Evaluate -5 1/4-(-7 1/2)

$- 5 \frac{1}{4} - (- 7 \frac{1}{2})$

Step 1

Convert $5 \frac{1}{4}$ to an improper fraction.

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

$- (5 + \frac{1}{4}) - (- 7 \frac{1}{2})$

Add $5$ and $\frac{1}{4}$ .

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

$- (5 \cdot \frac{4}{4} + \frac{1}{4}) - (- 7 \frac{1}{2})$

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

$- (\frac{5 \cdot 4}{4} + \frac{1}{4}) - (- 7 \frac{1}{2})$

Combine the numerators over the common denominator.

$- \frac{5 \cdot 4 + 1}{4} - (- 7 \frac{1}{2})$

Simplify the numerator.

Multiply $5$ by $4$ .

$- \frac{20 + 1}{4} - (- 7 \frac{1}{2})$

Add $20$ and $1$ .

$- \frac{21}{4} - (- 7 \frac{1}{2})$

Step 2

Convert $7 \frac{1}{2}$ to an improper fraction.

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

$- \frac{21}{4} - - (7 + \frac{1}{2})$

Add $7$ and $\frac{1}{2}$ .

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

$- \frac{21}{4} - - (7 \cdot \frac{2}{2} + \frac{1}{2})$

Combine $7$ and $\frac{2}{2}$ .

$- \frac{21}{4} - - (\frac{7 \cdot 2}{2} + \frac{1}{2})$

Combine the numerators over the common denominator.

$- \frac{21}{4} - - \frac{7 \cdot 2 + 1}{2}$

Simplify the numerator.

Multiply $7$ by $2$ .

$- \frac{21}{4} - - \frac{14 + 1}{2}$

Add $14$ and $1$ .

$- \frac{21}{4} - - \frac{15}{2}$

Step 3

Multiply $- - \frac{15}{2}$ .

Multiply $- 1$ by $- 1$ .

$- \frac{21}{4} + 1 (\frac{15}{2})$

Multiply $\frac{15}{2}$ by $1$ .

$- \frac{21}{4} + \frac{15}{2}$

Step 4

To write $\frac{15}{2}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$- \frac{21}{4} + \frac{15}{2} \cdot \frac{2}{2}$

Step 5

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

Multiply $\frac{15}{2}$ by $\frac{2}{2}$ .

$- \frac{21}{4} + \frac{15 \cdot 2}{2 \cdot 2}$

Multiply $2$ by $2$ .

$- \frac{21}{4} + \frac{15 \cdot 2}{4}$

Step 6

Combine the numerators over the common denominator.

$\frac{- 21 + 15 \cdot 2}{4}$

Step 7

Simplify the numerator.

Multiply $15$ by $2$ .

$\frac{- 21 + 30}{4}$

Add $- 21$ and $30$ .

$\frac{9}{4}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$\frac{9}{4}$

Decimal Form:

$2.25$

Mixed Number Form:

$2 \frac{1}{4}$

Evaluate -5 1/4-(-7 1/2)

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