Basic Math Examples

$6 f + (- 5 f - f) + \frac{7}{7}$

Step 1

Remove parentheses.

$6 f - 5 f - f + \frac{7}{7}$

Step 2

Find the common denominator.

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Step 2.1

Write $6 f$ as a fraction with denominator $1$ .

$\frac{6 f}{1} - 5 f - f + \frac{7}{7}$

Step 2.2

Multiply $\frac{6 f}{1}$ by $\frac{7}{7}$ .

$\frac{6 f}{1} \cdot \frac{7}{7} - 5 f - f + \frac{7}{7}$

Step 2.3

Multiply $\frac{6 f}{1}$ by $\frac{7}{7}$ .

$\frac{6 f \cdot 7}{7} - 5 f - f + \frac{7}{7}$

Step 2.4

Write $- 5 f$ as a fraction with denominator $1$ .

$\frac{6 f \cdot 7}{7} + \frac{- 5 f}{1} - f + \frac{7}{7}$

Step 2.5

Multiply $\frac{- 5 f}{1}$ by $\frac{7}{7}$ .

$\frac{6 f \cdot 7}{7} + \frac{- 5 f}{1} \cdot \frac{7}{7} - f + \frac{7}{7}$

Step 2.6

Multiply $\frac{- 5 f}{1}$ by $\frac{7}{7}$ .

$\frac{6 f \cdot 7}{7} + \frac{- 5 f \cdot 7}{7} - f + \frac{7}{7}$

Step 2.7

Write $- f$ as a fraction with denominator $1$ .

$\frac{6 f \cdot 7}{7} + \frac{- 5 f \cdot 7}{7} + \frac{- f}{1} + \frac{7}{7}$

Step 2.8

Multiply $\frac{- f}{1}$ by $\frac{7}{7}$ .

$\frac{6 f \cdot 7}{7} + \frac{- 5 f \cdot 7}{7} + \frac{- f}{1} \cdot \frac{7}{7} + \frac{7}{7}$

Step 2.9

Multiply $\frac{- f}{1}$ by $\frac{7}{7}$ .

$\frac{6 f \cdot 7}{7} + \frac{- 5 f \cdot 7}{7} + \frac{- f \cdot 7}{7} + \frac{7}{7}$

Step 3

Combine the numerators over the common denominator.

$\frac{6 f \cdot 7 - 5 f \cdot 7 - f \cdot 7 + 7}{7}$

Step 4

Simplify each term.

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Step 4.1

Multiply $7$ by $6$ .

$\frac{42 f - 5 f \cdot 7 - f \cdot 7 + 7}{7}$

Step 4.2

Multiply $7$ by $- 5$ .

$\frac{42 f - 35 f - f \cdot 7 + 7}{7}$

Step 4.3

Multiply $7$ by $- 1$ .

$\frac{42 f - 35 f - 7 f + 7}{7}$

Step 5

Simplify by adding terms.

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Step 5.1

Subtract $35 f$ from $42 f$ .

$\frac{7 f - 7 f + 7}{7}$

Step 5.2

Subtract $7 f$ from $7 f$ .

$\frac{0 + 7}{7}$

Step 5.3

Simplify the expression.

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Step 5.3.1

Add $0$ and $7$ .

$\frac{7}{7}$

Step 5.3.2

Divide $7$ by $7$ .

$1$