Evaluate (12/3)÷(8/5)+10-5/7+8 2/4

$\frac{12}{3} \div \frac{8}{5} + 10 - \frac{5}{7} + 8 \frac{2}{4}$

Step 1

Convert $8 \frac{2}{4}$ to an improper fraction.

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

$\frac{12}{3} \div \frac{8}{5} + 10 - \frac{5}{7} + 8 + \frac{2}{4}$

Add $8$ and $\frac{2}{4}$ .

To write $8$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{12}{3} \div \frac{8}{5} + 10 - \frac{5}{7} + 8 \cdot \frac{4}{4} + \frac{2}{4}$

Combine $8$ and $\frac{4}{4}$ .

$\frac{12}{3} \div \frac{8}{5} + 10 - \frac{5}{7} + \frac{8 \cdot 4}{4} + \frac{2}{4}$

Combine the numerators over the common denominator.

$\frac{12}{3} \div \frac{8}{5} + 10 - \frac{5}{7} + \frac{8 \cdot 4 + 2}{4}$

Simplify the numerator.

Multiply $8$ by $4$ .

$\frac{12}{3} \div \frac{8}{5} + 10 - \frac{5}{7} + \frac{32 + 2}{4}$

Add $32$ and $2$ .

$\frac{12}{3} \div \frac{8}{5} + 10 - \frac{5}{7} + \frac{34}{4}$

Step 2

Simplify each term.

To divide by a fraction, multiply by its reciprocal.

$\frac{12}{3} \cdot \frac{5}{8} + 10 - \frac{5}{7} + \frac{34}{4}$

Cancel the common factor of $4$ .

Factor $4$ out of $12$ .

$\frac{4 (3)}{3} \cdot \frac{5}{8} + 10 - \frac{5}{7} + \frac{34}{4}$

Factor $4$ out of $8$ .

$\frac{4 \cdot 3}{3} \cdot \frac{5}{4 \cdot 2} + 10 - \frac{5}{7} + \frac{34}{4}$

Cancel the common factor.

$\frac{4 \cdot 3}{3} \cdot \frac{5}{4 \cdot 2} + 10 - \frac{5}{7} + \frac{34}{4}$

Rewrite the expression.

$\frac{3}{3} \cdot \frac{5}{2} + 10 - \frac{5}{7} + \frac{34}{4}$

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

$\frac{3 \cdot 5}{3 \cdot 2} + 10 - \frac{5}{7} + \frac{34}{4}$

Multiply $3$ by $5$ .

$\frac{15}{3 \cdot 2} + 10 - \frac{5}{7} + \frac{34}{4}$

Multiply $3$ by $2$ .

$\frac{15}{6} + 10 - \frac{5}{7} + \frac{34}{4}$

Cancel the common factor of $15$ and $6$ .

Factor $3$ out of $15$ .

$\frac{3 (5)}{6} + 10 - \frac{5}{7} + \frac{34}{4}$

Cancel the common factors.

Factor $3$ out of $6$ .

$\frac{3 \cdot 5}{3 \cdot 2} + 10 - \frac{5}{7} + \frac{34}{4}$

Cancel the common factor.

$\frac{3 \cdot 5}{3 \cdot 2} + 10 - \frac{5}{7} + \frac{34}{4}$

Rewrite the expression.

$\frac{5}{2} + 10 - \frac{5}{7} + \frac{34}{4}$

Cancel the common factor of $34$ and $4$ .

Factor $2$ out of $34$ .

$\frac{5}{2} + 10 - \frac{5}{7} + \frac{2 (17)}{4}$

Cancel the common factors.

Factor $2$ out of $4$ .

$\frac{5}{2} + 10 - \frac{5}{7} + \frac{2 \cdot 17}{2 \cdot 2}$

Cancel the common factor.

$\frac{5}{2} + 10 - \frac{5}{7} + \frac{2 \cdot 17}{2 \cdot 2}$

Rewrite the expression.

$\frac{5}{2} + 10 - \frac{5}{7} + \frac{17}{2}$

Step 3

Combine fractions.

Combine the numerators over the common denominator.

$10 + \frac{5 + 17}{2} + \frac{- 5}{7}$

Add $5$ and $17$ .

$10 + \frac{22}{2} + \frac{- 5}{7}$

Step 4

Find the common denominator.

Write $10$ as a fraction with denominator $1$ .

$\frac{10}{1} + \frac{22}{2} + \frac{- 5}{7}$

Multiply $\frac{10}{1}$ by $\frac{14}{14}$ .

$\frac{10}{1} \cdot \frac{14}{14} + \frac{22}{2} + \frac{- 5}{7}$

Multiply $\frac{10}{1}$ by $\frac{14}{14}$ .

$\frac{10 \cdot 14}{14} + \frac{22}{2} + \frac{- 5}{7}$

Multiply $\frac{22}{2}$ by $\frac{7}{7}$ .

$\frac{10 \cdot 14}{14} + \frac{22}{2} \cdot \frac{7}{7} + \frac{- 5}{7}$

Multiply $\frac{22}{2}$ by $\frac{7}{7}$ .

$\frac{10 \cdot 14}{14} + \frac{22 \cdot 7}{2 \cdot 7} + \frac{- 5}{7}$

Multiply $\frac{- 5}{7}$ by $\frac{2}{2}$ .

$\frac{10 \cdot 14}{14} + \frac{22 \cdot 7}{2 \cdot 7} + \frac{- 5}{7} \cdot \frac{2}{2}$

Multiply $\frac{- 5}{7}$ by $\frac{2}{2}$ .

$\frac{10 \cdot 14}{14} + \frac{22 \cdot 7}{2 \cdot 7} + \frac{- 5 \cdot 2}{7 \cdot 2}$

Multiply $2$ by $7$ .

$\frac{10 \cdot 14}{14} + \frac{22 \cdot 7}{14} + \frac{- 5 \cdot 2}{7 \cdot 2}$

Reorder the factors of $7 \cdot 2$ .

$\frac{10 \cdot 14}{14} + \frac{22 \cdot 7}{14} + \frac{- 5 \cdot 2}{2 \cdot 7}$

Multiply $2$ by $7$ .

$\frac{10 \cdot 14}{14} + \frac{22 \cdot 7}{14} + \frac{- 5 \cdot 2}{14}$

Step 5

Combine the numerators over the common denominator.

$\frac{10 \cdot 14 + 22 \cdot 7 - 5 \cdot 2}{14}$

Step 6

Simplify each term.

Multiply $10$ by $14$ .

$\frac{140 + 22 \cdot 7 - 5 \cdot 2}{14}$

Multiply $22$ by $7$ .

$\frac{140 + 154 - 5 \cdot 2}{14}$

Multiply $- 5$ by $2$ .

$\frac{140 + 154 - 10}{14}$

Step 7

Reduce the expression by cancelling the common factors.

Add $140$ and $154$ .

$\frac{294 - 10}{14}$

Subtract $10$ from $294$ .

$\frac{284}{14}$

Cancel the common factor of $284$ and $14$ .

Factor $2$ out of $284$ .

$\frac{2 (142)}{14}$

Cancel the common factors.

Factor $2$ out of $14$ .

$\frac{2 \cdot 142}{2 \cdot 7}$

Cancel the common factor.

$\frac{2 \cdot 142}{2 \cdot 7}$

Rewrite the expression.

$\frac{142}{7}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$\frac{142}{7}$

Decimal Form:

$20.28571428 \dots$

Mixed Number Form:

$20 \frac{2}{7}$

Evaluate (12/3)÷(8/5)+10-5/7+8 2/4

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