Finite Math Examples

$\frac{5 x}{58} + \frac{6 x + 3}{69}$

Step 1

Cancel the common factor of $6 x + 3$ and $69$ .

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Step 1.1

Factor $3$ out of $6 x$ .

$\frac{5 x}{58} + \frac{3 (2 x) + 3}{69}$

Step 1.2

Factor $3$ out of $3$ .

$\frac{5 x}{58} + \frac{3 (2 x) + 3 (1)}{69}$

Step 1.3

Factor $3$ out of $3 (2 x) + 3 (1)$ .

$\frac{5 x}{58} + \frac{3 (2 x + 1)}{69}$

Step 1.4

Cancel the common factors.

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Step 1.4.1

Factor $3$ out of $69$ .

$\frac{5 x}{58} + \frac{3 (2 x + 1)}{3 (23)}$

Step 1.4.2

Cancel the common factor.

$\frac{5 x}{58} + \frac{3 (2 x + 1)}{3 \cdot 23}$

Step 1.4.3

Rewrite the expression.

$\frac{5 x}{58} + \frac{2 x + 1}{23}$

Step 2

To write $\frac{5 x}{58}$ as a fraction with a common denominator, multiply by $\frac{23}{23}$ .

$\frac{5 x}{58} \cdot \frac{23}{23} + \frac{2 x + 1}{23}$

Step 3

To write $\frac{2 x + 1}{23}$ as a fraction with a common denominator, multiply by $\frac{58}{58}$ .

$\frac{5 x}{58} \cdot \frac{23}{23} + \frac{2 x + 1}{23} \cdot \frac{58}{58}$

Step 4

Write each expression with a common denominator of $1334$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.1

Multiply $\frac{5 x}{58}$ by $\frac{23}{23}$ .

$\frac{5 x \cdot 23}{58 \cdot 23} + \frac{2 x + 1}{23} \cdot \frac{58}{58}$

Step 4.2

Multiply $58$ by $23$ .

$\frac{5 x \cdot 23}{1334} + \frac{2 x + 1}{23} \cdot \frac{58}{58}$

Step 4.3

Multiply $\frac{2 x + 1}{23}$ by $\frac{58}{58}$ .

$\frac{5 x \cdot 23}{1334} + \frac{(2 x + 1) \cdot 58}{23 \cdot 58}$

Step 4.4

Multiply $23$ by $58$ .

$\frac{5 x \cdot 23}{1334} + \frac{(2 x + 1) \cdot 58}{1334}$

Step 5

Combine the numerators over the common denominator.

$\frac{5 x \cdot 23 + (2 x + 1) \cdot 58}{1334}$

Step 6

Simplify the numerator.

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Step 6.1

Multiply $23$ by $5$ .

$\frac{115 x + (2 x + 1) \cdot 58}{1334}$

Step 6.2

Apply the distributive property.

$\frac{115 x + 2 x \cdot 58 + 1 \cdot 58}{1334}$

Step 6.3

Multiply $58$ by $2$ .

$\frac{115 x + 116 x + 1 \cdot 58}{1334}$

Step 6.4

Multiply $58$ by $1$ .

$\frac{115 x + 116 x + 58}{1334}$

Step 6.5

Add $115 x$ and $116 x$ .

$\frac{231 x + 58}{1334}$