Find the Exact Value -5 3/4-3 1/2

$- 5 \frac{3}{4} - 3 \frac{1}{2}$

Step 1

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

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

$- (5 + \frac{3}{4}) - 3 \frac{1}{2}$

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

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

$- (5 \cdot \frac{4}{4} + \frac{3}{4}) - 3 \frac{1}{2}$

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

$- (\frac{5 \cdot 4}{4} + \frac{3}{4}) - 3 \frac{1}{2}$

Combine the numerators over the common denominator.

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

Simplify the numerator.

Multiply $5$ by $4$ .

$- \frac{20 + 3}{4} - 3 \frac{1}{2}$

Add $20$ and $3$ .

$- \frac{23}{4} - 3 \frac{1}{2}$

Step 2

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

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

$- \frac{23}{4} - (3 + \frac{1}{2})$

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

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

$- \frac{23}{4} - (3 \cdot \frac{2}{2} + \frac{1}{2})$

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

$- \frac{23}{4} - (\frac{3 \cdot 2}{2} + \frac{1}{2})$

Combine the numerators over the common denominator.

$- \frac{23}{4} - \frac{3 \cdot 2 + 1}{2}$

Simplify the numerator.

Multiply $3$ by $2$ .

$- \frac{23}{4} - \frac{6 + 1}{2}$

Add $6$ and $1$ .

$- \frac{23}{4} - \frac{7}{2}$

Step 3

To write $- \frac{7}{2}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$- \frac{23}{4} - \frac{7}{2} \cdot \frac{2}{2}$

Step 4

Write each expression with a common denominator of $4$ , by multiplying each by an appropriate factor of $1$ .

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

$- \frac{23}{4} - \frac{7 \cdot 2}{2 \cdot 2}$

Multiply $2$ by $2$ .

$- \frac{23}{4} - \frac{7 \cdot 2}{4}$

Step 5

Combine the numerators over the common denominator.

$\frac{- 23 - 7 \cdot 2}{4}$

Step 6

Simplify the numerator.

Multiply $- 7$ by $2$ .

$\frac{- 23 - 14}{4}$

Subtract $14$ from $- 23$ .

$\frac{- 37}{4}$

Step 7

Move the negative in front of the fraction.

$- \frac{37}{4}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$- \frac{37}{4}$

Decimal Form:

$- 9.25$

Mixed Number Form:

$- 9 \frac{1}{4}$

Find the Exact Value -5 3/4-3 1/2

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