Basic Math Examples

$\frac{9}{5} = \frac{12}{2 t + 3}$

Step 1

Rewrite the equation as $\frac{12}{2 t + 3} = \frac{9}{5}$ .

$\frac{12}{2 t + 3} = \frac{9}{5}$

Step 2

Multiply the numerator of the first fraction by the denominator of the second fraction. Set this equal to the product of the denominator of the first fraction and the numerator of the second fraction.

$12 \cdot 5 = (2 t + 3) \cdot 9$

Step 3

Solve the equation for $t$ .

Tap for more steps...

Step 3.1

Rewrite the equation as $(2 t + 3) \cdot 9 = 12 \cdot 5$ .

$(2 t + 3) \cdot 9 = 12 \cdot 5$

Step 3.2

Multiply $12$ by $5$ .

$(2 t + 3) \cdot 9 = 60$

Step 3.3

Divide each term in $(2 t + 3) \cdot 9 = 60$ by $9$ and simplify.

Tap for more steps...

Step 3.3.1

Divide each term in $(2 t + 3) \cdot 9 = 60$ by $9$ .

$\frac{(2 t + 3) \cdot 9}{9} = \frac{60}{9}$

Step 3.3.2

Simplify the left side.

Tap for more steps...

Step 3.3.2.1

Cancel the common factor of $9$ .

Tap for more steps...

Step 3.3.2.1.1

Cancel the common factor.

$\frac{(2 t + 3) \cdot 9}{9} = \frac{60}{9}$

Step 3.3.2.1.2

Divide $2 t + 3$ by $1$ .

$2 t + 3 = \frac{60}{9}$

Step 3.3.3

Simplify the right side.

Tap for more steps...

Step 3.3.3.1

Cancel the common factor of $60$ and $9$ .

Tap for more steps...

Step 3.3.3.1.1

Factor $3$ out of $60$ .

$2 t + 3 = \frac{3 (20)}{9}$

Step 3.3.3.1.2

Cancel the common factors.

Tap for more steps...

Step 3.3.3.1.2.1

Factor $3$ out of $9$ .

$2 t + 3 = \frac{3 \cdot 20}{3 \cdot 3}$

Step 3.3.3.1.2.2

Cancel the common factor.

$2 t + 3 = \frac{3 \cdot 20}{3 \cdot 3}$

Step 3.3.3.1.2.3

Rewrite the expression.

$2 t + 3 = \frac{20}{3}$

Step 3.4

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

Tap for more steps...

Step 3.4.1

Subtract $3$ from both sides of the equation.

$2 t = \frac{20}{3} - 3$

Step 3.4.2

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

$2 t = \frac{20}{3} - 3 \cdot \frac{3}{3}$

Step 3.4.3

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

$2 t = \frac{20}{3} + \frac{- 3 \cdot 3}{3}$

Step 3.4.4

Combine the numerators over the common denominator.

$2 t = \frac{20 - 3 \cdot 3}{3}$

Step 3.4.5

Simplify the numerator.

Tap for more steps...

Step 3.4.5.1

Multiply $- 3$ by $3$ .

$2 t = \frac{20 - 9}{3}$

Step 3.4.5.2

Subtract $9$ from $20$ .

$2 t = \frac{11}{3}$

Step 3.5

Divide each term in $2 t = \frac{11}{3}$ by $2$ and simplify.

Tap for more steps...

Step 3.5.1

Divide each term in $2 t = \frac{11}{3}$ by $2$ .

$\frac{2 t}{2} = \frac{\frac{11}{3}}{2}$

Step 3.5.2

Simplify the left side.

Tap for more steps...

Step 3.5.2.1

Cancel the common factor of $2$ .

Tap for more steps...

Step 3.5.2.1.1

Cancel the common factor.

$\frac{2 t}{2} = \frac{\frac{11}{3}}{2}$

Step 3.5.2.1.2

Divide $t$ by $1$ .

$t = \frac{\frac{11}{3}}{2}$

Step 3.5.3

Simplify the right side.

Tap for more steps...

Step 3.5.3.1

Multiply the numerator by the reciprocal of the denominator.

$t = \frac{11}{3} \cdot \frac{1}{2}$

Step 3.5.3.2

Multiply $\frac{11}{3} \cdot \frac{1}{2}$ .

Tap for more steps...

Step 3.5.3.2.1

Multiply $\frac{11}{3}$ by $\frac{1}{2}$ .

$t = \frac{11}{3 \cdot 2}$

Step 3.5.3.2.2

Multiply $3$ by $2$ .

$t = \frac{11}{6}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$t = \frac{11}{6}$

Decimal Form:

$t = 1.8\overline{3}$

Mixed Number Form:

$t = 1 \frac{5}{6}$