Basic Math Examples

$\frac{c}{3} + \frac{c}{2} = \frac{5}{6}$

Step 1

Simplify $\frac{c}{3} + \frac{c}{2}$ .

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Step 1.1

To write $\frac{c}{3}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{c}{3} \cdot \frac{2}{2} + \frac{c}{2} = \frac{5}{6}$

Step 1.2

To write $\frac{c}{2}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{c}{3} \cdot \frac{2}{2} + \frac{c}{2} \cdot \frac{3}{3} = \frac{5}{6}$

Step 1.3

Write each expression with a common denominator of $6$ , by multiplying each by an appropriate factor of $1$ .

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Step 1.3.1

Multiply $\frac{c}{3}$ by $\frac{2}{2}$ .

$\frac{c \cdot 2}{3 \cdot 2} + \frac{c}{2} \cdot \frac{3}{3} = \frac{5}{6}$

Step 1.3.2

Multiply $3$ by $2$ .

$\frac{c \cdot 2}{6} + \frac{c}{2} \cdot \frac{3}{3} = \frac{5}{6}$

Step 1.3.3

Multiply $\frac{c}{2}$ by $\frac{3}{3}$ .

$\frac{c \cdot 2}{6} + \frac{c \cdot 3}{2 \cdot 3} = \frac{5}{6}$

Step 1.3.4

Multiply $2$ by $3$ .

$\frac{c \cdot 2}{6} + \frac{c \cdot 3}{6} = \frac{5}{6}$

Step 1.4

Combine the numerators over the common denominator.

$\frac{c \cdot 2 + c \cdot 3}{6} = \frac{5}{6}$

Step 1.5

Simplify the numerator.

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Step 1.5.1

Move $2$ to the left of $c$ .

$\frac{2 \cdot c + c \cdot 3}{6} = \frac{5}{6}$

Step 1.5.2

Move $3$ to the left of $c$ .

$\frac{2 c + 3 \cdot c}{6} = \frac{5}{6}$

Step 1.5.3

Add $2 c$ and $3 c$ .

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

Step 2

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

$5 c = 5$

Step 3

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

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Step 3.1

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

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

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $5$ .

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Step 3.2.1.1

Cancel the common factor.

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

Step 3.2.1.2

Divide $c$ by $1$ .

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

Step 3.3

Simplify the right side.

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Step 3.3.1

Divide $5$ by $5$ .

$c = 1$