Evaluate 1 5/7-2 1/14-3 1/2

$1 \frac{5}{7} - 2 \frac{1}{14} - 3 \frac{1}{2}$

Step 1

Convert $1 \frac{5}{7}$ to an improper fraction.

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

$1 + \frac{5}{7} - 2 \frac{1}{14} - 3 \frac{1}{2}$

Add $1$ and $\frac{5}{7}$ .

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

$\frac{7}{7} + \frac{5}{7} - 2 \frac{1}{14} - 3 \frac{1}{2}$

Combine the numerators over the common denominator.

$\frac{7 + 5}{7} - 2 \frac{1}{14} - 3 \frac{1}{2}$

Add $7$ and $5$ .

$\frac{12}{7} - 2 \frac{1}{14} - 3 \frac{1}{2}$

Step 2

Convert $2 \frac{1}{14}$ to an improper fraction.

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

$\frac{12}{7} - (2 + \frac{1}{14}) - 3 \frac{1}{2}$

Add $2$ and $\frac{1}{14}$ .

To write $2$ as a fraction with a common denominator, multiply by $\frac{14}{14}$ .

$\frac{12}{7} - (2 \cdot \frac{14}{14} + \frac{1}{14}) - 3 \frac{1}{2}$

Combine $2$ and $\frac{14}{14}$ .

$\frac{12}{7} - (\frac{2 \cdot 14}{14} + \frac{1}{14}) - 3 \frac{1}{2}$

Combine the numerators over the common denominator.

$\frac{12}{7} - \frac{2 \cdot 14 + 1}{14} - 3 \frac{1}{2}$

Simplify the numerator.

Multiply $2$ by $14$ .

$\frac{12}{7} - \frac{28 + 1}{14} - 3 \frac{1}{2}$

Add $28$ and $1$ .

$\frac{12}{7} - \frac{29}{14} - 3 \frac{1}{2}$

Step 3

Convert $3 \frac{1}{2}$ to an improper fraction.

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

$\frac{12}{7} - \frac{29}{14} - (3 + \frac{1}{2})$

Add $3$ and $\frac{1}{2}$ .

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

$\frac{12}{7} - \frac{29}{14} - (3 \cdot \frac{2}{2} + \frac{1}{2})$

Combine $3$ and $\frac{2}{2}$ .

$\frac{12}{7} - \frac{29}{14} - (\frac{3 \cdot 2}{2} + \frac{1}{2})$

Combine the numerators over the common denominator.

$\frac{12}{7} - \frac{29}{14} - \frac{3 \cdot 2 + 1}{2}$

Simplify the numerator.

Multiply $3$ by $2$ .

$\frac{12}{7} - \frac{29}{14} - \frac{6 + 1}{2}$

Add $6$ and $1$ .

$\frac{12}{7} - \frac{29}{14} - \frac{7}{2}$

Step 4

Find the common denominator.

Multiply $\frac{12}{7}$ by $\frac{2}{2}$ .

$\frac{12}{7} \cdot \frac{2}{2} - \frac{29}{14} - \frac{7}{2}$

Multiply $\frac{12}{7}$ by $\frac{2}{2}$ .

$\frac{12 \cdot 2}{7 \cdot 2} - \frac{29}{14} - \frac{7}{2}$

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

$\frac{12 \cdot 2}{7 \cdot 2} - \frac{29}{14} - (\frac{7}{2} \cdot \frac{7}{7})$

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

$\frac{12 \cdot 2}{7 \cdot 2} - \frac{29}{14} - \frac{7 \cdot 7}{2 \cdot 7}$

Reorder the factors of $7 \cdot 2$ .

$\frac{12 \cdot 2}{2 \cdot 7} - \frac{29}{14} - \frac{7 \cdot 7}{2 \cdot 7}$

Multiply $2$ by $7$ .

$\frac{12 \cdot 2}{14} - \frac{29}{14} - \frac{7 \cdot 7}{2 \cdot 7}$

Multiply $2$ by $7$ .

$\frac{12 \cdot 2}{14} - \frac{29}{14} - \frac{7 \cdot 7}{14}$

Step 5

Combine the numerators over the common denominator.

$\frac{12 \cdot 2 - 29 - 7 \cdot 7}{14}$

Step 6

Simplify each term.

Multiply $12$ by $2$ .

$\frac{24 - 29 - 7 \cdot 7}{14}$

Multiply $- 7$ by $7$ .

$\frac{24 - 29 - 49}{14}$

Step 7

Reduce the expression by cancelling the common factors.

Subtract $29$ from $24$ .

$\frac{- 5 - 49}{14}$

Subtract $49$ from $- 5$ .

$\frac{- 54}{14}$

Cancel the common factor of $- 54$ and $14$ .

Factor $2$ out of $- 54$ .

$\frac{2 (- 27)}{14}$

Cancel the common factors.

Factor $2$ out of $14$ .

$\frac{2 \cdot - 27}{2 \cdot 7}$

Cancel the common factor.

$\frac{2 \cdot - 27}{2 \cdot 7}$

Rewrite the expression.

$\frac{- 27}{7}$

Move the negative in front of the fraction.

$- \frac{27}{7}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$- \frac{27}{7}$

Decimal Form:

$- 3.\overline{857142}$

Mixed Number Form:

$- 3 \frac{6}{7}$

Evaluate 1 5/7-2 1/14-3 1/2

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