Basic Math Examples

$m - (\frac{m}{2} - \frac{1}{2}) = 1 - (\frac{m}{5} - \frac{2}{5})$

Step 1

Simplify $m - (\frac{m}{2} - \frac{1}{2})$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Apply the distributive property.

$m - \frac{m}{2} - - \frac{1}{2} = 1 - (\frac{m}{5} - \frac{2}{5})$

Step 1.1.2

Multiply $- - \frac{1}{2}$ .

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Step 1.1.2.1

Multiply $- 1$ by $- 1$ .

$m - \frac{m}{2} + 1 (\frac{1}{2}) = 1 - (\frac{m}{5} - \frac{2}{5})$

Step 1.1.2.2

Multiply $\frac{1}{2}$ by $1$ .

$m - \frac{m}{2} + \frac{1}{2} = 1 - (\frac{m}{5} - \frac{2}{5})$

Step 1.2

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

$m \cdot \frac{2}{2} - \frac{m}{2} + \frac{1}{2} = 1 - (\frac{m}{5} - \frac{2}{5})$

Step 1.3

Simplify terms.

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Step 1.3.1

Combine $m$ and $\frac{2}{2}$ .

$\frac{m \cdot 2}{2} - \frac{m}{2} + \frac{1}{2} = 1 - (\frac{m}{5} - \frac{2}{5})$

Step 1.3.2

Combine the numerators over the common denominator.

$\frac{m \cdot 2 - m}{2} + \frac{1}{2} = 1 - (\frac{m}{5} - \frac{2}{5})$

Step 1.3.3

Combine the numerators over the common denominator.

$\frac{m \cdot 2 - m + 1}{2} = 1 - (\frac{m}{5} - \frac{2}{5})$

Step 1.4

Move $2$ to the left of $m$ .

$\frac{2 m - m + 1}{2} = 1 - (\frac{m}{5} - \frac{2}{5})$

Step 1.5

Subtract $m$ from $2 m$ .

$\frac{m + 1}{2} = 1 - (\frac{m}{5} - \frac{2}{5})$

Step 2

Simplify $1 - (\frac{m}{5} - \frac{2}{5})$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Apply the distributive property.

$\frac{m + 1}{2} = 1 - \frac{m}{5} - - \frac{2}{5}$

Step 2.1.2

Multiply $- - \frac{2}{5}$ .

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Step 2.1.2.1

Multiply $- 1$ by $- 1$ .

$\frac{m + 1}{2} = 1 - \frac{m}{5} + 1 (\frac{2}{5})$

Step 2.1.2.2

Multiply $\frac{2}{5}$ by $1$ .

$\frac{m + 1}{2} = 1 - \frac{m}{5} + \frac{2}{5}$

Step 2.2

Simplify the expression.

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Step 2.2.1

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

$\frac{m + 1}{2} = - \frac{m}{5} + \frac{5}{5} + \frac{2}{5}$

Step 2.2.2

Combine the numerators over the common denominator.

$\frac{m + 1}{2} = - \frac{m}{5} + \frac{5 + 2}{5}$

Step 2.2.3

Add $5$ and $2$ .

$\frac{m + 1}{2} = - \frac{m}{5} + \frac{7}{5}$

Step 3

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

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Step 3.1

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

$\frac{m + 1}{2} + \frac{m}{5} = \frac{7}{5}$

Step 3.2

To write $\frac{m + 1}{2}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{m + 1}{2} \cdot \frac{5}{5} + \frac{m}{5} = \frac{7}{5}$

Step 3.3

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

$\frac{m + 1}{2} \cdot \frac{5}{5} + \frac{m}{5} \cdot \frac{2}{2} = \frac{7}{5}$

Step 3.4

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

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Step 3.4.1

Multiply $\frac{m + 1}{2}$ by $\frac{5}{5}$ .

