Basic Math Examples

$\frac{5}{6} c + \frac{3}{4} = \frac{11}{12}$

Step 1

Combine $\frac{5}{6}$ and $c$ .

$\frac{5 c}{6} + \frac{3}{4} = \frac{11}{12}$

Step 2

Move all terms not containing $c$ to the right side of the equation.

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Step 2.1

Subtract $\frac{3}{4}$ from both sides of the equation.

$\frac{5 c}{6} = \frac{11}{12} - \frac{3}{4}$

Step 2.2

To write $- \frac{3}{4}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{5 c}{6} = \frac{11}{12} - \frac{3}{4} \cdot \frac{3}{3}$

Step 2.3

Write each expression with a common denominator of $12$ , by multiplying each by an appropriate factor of $1$ .

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Step 2.3.1

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

$\frac{5 c}{6} = \frac{11}{12} - \frac{3 \cdot 3}{4 \cdot 3}$

Step 2.3.2

Multiply $4$ by $3$ .

$\frac{5 c}{6} = \frac{11}{12} - \frac{3 \cdot 3}{12}$

Step 2.4

Combine the numerators over the common denominator.

$\frac{5 c}{6} = \frac{11 - 3 \cdot 3}{12}$

Step 2.5

Simplify the numerator.

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Step 2.5.1

Multiply $- 3$ by $3$ .

$\frac{5 c}{6} = \frac{11 - 9}{12}$

Step 2.5.2

Subtract $9$ from $11$ .

$\frac{5 c}{6} = \frac{2}{12}$

Step 2.6

Cancel the common factor of $2$ and $12$ .

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Step 2.6.1

Factor $2$ out of $2$ .

$\frac{5 c}{6} = \frac{2 (1)}{12}$

Step 2.6.2

Cancel the common factors.

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Step 2.6.2.1

Factor $2$ out of $12$ .

$\frac{5 c}{6} = \frac{2 \cdot 1}{2 \cdot 6}$

Step 2.6.2.2

Cancel the common factor.

$\frac{5 c}{6} = \frac{2 \cdot 1}{2 \cdot 6}$

Step 2.6.2.3

Rewrite the expression.

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

Step 3

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

$5 c = 1$

Step 4

Divide each term in $5 c = 1$ by $5$ and simplify.

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Step 4.1

Divide each term in $5 c = 1$ by $5$ .

$\frac{5 c}{5} = \frac{1}{5}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $5$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{5 c}{5} = \frac{1}{5}$

Step 4.2.1.2

Divide $c$ by $1$ .

$c = \frac{1}{5}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$c = \frac{1}{5}$

Decimal Form:

$c = 0.2$