Calculus Examples

$\frac{45}{2} - (- \frac{104}{3})$

Step 1

Multiply $- (- \frac{104}{3})$ .

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Step 1.1

Multiply $- 1$ by $- 1$ .

$\frac{45}{2} + 1 (\frac{104}{3})$

Step 1.2

Multiply $\frac{104}{3}$ by $1$ .

$\frac{45}{2} + \frac{104}{3}$

Step 2

To write $\frac{45}{2}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{45}{2} \cdot \frac{3}{3} + \frac{104}{3}$

Step 3

To write $\frac{104}{3}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{45}{2} \cdot \frac{3}{3} + \frac{104}{3} \cdot \frac{2}{2}$

Step 4

Write each expression with a common denominator of $6$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.1

Multiply $\frac{45}{2}$ by $\frac{3}{3}$ .

$\frac{45 \cdot 3}{2 \cdot 3} + \frac{104}{3} \cdot \frac{2}{2}$

Step 4.2

Multiply $2$ by $3$ .

$\frac{45 \cdot 3}{6} + \frac{104}{3} \cdot \frac{2}{2}$

Step 4.3

Multiply $\frac{104}{3}$ by $\frac{2}{2}$ .

$\frac{45 \cdot 3}{6} + \frac{104 \cdot 2}{3 \cdot 2}$

Step 4.4

Multiply $3$ by $2$ .

$\frac{45 \cdot 3}{6} + \frac{104 \cdot 2}{6}$

Step 5

Combine the numerators over the common denominator.

$\frac{45 \cdot 3 + 104 \cdot 2}{6}$

Step 6

Simplify the numerator.

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Step 6.1

Multiply $45$ by $3$ .

$\frac{135 + 104 \cdot 2}{6}$

Step 6.2

Multiply $104$ by $2$ .

$\frac{135 + 208}{6}$

Step 6.3

Add $135$ and $208$ .

$\frac{343}{6}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{343}{6}$

Decimal Form:

$57.1\overline{6}$

Mixed Number Form:

$57 \frac{1}{6}$