Basic Math Examples

$6 \frac{1}{3} - m = 3$

Step 1

Simplify the left side.

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Step 1.1

Convert $6 \frac{1}{3}$ to an improper fraction.

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Step 1.1.1

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

$6 + \frac{1}{3} - m = 3$

Step 1.1.2

Add $6$ and $\frac{1}{3}$ .

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Step 1.1.2.1

To write $6$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$6 \cdot \frac{3}{3} + \frac{1}{3} - m = 3$

Step 1.1.2.2

Combine $6$ and $\frac{3}{3}$ .

$\frac{6 \cdot 3}{3} + \frac{1}{3} - m = 3$

Step 1.1.2.3

Combine the numerators over the common denominator.

$\frac{6 \cdot 3 + 1}{3} - m = 3$

Step 1.1.2.4

Simplify the numerator.

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Step 1.1.2.4.1

Multiply $6$ by $3$ .

$\frac{18 + 1}{3} - m = 3$

Step 1.1.2.4.2

Add $18$ and $1$ .

$\frac{19}{3} - m = 3$

Step 2

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

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Step 2.1

Subtract $\frac{19}{3}$ from both sides of the equation.

$- m = 3 - \frac{19}{3}$

Step 2.2

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

$- m = 3 \cdot \frac{3}{3} - \frac{19}{3}$

Step 2.3

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

$- m = \frac{3 \cdot 3}{3} - \frac{19}{3}$

Step 2.4

Combine the numerators over the common denominator.

$- m = \frac{3 \cdot 3 - 19}{3}$

Step 2.5

Simplify the numerator.

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Step 2.5.1

Multiply $3$ by $3$ .

$- m = \frac{9 - 19}{3}$

Step 2.5.2

Subtract $19$ from $9$ .

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

Step 2.6

Move the negative in front of the fraction.

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

Step 3

Divide each term in $- m = - \frac{10}{3}$ by $- 1$ and simplify.

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Step 3.1

Divide each term in $- m = - \frac{10}{3}$ by $- 1$ .

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

Step 3.2

Simplify the left side.

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Step 3.2.1

Dividing two negative values results in a positive value.

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

Step 3.2.2

Divide $m$ by $1$ .

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

Step 3.3

Simplify the right side.

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Step 3.3.1

Dividing two negative values results in a positive value.

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

Step 3.3.2

Divide $\frac{10}{3}$ by $1$ .

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

Step 4

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$m = 3.\overline{3}$

Mixed Number Form:

$m = 3 \frac{1}{3}$