Solve for m 2 2/9=-4/5m

$2 \frac{2}{9} = - \frac{4}{5} m$

Step 1

Simplify the left side.

Convert $2 \frac{2}{9}$ to an improper fraction.

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

$2 + \frac{2}{9} = - \frac{4}{5} m$

Add $2$ and $\frac{2}{9}$ .

To write $2$ as a fraction with a common denominator, multiply by $\frac{9}{9}$ .

$2 \cdot \frac{9}{9} + \frac{2}{9} = - \frac{4}{5} m$

Combine $2$ and $\frac{9}{9}$ .

$\frac{2 \cdot 9}{9} + \frac{2}{9} = - \frac{4}{5} m$

Combine the numerators over the common denominator.

$\frac{2 \cdot 9 + 2}{9} = - \frac{4}{5} m$

Simplify the numerator.

Multiply $2$ by $9$ .

$\frac{18 + 2}{9} = - \frac{4}{5} m$

Add $18$ and $2$ .

$\frac{20}{9} = - \frac{4}{5} m$

Step 2

Simplify the right side.

Simplify $- \frac{4}{5} m$ .

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

$\frac{20}{9} = - \frac{m \cdot 4}{5}$

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

$\frac{20}{9} = - \frac{4 m}{5}$

Step 3

Rewrite the equation as $- \frac{4 m}{5} = \frac{20}{9}$ .

$- \frac{4 m}{5} = \frac{20}{9}$

Step 4

Multiply both sides of the equation by $- \frac{5}{4}$ .

$- \frac{5}{4} (- \frac{4 m}{5}) = - \frac{5}{4} \cdot \frac{20}{9}$

Step 5

Simplify both sides of the equation.

Simplify the left side.

Simplify $- \frac{5}{4} (- \frac{4 m}{5})$ .

Cancel the common factor of $5$ .

Move the leading negative in $- \frac{5}{4}$ into the numerator.

$\frac{- 5}{4} (- \frac{4 m}{5}) = - \frac{5}{4} \cdot \frac{20}{9}$

Move the leading negative in $- \frac{4 m}{5}$ into the numerator.

$\frac{- 5}{4} \cdot \frac{- 4 m}{5} = - \frac{5}{4} \cdot \frac{20}{9}$

Factor $5$ out of $- 5$ .

$\frac{5 (- 1)}{4} \cdot \frac{- 4 m}{5} = - \frac{5}{4} \cdot \frac{20}{9}$

Cancel the common factor.

$\frac{5 \cdot - 1}{4} \cdot \frac{- 4 m}{5} = - \frac{5}{4} \cdot \frac{20}{9}$

Rewrite the expression.

$\frac{- 1}{4} (- 4 m) = - \frac{5}{4} \cdot \frac{20}{9}$

Cancel the common factor of $4$ .

Factor $4$ out of $- 4 m$ .

$\frac{- 1}{4} (4 (- m)) = - \frac{5}{4} \cdot \frac{20}{9}$

Cancel the common factor.

$\frac{- 1}{4} (4 (- m)) = - \frac{5}{4} \cdot \frac{20}{9}$

Rewrite the expression.

$- - m = - \frac{5}{4} \cdot \frac{20}{9}$

Multiply.

Multiply $- 1$ by $- 1$ .

$1 m = - \frac{5}{4} \cdot \frac{20}{9}$

Multiply $m$ by $1$ .

$m = - \frac{5}{4} \cdot \frac{20}{9}$

Simplify the right side.

Simplify $- \frac{5}{4} \cdot \frac{20}{9}$ .

Cancel the common factor of $4$ .

Move the leading negative in $- \frac{5}{4}$ into the numerator.

$m = \frac{- 5}{4} \cdot \frac{20}{9}$

Factor $4$ out of $20$ .

$m = \frac{- 5}{4} \cdot \frac{4 (5)}{9}$

Cancel the common factor.

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

Rewrite the expression.

$m = - 5 (\frac{5}{9})$

Combine $- 5$ and $\frac{5}{9}$ .

$m = \frac{- 5 \cdot 5}{9}$

Simplify the expression.

Multiply $- 5$ by $5$ .

$m = \frac{- 25}{9}$

Move the negative in front of the fraction.

$m = - \frac{25}{9}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$m = - \frac{25}{9}$

Decimal Form:

$m = - 2.\overline{7}$

Mixed Number Form:

$m = - 2 \frac{7}{9}$

Solve for m 2 2/9=-4/5m

Related Questions

Support LCMGCF.com by disabling your adblocker.