Basic Math Examples

$\frac{4}{5} c - 7 = \frac{1}{10} c$

Step 1

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

$\frac{4 c}{5} - 7 = \frac{1}{10} c$

Step 2

Combine $\frac{1}{10}$ and $c$ .

$\frac{4 c}{5} - 7 = \frac{c}{10}$

Step 3

Move all terms containing $c$ to the left side of the equation.

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Step 3.1

Subtract $\frac{c}{10}$ from both sides of the equation.

$\frac{4 c}{5} - 7 - \frac{c}{10} = 0$

Step 3.2

To write $\frac{4 c}{5}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{4 c}{5} \cdot \frac{2}{2} - \frac{c}{10} - 7 = 0$

Step 3.3

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

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Step 3.3.1

Multiply $\frac{4 c}{5}$ by $\frac{2}{2}$ .

$\frac{4 c \cdot 2}{5 \cdot 2} - \frac{c}{10} - 7 = 0$

Step 3.3.2

Multiply $5$ by $2$ .

$\frac{4 c \cdot 2}{10} - \frac{c}{10} - 7 = 0$

Step 3.4

Combine the numerators over the common denominator.

$\frac{4 c \cdot 2 - c}{10} - 7 = 0$

Step 3.5

Simplify each term.

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Step 3.5.1

Simplify the numerator.

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Step 3.5.1.1

Factor $c$ out of $4 c \cdot 2 - c$ .

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Step 3.5.1.1.1

Factor $c$ out of $4 c \cdot 2$ .

$\frac{c (4 \cdot 2) - c}{10} - 7 = 0$

Step 3.5.1.1.2

Factor $c$ out of $- c$ .

$\frac{c (4 \cdot 2) + c \cdot - 1}{10} - 7 = 0$

Step 3.5.1.1.3

Factor $c$ out of $c (4 \cdot 2) + c \cdot - 1$ .

$\frac{c (4 \cdot 2 - 1)}{10} - 7 = 0$

Step 3.5.1.2

Multiply $4$ by $2$ .

$\frac{c (8 - 1)}{10} - 7 = 0$

Step 3.5.1.3

Subtract $1$ from $8$ .

$\frac{c \cdot 7}{10} - 7 = 0$

Step 3.5.2

Move $7$ to the left of $c$ .

$\frac{7 c}{10} - 7 = 0$

Step 4

Add $7$ to both sides of the equation.

$\frac{7 c}{10} = 7$

Step 5

Multiply both sides of the equation by $\frac{10}{7}$ .

$\frac{10}{7} \cdot \frac{7 c}{10} = \frac{10}{7} \cdot 7$

Step 6

Simplify both sides of the equation.

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Step 6.1

Simplify the left side.

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Step 6.1.1

Simplify $\frac{10}{7} \cdot \frac{7 c}{10}$ .

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Step 6.1.1.1

Cancel the common factor of $10$ .

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Step 6.1.1.1.1

Cancel the common factor.

$\frac{10}{7} \cdot \frac{7 c}{10} = \frac{10}{7} \cdot 7$

Step 6.1.1.1.2

Rewrite the expression.

$\frac{1}{7} (7 c) = \frac{10}{7} \cdot 7$

Step 6.1.1.2

Cancel the common factor of $7$ .

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Step 6.1.1.2.1

Factor $7$ out of $7 c$ .

$\frac{1}{7} (7 (c)) = \frac{10}{7} \cdot 7$

Step 6.1.1.2.2

Cancel the common factor.

$\frac{1}{7} (7 c) = \frac{10}{7} \cdot 7$

Step 6.1.1.2.3

Rewrite the expression.

$c = \frac{10}{7} \cdot 7$

Step 6.2

Simplify the right side.

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Step 6.2.1

Cancel the common factor of $7$ .

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Step 6.2.1.1

Cancel the common factor.

$c = \frac{10}{7} \cdot 7$

Step 6.2.1.2

Rewrite the expression.

$c = 10$