Simplify 2 5/8-5 3/4+2

$2 \frac{5}{8} - 5 \frac{3}{4} + 2$

Step 1

Convert $2 \frac{5}{8}$ to an improper fraction.

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

$2 + \frac{5}{8} - 5 \frac{3}{4} + 2$

Add $2$ and $\frac{5}{8}$ .

To write $2$ as a fraction with a common denominator, multiply by $\frac{8}{8}$ .

$2 \cdot \frac{8}{8} + \frac{5}{8} - 5 \frac{3}{4} + 2$

Combine $2$ and $\frac{8}{8}$ .

$\frac{2 \cdot 8}{8} + \frac{5}{8} - 5 \frac{3}{4} + 2$

Combine the numerators over the common denominator.

$\frac{2 \cdot 8 + 5}{8} - 5 \frac{3}{4} + 2$

Simplify the numerator.

Multiply $2$ by $8$ .

$\frac{16 + 5}{8} - 5 \frac{3}{4} + 2$

Add $16$ and $5$ .

$\frac{21}{8} - 5 \frac{3}{4} + 2$

Step 2

Convert $5 \frac{3}{4}$ to an improper fraction.

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

$\frac{21}{8} - (5 + \frac{3}{4}) + 2$

Add $5$ and $\frac{3}{4}$ .

To write $5$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{21}{8} - (5 \cdot \frac{4}{4} + \frac{3}{4}) + 2$

Combine $5$ and $\frac{4}{4}$ .

$\frac{21}{8} - (\frac{5 \cdot 4}{4} + \frac{3}{4}) + 2$

Combine the numerators over the common denominator.

$\frac{21}{8} - \frac{5 \cdot 4 + 3}{4} + 2$

Simplify the numerator.

Multiply $5$ by $4$ .

$\frac{21}{8} - \frac{20 + 3}{4} + 2$

Add $20$ and $3$ .

$\frac{21}{8} - \frac{23}{4} + 2$

Step 3

Find the common denominator.

Multiply $\frac{23}{4}$ by $\frac{2}{2}$ .

$\frac{21}{8} - (\frac{23}{4} \cdot \frac{2}{2}) + 2$

Multiply $\frac{23}{4}$ by $\frac{2}{2}$ .

$\frac{21}{8} - \frac{23 \cdot 2}{4 \cdot 2} + 2$

Write $2$ as a fraction with denominator $1$ .

$\frac{21}{8} - \frac{23 \cdot 2}{4 \cdot 2} + \frac{2}{1}$

Multiply $\frac{2}{1}$ by $\frac{8}{8}$ .

$\frac{21}{8} - \frac{23 \cdot 2}{4 \cdot 2} + \frac{2}{1} \cdot \frac{8}{8}$

Multiply $\frac{2}{1}$ by $\frac{8}{8}$ .

$\frac{21}{8} - \frac{23 \cdot 2}{4 \cdot 2} + \frac{2 \cdot 8}{8}$

Reorder the factors of $4 \cdot 2$ .

$\frac{21}{8} - \frac{23 \cdot 2}{2 \cdot 4} + \frac{2 \cdot 8}{8}$

Multiply $2$ by $4$ .

$\frac{21}{8} - \frac{23 \cdot 2}{8} + \frac{2 \cdot 8}{8}$

Step 4

Combine the numerators over the common denominator.

$\frac{21 - 23 \cdot 2 + 2 \cdot 8}{8}$

Step 5

Simplify each term.

Multiply $- 23$ by $2$ .

$\frac{21 - 46 + 2 \cdot 8}{8}$

Multiply $2$ by $8$ .

$\frac{21 - 46 + 16}{8}$

Step 6

Simplify the expression.

Subtract $46$ from $21$ .

$\frac{- 25 + 16}{8}$

Add $- 25$ and $16$ .

$\frac{- 9}{8}$

Move the negative in front of the fraction.

$- \frac{9}{8}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$- \frac{9}{8}$

Decimal Form:

$- 1.125$

Mixed Number Form:

$- 1 \frac{1}{8}$

Simplify 2 5/8-5 3/4+2

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