Solve for w w-4 2/5=1/10

$w - 4 \frac{2}{5} = \frac{1}{10}$

Simplify the left side.

Convert $4 \frac{2}{5}$ to an improper fraction.

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

$w - (4 + \frac{2}{5}) = \frac{1}{10}$

Add $4$ and $\frac{2}{5}$ .

To write $4$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$w - (4 \cdot \frac{5}{5} + \frac{2}{5}) = \frac{1}{10}$

Combine $4$ and $\frac{5}{5}$ .

$w - (\frac{4 \cdot 5}{5} + \frac{2}{5}) = \frac{1}{10}$

Combine the numerators over the common denominator.

$w - \frac{4 \cdot 5 + 2}{5} = \frac{1}{10}$

Simplify the numerator.

Multiply $4$ by $5$ .

$w - \frac{20 + 2}{5} = \frac{1}{10}$

Add $20$ and $2$ .

$w - \frac{22}{5} = \frac{1}{10}$

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

Add $\frac{22}{5}$ to both sides of the equation.

$w = \frac{1}{10} + \frac{22}{5}$

To write $\frac{22}{5}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$w = \frac{1}{10} + \frac{22}{5} \cdot \frac{2}{2}$

Write each expression with a common denominator of $10$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{22}{5}$ by $\frac{2}{2}$ .

$w = \frac{1}{10} + \frac{22 \cdot 2}{5 \cdot 2}$

Multiply $5$ by $2$ .

$w = \frac{1}{10} + \frac{22 \cdot 2}{10}$

Combine the numerators over the common denominator.

$w = \frac{1 + 22 \cdot 2}{10}$

Simplify the numerator.

Multiply $22$ by $2$ .

$w = \frac{1 + 44}{10}$

Add $1$ and $44$ .

$w = \frac{45}{10}$

Cancel the common factor of $45$ and $10$ .

Factor $5$ out of $45$ .

$w = \frac{5 (9)}{10}$

Cancel the common factors.

Factor $5$ out of $10$ .

$w = \frac{5 \cdot 9}{5 \cdot 2}$

Cancel the common factor.

$w = \frac{5 \cdot 9}{5 \cdot 2}$

Rewrite the expression.

$w = \frac{9}{2}$

The result can be shown in multiple forms.

Exact Form:

$w = \frac{9}{2}$

Decimal Form:

$w = 4.5$

Mixed Number Form:

$w = 4 \frac{1}{2}$

Solve for w w-4 2/5=1/10

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