Solve for c c-8 1/5=10 3/10

$c - 8 \frac{1}{5} = 10 \frac{3}{10}$

Step 1

Simplify the left side.

Convert $8 \frac{1}{5}$ to an improper fraction.

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

$c - (8 + \frac{1}{5}) = 10 \frac{3}{10}$

Add $8$ and $\frac{1}{5}$ .

To write $8$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$c - (8 \cdot \frac{5}{5} + \frac{1}{5}) = 10 \frac{3}{10}$

Combine $8$ and $\frac{5}{5}$ .

$c - (\frac{8 \cdot 5}{5} + \frac{1}{5}) = 10 \frac{3}{10}$

Combine the numerators over the common denominator.

$c - \frac{8 \cdot 5 + 1}{5} = 10 \frac{3}{10}$

Simplify the numerator.

Multiply $8$ by $5$ .

$c - \frac{40 + 1}{5} = 10 \frac{3}{10}$

Add $40$ and $1$ .

$c - \frac{41}{5} = 10 \frac{3}{10}$

Step 2

Simplify the right side.

Convert $10 \frac{3}{10}$ to an improper fraction.

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

$c - \frac{41}{5} = 10 + \frac{3}{10}$

Add $10$ and $\frac{3}{10}$ .

To write $10$ as a fraction with a common denominator, multiply by $\frac{10}{10}$ .

$c - \frac{41}{5} = 10 \cdot \frac{10}{10} + \frac{3}{10}$

Combine $10$ and $\frac{10}{10}$ .

$c - \frac{41}{5} = \frac{10 \cdot 10}{10} + \frac{3}{10}$

Combine the numerators over the common denominator.

$c - \frac{41}{5} = \frac{10 \cdot 10 + 3}{10}$

Simplify the numerator.

Multiply $10$ by $10$ .

$c - \frac{41}{5} = \frac{100 + 3}{10}$

Add $100$ and $3$ .

$c - \frac{41}{5} = \frac{103}{10}$

Step 3

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

Add $\frac{41}{5}$ to both sides of the equation.

$c = \frac{103}{10} + \frac{41}{5}$

To write $\frac{41}{5}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$c = \frac{103}{10} + \frac{41}{5} \cdot \frac{2}{2}$

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

Multiply $\frac{41}{5}$ by $\frac{2}{2}$ .

$c = \frac{103}{10} + \frac{41 \cdot 2}{5 \cdot 2}$

Multiply $5$ by $2$ .

$c = \frac{103}{10} + \frac{41 \cdot 2}{10}$

Combine the numerators over the common denominator.

$c = \frac{103 + 41 \cdot 2}{10}$

Simplify the numerator.

Multiply $41$ by $2$ .

$c = \frac{103 + 82}{10}$

Add $103$ and $82$ .

$c = \frac{185}{10}$

Cancel the common factor of $185$ and $10$ .

Factor $5$ out of $185$ .

$c = \frac{5 (37)}{10}$

Cancel the common factors.

Factor $5$ out of $10$ .

$c = \frac{5 \cdot 37}{5 \cdot 2}$

Cancel the common factor.

$c = \frac{5 \cdot 37}{5 \cdot 2}$

Rewrite the expression.

$c = \frac{37}{2}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$c = \frac{37}{2}$

Decimal Form:

$c = 18.5$

Mixed Number Form:

$c = 18 \frac{1}{2}$

Solve for c c-8 1/5=10 3/10

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