Solve for t 2 2/5t=9/10

$2 \frac{2}{5} t = \frac{9}{10}$

Step 1

Simplify the left side.

Simplify $2 \frac{2}{5} t$ .

Convert $2 \frac{2}{5}$ to an improper fraction.

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

$(2 + \frac{2}{5}) t = \frac{9}{10}$

Add $2$ and $\frac{2}{5}$ .

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

$(2 \cdot \frac{5}{5} + \frac{2}{5}) t = \frac{9}{10}$

Combine $2$ and $\frac{5}{5}$ .

$(\frac{2 \cdot 5}{5} + \frac{2}{5}) t = \frac{9}{10}$

Combine the numerators over the common denominator.

$\frac{2 \cdot 5 + 2}{5} t = \frac{9}{10}$

Simplify the numerator.

Multiply $2$ by $5$ .

$\frac{10 + 2}{5} t = \frac{9}{10}$

Add $10$ and $2$ .

$\frac{12}{5} t = \frac{9}{10}$

Combine $\frac{12}{5}$ and $t$ .

$\frac{12 t}{5} = \frac{9}{10}$

Step 2

Multiply both sides of the equation by $\frac{5}{12}$ .

$\frac{5}{12} \cdot \frac{12 t}{5} = \frac{5}{12} \cdot \frac{9}{10}$

Step 3

Simplify both sides of the equation.

Simplify the left side.

Simplify $\frac{5}{12} \cdot \frac{12 t}{5}$ .

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5}{12} \cdot \frac{12 t}{5} = \frac{5}{12} \cdot \frac{9}{10}$

Rewrite the expression.

$\frac{1}{12} (12 t) = \frac{5}{12} \cdot \frac{9}{10}$

Cancel the common factor of $12$ .

Factor $12$ out of $12 t$ .

$\frac{1}{12} (12 (t)) = \frac{5}{12} \cdot \frac{9}{10}$

Cancel the common factor.

$\frac{1}{12} (12 t) = \frac{5}{12} \cdot \frac{9}{10}$

Rewrite the expression.

$t = \frac{5}{12} \cdot \frac{9}{10}$

Simplify the right side.

Simplify $\frac{5}{12} \cdot \frac{9}{10}$ .

Cancel the common factor of $5$ .

Factor $5$ out of $10$ .

$t = \frac{5}{12} \cdot \frac{9}{5 (2)}$

Cancel the common factor.

$t = \frac{5}{12} \cdot \frac{9}{5 \cdot 2}$

Rewrite the expression.

$t = \frac{1}{12} \cdot \frac{9}{2}$

Cancel the common factor of $3$ .

Factor $3$ out of $12$ .

$t = \frac{1}{3 (4)} \cdot \frac{9}{2}$

Factor $3$ out of $9$ .

$t = \frac{1}{3 \cdot 4} \cdot \frac{3 \cdot 3}{2}$

Cancel the common factor.

$t = \frac{1}{3 \cdot 4} \cdot \frac{3 \cdot 3}{2}$

Rewrite the expression.

$t = \frac{1}{4} \cdot \frac{3}{2}$

Multiply $\frac{1}{4}$ by $\frac{3}{2}$ .

$t = \frac{3}{4 \cdot 2}$

Multiply $4$ by $2$ .

$t = \frac{3}{8}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$t = \frac{3}{8}$

Decimal Form:

$t = 0.375$

Solve for t 2 2/5t=9/10

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