Simplify -4 1/2+2 3/8

$- 4 \frac{1}{2} + 2 \frac{3}{8}$

Step 1

Convert $4 \frac{1}{2}$ to an improper fraction.

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

$- (4 + \frac{1}{2}) + 2 \frac{3}{8}$

Add $4$ and $\frac{1}{2}$ .

To write $4$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$- (4 \cdot \frac{2}{2} + \frac{1}{2}) + 2 \frac{3}{8}$

Combine $4$ and $\frac{2}{2}$ .

$- (\frac{4 \cdot 2}{2} + \frac{1}{2}) + 2 \frac{3}{8}$

Combine the numerators over the common denominator.

$- \frac{4 \cdot 2 + 1}{2} + 2 \frac{3}{8}$

Simplify the numerator.

Multiply $4$ by $2$ .

$- \frac{8 + 1}{2} + 2 \frac{3}{8}$

Add $8$ and $1$ .

$- \frac{9}{2} + 2 \frac{3}{8}$

Step 2

Convert $2 \frac{3}{8}$ to an improper fraction.

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

$- \frac{9}{2} + 2 + \frac{3}{8}$

Add $2$ and $\frac{3}{8}$ .

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

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

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

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

Multiply $2$ by $8$ .

$- \frac{9}{2} + \frac{16 + 3}{8}$

Add $16$ and $3$ .

$- \frac{9}{2} + \frac{19}{8}$

Step 3

To write $- \frac{9}{2}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$- \frac{9}{2} \cdot \frac{4}{4} + \frac{19}{8}$

Step 4

Write each expression with a common denominator of $8$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{9}{2}$ by $\frac{4}{4}$ .

$- \frac{9 \cdot 4}{2 \cdot 4} + \frac{19}{8}$

Multiply $2$ by $4$ .

$- \frac{9 \cdot 4}{8} + \frac{19}{8}$

Step 5

Combine the numerators over the common denominator.

$\frac{- 9 \cdot 4 + 19}{8}$

Step 6

Simplify the numerator.

Multiply $- 9$ by $4$ .

$\frac{- 36 + 19}{8}$

Add $- 36$ and $19$ .

$\frac{- 17}{8}$

Step 7

Move the negative in front of the fraction.

$- \frac{17}{8}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$- \frac{17}{8}$

Decimal Form:

$- 2.125$

Mixed Number Form:

$- 2 \frac{1}{8}$

Simplify -4 1/2+2 3/8

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