Evaluate 0.25+4/6-2/3+(9/8)÷(5/2)*2/6

$0.25 + \frac{4}{6} - \frac{2}{3} + \frac{9}{8} \div \frac{5}{2} \cdot \frac{2}{6}$

Step 1

Simplify each term.

Cancel the common factor of $4$ and $6$ .

Factor $2$ out of $4$ .

$0.25 + \frac{2 (2)}{6} - \frac{2}{3} + \frac{9}{8} \div \frac{5}{2} \cdot \frac{2}{6}$

Cancel the common factors.

Factor $2$ out of $6$ .

$0.25 + \frac{2 \cdot 2}{2 \cdot 3} - \frac{2}{3} + \frac{9}{8} \div \frac{5}{2} \cdot \frac{2}{6}$

Cancel the common factor.

$0.25 + \frac{2 \cdot 2}{2 \cdot 3} - \frac{2}{3} + \frac{9}{8} \div \frac{5}{2} \cdot \frac{2}{6}$

Rewrite the expression.

$0.25 + \frac{2}{3} - \frac{2}{3} + \frac{9}{8} \div \frac{5}{2} \cdot \frac{2}{6}$

To divide by a fraction, multiply by its reciprocal.

$0.25 + \frac{2}{3} - \frac{2}{3} + \frac{9}{8} \cdot \frac{2}{5} \cdot \frac{2}{6}$

Cancel the common factor of $2$ .

Factor $2$ out of $8$ .

$0.25 + \frac{2}{3} - \frac{2}{3} + \frac{9}{2 (4)} \cdot \frac{2}{5} \cdot \frac{2}{6}$

Cancel the common factor.

$0.25 + \frac{2}{3} - \frac{2}{3} + \frac{9}{2 \cdot 4} \cdot \frac{2}{5} \cdot \frac{2}{6}$

Rewrite the expression.

$0.25 + \frac{2}{3} - \frac{2}{3} + \frac{9}{4} \cdot \frac{1}{5} \cdot \frac{2}{6}$

Multiply $\frac{9}{4}$ by $\frac{1}{5}$ .

$0.25 + \frac{2}{3} - \frac{2}{3} + \frac{9}{4 \cdot 5} \cdot \frac{2}{6}$

Multiply $4$ by $5$ .

$0.25 + \frac{2}{3} - \frac{2}{3} + \frac{9}{20} \cdot \frac{2}{6}$

Cancel the common factor of $3$ .

Factor $3$ out of $9$ .

$0.25 + \frac{2}{3} - \frac{2}{3} + \frac{3 (3)}{20} \cdot \frac{2}{6}$

Factor $3$ out of $6$ .

$0.25 + \frac{2}{3} - \frac{2}{3} + \frac{3 \cdot 3}{20} \cdot \frac{2}{3 \cdot 2}$

Cancel the common factor.

$0.25 + \frac{2}{3} - \frac{2}{3} + \frac{3 \cdot 3}{20} \cdot \frac{2}{3 \cdot 2}$

Rewrite the expression.

$0.25 + \frac{2}{3} - \frac{2}{3} + \frac{3}{20} \cdot \frac{2}{2}$

Cancel the common factor of $2$ .

Factor $2$ out of $20$ .

$0.25 + \frac{2}{3} - \frac{2}{3} + \frac{3}{2 (10)} \cdot \frac{2}{2}$

Cancel the common factor.

$0.25 + \frac{2}{3} - \frac{2}{3} + \frac{3}{2 \cdot 10} \cdot \frac{2}{2}$

Rewrite the expression.

$0.25 + \frac{2}{3} - \frac{2}{3} + \frac{3}{10} \cdot \frac{1}{2}$

Multiply $\frac{3}{10}$ by $\frac{1}{2}$ .

$0.25 + \frac{2}{3} - \frac{2}{3} + \frac{3}{10 \cdot 2}$

Multiply $10$ by $2$ .

$0.25 + \frac{2}{3} - \frac{2}{3} + \frac{3}{20}$

Step 2

Combine fractions.

Combine the numerators over the common denominator.

$0.25 + \frac{2 - 2}{3} + \frac{3}{20}$

Subtract $2$ from $2$ .

$0.25 + \frac{0}{3} + \frac{3}{20}$

Step 3

Find the common denominator.

Write $0.25$ as a fraction with denominator $1$ .

$\frac{0.25}{1} + \frac{0}{3} + \frac{3}{20}$

Multiply $\frac{0.25}{1}$ by $\frac{60}{60}$ .

$\frac{0.25}{1} \cdot \frac{60}{60} + \frac{0}{3} + \frac{3}{20}$

Multiply $\frac{0.25}{1}$ by $\frac{60}{60}$ .

$\frac{0.25 \cdot 60}{60} + \frac{0}{3} + \frac{3}{20}$

Multiply $\frac{0}{3}$ by $\frac{20}{20}$ .

$\frac{0.25 \cdot 60}{60} + \frac{0}{3} \cdot \frac{20}{20} + \frac{3}{20}$

Multiply $\frac{0}{3}$ by $\frac{20}{20}$ .

$\frac{0.25 \cdot 60}{60} + \frac{0 \cdot 20}{3 \cdot 20} + \frac{3}{20}$

Multiply $\frac{3}{20}$ by $\frac{3}{3}$ .

$\frac{0.25 \cdot 60}{60} + \frac{0 \cdot 20}{3 \cdot 20} + \frac{3}{20} \cdot \frac{3}{3}$

Multiply $\frac{3}{20}$ by $\frac{3}{3}$ .

$\frac{0.25 \cdot 60}{60} + \frac{0 \cdot 20}{3 \cdot 20} + \frac{3 \cdot 3}{20 \cdot 3}$

Multiply $3$ by $20$ .

$\frac{0.25 \cdot 60}{60} + \frac{0 \cdot 20}{60} + \frac{3 \cdot 3}{20 \cdot 3}$

Reorder the factors of $20 \cdot 3$ .

$\frac{0.25 \cdot 60}{60} + \frac{0 \cdot 20}{60} + \frac{3 \cdot 3}{3 \cdot 20}$

Multiply $3$ by $20$ .

$\frac{0.25 \cdot 60}{60} + \frac{0 \cdot 20}{60} + \frac{3 \cdot 3}{60}$

Step 4

Combine the numerators over the common denominator.

$\frac{0.25 \cdot 60 + 0 \cdot 20 + 3 \cdot 3}{60}$

Step 5

Simplify each term.

Multiply $0.25$ by $60$ .

$\frac{15 + 0 \cdot 20 + 3 \cdot 3}{60}$

Multiply $0$ by $20$ .

$\frac{15 + 0 + 3 \cdot 3}{60}$

Multiply $3$ by $3$ .

$\frac{15 + 0 + 9}{60}$

Step 6

Reduce the expression by cancelling the common factors.

Add $15$ and $0$ .

$\frac{15 + 9}{60}$

Add $15$ and $9$ .

$\frac{24}{60}$

Cancel the common factor of $24$ and $60$ .

Factor $12$ out of $24$ .

$\frac{12 (2)}{60}$

Cancel the common factors.

Factor $12$ out of $60$ .

$\frac{12 \cdot 2}{12 \cdot 5}$

Cancel the common factor.

$\frac{12 \cdot 2}{12 \cdot 5}$

Rewrite the expression.

$\frac{2}{5}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{2}{5}$

Decimal Form:

$0.4$

Evaluate 0.25+4/6-2/3+(9/8)÷(5/2)*2/6

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