Step 4.2.1

Multiply $\frac{5}{3} \cdot \frac{25}{4}$ .

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Step 4.2.1.1

Multiply $\frac{5}{3}$ by $\frac{25}{4}$ .

$c = \frac{5 \cdot 25}{3 \cdot 4}$

Step 4.2.1.2

Multiply $5$ by $25$ .

$c = \frac{125}{3 \cdot 4}$

Step 4.2.1.3

Multiply $3$ by $4$ .

$c = \frac{125}{12}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$c = \frac{125}{12}$

Decimal Form:

$c = 10.41\overline{6}$

Mixed Number Form:

$c = 10 \frac{5}{12}$