Solve for m 2/3+(3m)/5=31/15

$\frac{2}{3} + \frac{3 m}{5} = \frac{31}{15}$

Step 1

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

Subtract $\frac{2}{3}$ from both sides of the equation.

$\frac{3 m}{5} = \frac{31}{15} - \frac{2}{3}$

To write $- \frac{2}{3}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{3 m}{5} = \frac{31}{15} - \frac{2}{3} \cdot \frac{5}{5}$

Write each expression with a common denominator of $15$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{2}{3}$ by $\frac{5}{5}$ .

$\frac{3 m}{5} = \frac{31}{15} - \frac{2 \cdot 5}{3 \cdot 5}$

Multiply $3$ by $5$ .

$\frac{3 m}{5} = \frac{31}{15} - \frac{2 \cdot 5}{15}$

Combine the numerators over the common denominator.

$\frac{3 m}{5} = \frac{31 - 2 \cdot 5}{15}$

Simplify the numerator.

Multiply $- 2$ by $5$ .

$\frac{3 m}{5} = \frac{31 - 10}{15}$

Subtract $10$ from $31$ .

$\frac{3 m}{5} = \frac{21}{15}$

Cancel the common factor of $21$ and $15$ .

Factor $3$ out of $21$ .

$\frac{3 m}{5} = \frac{3 (7)}{15}$

Cancel the common factors.

Factor $3$ out of $15$ .

$\frac{3 m}{5} = \frac{3 \cdot 7}{3 \cdot 5}$

Cancel the common factor.

$\frac{3 m}{5} = \frac{3 \cdot 7}{3 \cdot 5}$

Rewrite the expression.

$\frac{3 m}{5} = \frac{7}{5}$

Step 2

Since the expression on each side of the equation has the same denominator, the numerators must be equal.

$3 m = 7$

Step 3

Divide each term in $3 m = 7$ by $3$ and simplify.

Divide each term in $3 m = 7$ by $3$ .

$\frac{3 m}{3} = \frac{7}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 m}{3} = \frac{7}{3}$

Divide $m$ by $1$ .

$m = \frac{7}{3}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$m = \frac{7}{3}$

Decimal Form:

$m = 2.\overline{3}$

Mixed Number Form:

$m = 2 \frac{1}{3}$

Solve for m 2/3+(3m)/5=31/15

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