Basic Math Examples

$\frac{9}{10} - \frac{4}{5} m = \frac{m}{10} - \frac{1}{3}$

Step 1

Simplify each term.

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Step 1.1

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

$\frac{9}{10} - \frac{m \cdot 4}{5} = \frac{m}{10} - \frac{1}{3}$

Step 1.2

Move $4$ to the left of $m$ .

$\frac{9}{10} - \frac{4 m}{5} = \frac{m}{10} - \frac{1}{3}$

Step 2

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

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Step 2.1

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

$\frac{9}{10} - \frac{4 m}{5} - \frac{m}{10} = - \frac{1}{3}$

Step 2.2

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

$\frac{9}{10} - \frac{4 m}{5} \cdot \frac{2}{2} - \frac{m}{10} = - \frac{1}{3}$

Step 2.3

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

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Step 2.3.1

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

$\frac{9}{10} - \frac{4 m \cdot 2}{5 \cdot 2} - \frac{m}{10} = - \frac{1}{3}$

Step 2.3.2

Multiply $5$ by $2$ .

$\frac{9}{10} - \frac{4 m \cdot 2}{10} - \frac{m}{10} = - \frac{1}{3}$

Step 2.4

Combine the numerators over the common denominator.

$\frac{9}{10} + \frac{- 4 m \cdot 2 - m}{10} = - \frac{1}{3}$

Step 2.5

Combine the numerators over the common denominator.

$\frac{9 - 4 m \cdot 2 - m}{10} = - \frac{1}{3}$

Step 2.6

Multiply $2$ by $- 4$ .

$\frac{9 - 8 m - m}{10} = - \frac{1}{3}$

Step 2.7

Subtract $m$ from $- 8 m$ .

$\frac{9 - 9 m}{10} = - \frac{1}{3}$

Step 2.8

Factor $9$ out of $9 - 9 m$ .

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Step 2.8.1

Factor $9$ out of $9$ .

$\frac{9 (1) - 9 m}{10} = - \frac{1}{3}$

Step 2.8.2

Factor $9$ out of $- 9 m$ .

$\frac{9 (1) + 9 (- m)}{10} = - \frac{1}{3}$

Step 2.8.3

Factor $9$ out of $9 (1) + 9 (- m)$ .

$\frac{9 (1 - m)}{10} = - \frac{1}{3}$

Step 3

Multiply both sides by $10$ .

$\frac{9 (1 - m)}{10} \cdot 10 = - \frac{1}{3} \cdot 10$

Step 4

Simplify.

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Step 4.1

Simplify the left side.

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Step 4.1.1

Simplify $\frac{9 (1 - m)}{10} \cdot 10$ .

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Step 4.1.1.1

Cancel the common factor of $10$ .

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Step 4.1.1.1.1

Cancel the common factor.

$\frac{9 (1 - m)}{10} \cdot 10 = - \frac{1}{3} \cdot 10$

Step 4.1.1.1.2

Rewrite the expression.

$9 (1 - m) = - \frac{1}{3} \cdot 10$

Step 4.1.1.2

Apply the distributive property.

$9 \cdot 1 + 9 (- m) = - \frac{1}{3} \cdot 10$

Step 4.1.1.3

Simplify the expression.

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Step 4.1.1.3.1

Multiply $9$ by $1$ .

$9 + 9 (- m) = - \frac{1}{3} \cdot 10$

Step 4.1.1.3.2

Multiply $- 1$ by $9$ .

$9 - 9 m = - \frac{1}{3} \cdot 10$

Step 4.1.1.3.3

Reorder $9$ and $- 9 m$ .

$- 9 m + 9 = - \frac{1}{3} \cdot 10$

Step 4.2

Simplify the right side.

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Step 4.2.1

Simplify $- \frac{1}{3} \cdot 10$ .

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Step 4.2.1.1

Multiply $- \frac{1}{3} \cdot 10$ .

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Step 4.2.1.1.1

Multiply $10$ by $- 1$ .

$- 9 m + 9 = - 10 (\frac{1}{3})$

Step 4.2.1.1.2

Combine $- 10$ and $\frac{1}{3}$ .

$- 9 m + 9 = \frac{- 10}{3}$

Step 4.2.1.2

Move the negative in front of the fraction.

$- 9 m + 9 = - \frac{10}{3}$

Step 5

Solve for $m$ .

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Step 5.1

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

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Step 5.1.1

Subtract $9$ from both sides of the equation.

$- 9 m = - \frac{10}{3} - 9$

Step 5.1.2

To write $- 9$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$- 9 m = - \frac{10}{3} - 9 \cdot \frac{3}{3}$

Step 5.1.3

Combine $- 9$ and $\frac{3}{3}$ .

$- 9 m = - \frac{10}{3} + \frac{- 9 \cdot 3}{3}$

Step 5.1.4

Combine the numerators over the common denominator.

$- 9 m = \frac{- 10 - 9 \cdot 3}{3}$

Step 5.1.5

Simplify the numerator.

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Step 5.1.5.1

Multiply $- 9$ by $3$ .

$- 9 m = \frac{- 10 - 27}{3}$

Step 5.1.5.2

Subtract $27$ from $- 10$ .

$- 9 m = \frac{- 37}{3}$

Step 5.1.6

Move the negative in front of the fraction.

$- 9 m = - \frac{37}{3}$

Step 5.2

Divide each term in $- 9 m = - \frac{37}{3}$ by $- 9$ and simplify.

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Step 5.2.1

Divide each term in $- 9 m = - \frac{37}{3}$ by $- 9$ .

$\frac{- 9 m}{- 9} = \frac{- \frac{37}{3}}{- 9}$

Step 5.2.2

Simplify the left side.

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Step 5.2.2.1

Cancel the common factor of $- 9$ .

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Step 5.2.2.1.1

Cancel the common factor.

$\frac{- 9 m}{- 9} = \frac{- \frac{37}{3}}{- 9}$

Step 5.2.2.1.2

Divide $m$ by $1$ .

$m = \frac{- \frac{37}{3}}{- 9}$

Step 5.2.3

Simplify the right side.

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Step 5.2.3.1

Multiply the numerator by the reciprocal of the denominator.

$m = - \frac{37}{3} \cdot \frac{1}{- 9}$

Step 5.2.3.2

Move the negative in front of the fraction.

$m = - \frac{37}{3} (- \frac{1}{9})$

Step 5.2.3.3

Multiply $- \frac{37}{3} (- \frac{1}{9})$ .

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Step 5.2.3.3.1

Multiply $- 1$ by $- 1$ .

$m = 1 (\frac{37}{3}) \frac{1}{9}$

Step 5.2.3.3.2

Multiply $\frac{37}{3}$ by $1$ .

$m = \frac{37}{3} \cdot \frac{1}{9}$

Step 5.2.3.3.3

Multiply $\frac{37}{3}$ by $\frac{1}{9}$ .

$m = \frac{37}{3 \cdot 9}$

Step 5.2.3.3.4

Multiply $3$ by $9$ .

$m = \frac{37}{27}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$m = \frac{37}{27}$

Decimal Form:

$m = 1.\overline{370}$

Mixed Number Form:

$m = 1 \frac{10}{27}$