Finite Math Examples

$\frac{f - 4}{49} - \frac{f + 5}{7}$

Step 1

To write $- \frac{f + 5}{7}$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$\frac{f - 4}{49} - \frac{f + 5}{7} \cdot \frac{7}{7}$

Step 2

Write each expression with a common denominator of $49$ , by multiplying each by an appropriate factor of $1$ .

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Step 2.1

Multiply $\frac{f + 5}{7}$ by $\frac{7}{7}$ .

$\frac{f - 4}{49} - \frac{(f + 5) \cdot 7}{7 \cdot 7}$

Step 2.2

Multiply $7$ by $7$ .

$\frac{f - 4}{49} - \frac{(f + 5) \cdot 7}{49}$

Step 3

Combine the numerators over the common denominator.

$\frac{f - 4 - (f + 5) \cdot 7}{49}$

Step 4

Simplify the numerator.

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Step 4.1

Apply the distributive property.

$\frac{f - 4 + (- f - 1 \cdot 5) \cdot 7}{49}$

Step 4.2

Multiply $- 1$ by $5$ .

$\frac{f - 4 + (- f - 5) \cdot 7}{49}$

Step 4.3

Apply the distributive property.

$\frac{f - 4 - f \cdot 7 - 5 \cdot 7}{49}$

Step 4.4

Multiply $7$ by $- 1$ .

$\frac{f - 4 - 7 f - 5 \cdot 7}{49}$

Step 4.5

Multiply $- 5$ by $7$ .

$\frac{f - 4 - 7 f - 35}{49}$

Step 4.6

Subtract $7 f$ from $f$ .

$\frac{- 6 f - 4 - 35}{49}$

Step 4.7

Subtract $35$ from $- 4$ .

$\frac{- 6 f - 39}{49}$

Step 4.8

Factor $3$ out of $- 6 f - 39$ .

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Step 4.8.1

Factor $3$ out of $- 6 f$ .

$\frac{3 (- 2 f) - 39}{49}$

Step 4.8.2

Factor $3$ out of $- 39$ .

$\frac{3 (- 2 f) + 3 (- 13)}{49}$

Step 4.8.3

Factor $3$ out of $3 (- 2 f) + 3 (- 13)$ .

$\frac{3 (- 2 f - 13)}{49}$

Step 5

Simplify with factoring out.

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Step 5.1

Factor $- 1$ out of $- 2 f$ .

$\frac{3 (- (2 f) - 13)}{49}$

Step 5.2

Rewrite $- 13$ as $- 1 (13)$ .

$\frac{3 (- (2 f) - 1 (13))}{49}$

Step 5.3

Factor $- 1$ out of $- (2 f) - 1 (13)$ .

$\frac{3 (- (2 f + 13))}{49}$

Step 5.4

Simplify the expression.

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Step 5.4.1

Rewrite $- (2 f + 13)$ as $- 1 (2 f + 13)$ .

$\frac{3 (- 1 (2 f + 13))}{49}$

Step 5.4.2

Move the negative in front of the fraction.

$- \frac{3 (2 f + 13)}{49}$