$\frac{(m + 1) \cdot 5}{2 \cdot 5} + \frac{m}{5} \cdot \frac{2}{2} = \frac{7}{5}$

Step 3.4.2

Multiply $2$ by $5$ .

$\frac{(m + 1) \cdot 5}{10} + \frac{m}{5} \cdot \frac{2}{2} = \frac{7}{5}$

Step 3.4.3

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

$\frac{(m + 1) \cdot 5}{10} + \frac{m \cdot 2}{5 \cdot 2} = \frac{7}{5}$

Step 3.4.4

Multiply $5$ by $2$ .

$\frac{(m + 1) \cdot 5}{10} + \frac{m \cdot 2}{10} = \frac{7}{5}$

Step 3.5

Combine the numerators over the common denominator.

$\frac{(m + 1) \cdot 5 + m \cdot 2}{10} = \frac{7}{5}$

Step 3.6

Simplify the numerator.

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Step 3.6.1

Apply the distributive property.

$\frac{m \cdot 5 + 1 \cdot 5 + m \cdot 2}{10} = \frac{7}{5}$

Step 3.6.2

Move $5$ to the left of $m$ .

$\frac{5 \cdot m + 1 \cdot 5 + m \cdot 2}{10} = \frac{7}{5}$

Step 3.6.3

Multiply $5$ by $1$ .

$\frac{5 \cdot m + 5 + m \cdot 2}{10} = \frac{7}{5}$

Step 3.6.4

Move $2$ to the left of $m$ .

$\frac{5 m + 5 + 2 \cdot m}{10} = \frac{7}{5}$

Step 3.6.5

Add $5 m$ and $2 m$ .

$\frac{7 m + 5}{10} = \frac{7}{5}$

Step 4

Multiply both sides by $10$ .

$\frac{7 m + 5}{10} \cdot 10 = \frac{7}{5} \cdot 10$

Step 5

Simplify.

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Step 5.1

Simplify the left side.

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Step 5.1.1

Cancel the common factor of $10$ .

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Step 5.1.1.1

Cancel the common factor.

$\frac{7 m + 5}{10} \cdot 10 = \frac{7}{5} \cdot 10$

Step 5.1.1.2

Rewrite the expression.

$7 m + 5 = \frac{7}{5} \cdot 10$

Step 5.2

Simplify the right side.

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Step 5.2.1

Simplify $\frac{7}{5} \cdot 10$ .

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Step 5.2.1.1

Cancel the common factor of $5$ .

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Step 5.2.1.1.1

Factor $5$ out of $10$ .

$7 m + 5 = \frac{7}{5} \cdot (5 (2))$

Step 5.2.1.1.2

Cancel the common factor.

$7 m + 5 = \frac{7}{5} \cdot (5 \cdot 2)$

Step 5.2.1.1.3

Rewrite the expression.

$7 m + 5 = 7 \cdot 2$

Step 5.2.1.2

Multiply $7$ by $2$ .

$7 m + 5 = 14$

Step 6

Solve for $m$ .

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Step 6.1

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

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Step 6.1.1

Subtract $5$ from both sides of the equation.

$7 m = 14 - 5$

Step 6.1.2

Subtract $5$ from $14$ .

$7 m = 9$

Step 6.2

Divide each term in $7 m = 9$ by $7$ and simplify.

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Step 6.2.1

Divide each term in $7 m = 9$ by $7$ .

$\frac{7 m}{7} = \frac{9}{7}$

Step 6.2.2

Simplify the left side.

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Step 6.2.2.1

Cancel the common factor of $7$ .

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Step 6.2.2.1.1

Cancel the common factor.

$\frac{7 m}{7} = \frac{9}{7}$

Step 6.2.2.1.2

Divide $m$ by $1$ .

$m = \frac{9}{7}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$m = \frac{9}{7}$

Decimal Form:

$m = 1.\overline{285714}$

Mixed Number Form:

$m = 1 \frac{2}{7}$