Basic Math Examples

$\frac{1}{6} w + 1 \frac{1}{6} = - 48$

Step 1

Simplify the left side.

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Step 1.1

Simplify $\frac{1}{6} w + 1 \frac{1}{6}$ .

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Step 1.1.1

Convert $1 \frac{1}{6}$ to an improper fraction.

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Step 1.1.1.1

A mixed number is an addition of its whole and fractional parts.

$\frac{1}{6} w + 1 + \frac{1}{6} = - 48$

Step 1.1.1.2

Add $1$ and $\frac{1}{6}$ .

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Step 1.1.1.2.1

Write $1$ as a fraction with a common denominator.

$\frac{1}{6} w + \frac{6}{6} + \frac{1}{6} = - 48$

Step 1.1.1.2.2

Combine the numerators over the common denominator.

$\frac{1}{6} w + \frac{6 + 1}{6} = - 48$

Step 1.1.1.2.3

Add $6$ and $1$ .

$\frac{1}{6} w + \frac{7}{6} = - 48$

Step 1.1.2

Combine $\frac{1}{6}$ and $w$ .

$\frac{w}{6} + \frac{7}{6} = - 48$

Step 2

Move all terms not containing $w$ to the right side of the equation.

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Step 2.1

Subtract $\frac{7}{6}$ from both sides of the equation.

$\frac{w}{6} = - 48 - \frac{7}{6}$

Step 2.2

To write $- 48$ as a fraction with a common denominator, multiply by $\frac{6}{6}$ .

$\frac{w}{6} = - 48 \cdot \frac{6}{6} - \frac{7}{6}$

Step 2.3

Combine $- 48$ and $\frac{6}{6}$ .

$\frac{w}{6} = \frac{- 48 \cdot 6}{6} - \frac{7}{6}$

Step 2.4

Combine the numerators over the common denominator.

$\frac{w}{6} = \frac{- 48 \cdot 6 - 7}{6}$

Step 2.5

Simplify the numerator.

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Step 2.5.1

Multiply $- 48$ by $6$ .

$\frac{w}{6} = \frac{- 288 - 7}{6}$

Step 2.5.2

Subtract $7$ from $- 288$ .

$\frac{w}{6} = \frac{- 295}{6}$

Step 2.6

Move the negative in front of the fraction.

$\frac{w}{6} = - \frac{295}{6}$

Step 3

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

$w = - 295$