Basic Math Examples

$\frac{c}{5} + \frac{c}{9} = \frac{14}{45}$

Step 1

Simplify $\frac{c}{5} + \frac{c}{9}$ .

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Step 1.1

To write $\frac{c}{5}$ as a fraction with a common denominator, multiply by $\frac{9}{9}$ .

$\frac{c}{5} \cdot \frac{9}{9} + \frac{c}{9} = \frac{14}{45}$

Step 1.2

To write $\frac{c}{9}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{c}{5} \cdot \frac{9}{9} + \frac{c}{9} \cdot \frac{5}{5} = \frac{14}{45}$

Step 1.3

Write each expression with a common denominator of $45$ , by multiplying each by an appropriate factor of $1$ .

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Step 1.3.1

Multiply $\frac{c}{5}$ by $\frac{9}{9}$ .

$\frac{c \cdot 9}{5 \cdot 9} + \frac{c}{9} \cdot \frac{5}{5} = \frac{14}{45}$

Step 1.3.2

Multiply $5$ by $9$ .

$\frac{c \cdot 9}{45} + \frac{c}{9} \cdot \frac{5}{5} = \frac{14}{45}$

Step 1.3.3

Multiply $\frac{c}{9}$ by $\frac{5}{5}$ .

$\frac{c \cdot 9}{45} + \frac{c \cdot 5}{9 \cdot 5} = \frac{14}{45}$

Step 1.3.4

Multiply $9$ by $5$ .

$\frac{c \cdot 9}{45} + \frac{c \cdot 5}{45} = \frac{14}{45}$

Step 1.4

Combine the numerators over the common denominator.

$\frac{c \cdot 9 + c \cdot 5}{45} = \frac{14}{45}$

Step 1.5

Simplify the numerator.

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Step 1.5.1

Move $9$ to the left of $c$ .

$\frac{9 \cdot c + c \cdot 5}{45} = \frac{14}{45}$

Step 1.5.2

Move $5$ to the left of $c$ .

$\frac{9 c + 5 \cdot c}{45} = \frac{14}{45}$

Step 1.5.3

Add $9 c$ and $5 c$ .

$\frac{14 c}{45} = \frac{14}{45}$

Step 2

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

$14 c = 14$

Step 3

Divide each term in $14 c = 14$ by $14$ and simplify.

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Step 3.1

Divide each term in $14 c = 14$ by $14$ .

$\frac{14 c}{14} = \frac{14}{14}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $14$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{14 c}{14} = \frac{14}{14}$

Step 3.2.1.2

Divide $c$ by $1$ .

$c = \frac{14}{14}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Divide $14$ by $14$ .

$c = 1$