Basic Math Examples

$\frac{1}{2} - \frac{1}{3} - \frac{2}{3} - \frac{4}{5} - \frac{1}{16}$

Step 1

Combine the numerators over the common denominator.

$\frac{1}{2} + \frac{- 1 - 2}{3} + \frac{- 4}{5} + \frac{- 1}{16}$

Step 2

Subtract $2$ from $- 1$ .

$\frac{1}{2} + \frac{- 3}{3} + \frac{- 4}{5} + \frac{- 1}{16}$

Step 3

Find the common denominator.

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Step 3.1

Multiply $\frac{1}{2}$ by $\frac{120}{120}$ .

$\frac{1}{2} \cdot \frac{120}{120} + \frac{- 3}{3} + \frac{- 4}{5} + \frac{- 1}{16}$

Step 3.2

Multiply $\frac{1}{2}$ by $\frac{120}{120}$ .

$\frac{120}{2 \cdot 120} + \frac{- 3}{3} + \frac{- 4}{5} + \frac{- 1}{16}$

Step 3.3

Multiply $\frac{- 3}{3}$ by $\frac{80}{80}$ .

$\frac{120}{2 \cdot 120} + \frac{- 3}{3} \cdot \frac{80}{80} + \frac{- 4}{5} + \frac{- 1}{16}$

Step 3.4

Multiply $\frac{- 3}{3}$ by $\frac{80}{80}$ .

$\frac{120}{2 \cdot 120} + \frac{- 3 \cdot 80}{3 \cdot 80} + \frac{- 4}{5} + \frac{- 1}{16}$

Step 3.5

Multiply $\frac{- 4}{5}$ by $\frac{48}{48}$ .

$\frac{120}{2 \cdot 120} + \frac{- 3 \cdot 80}{3 \cdot 80} + \frac{- 4}{5} \cdot \frac{48}{48} + \frac{- 1}{16}$

Step 3.6

Multiply $\frac{- 4}{5}$ by $\frac{48}{48}$ .

$\frac{120}{2 \cdot 120} + \frac{- 3 \cdot 80}{3 \cdot 80} + \frac{- 4 \cdot 48}{5 \cdot 48} + \frac{- 1}{16}$

Step 3.7

Multiply $\frac{- 1}{16}$ by $\frac{15}{15}$ .

$\frac{120}{2 \cdot 120} + \frac{- 3 \cdot 80}{3 \cdot 80} + \frac{- 4 \cdot 48}{5 \cdot 48} + \frac{- 1}{16} \cdot \frac{15}{15}$

Step 3.8

Multiply $\frac{- 1}{16}$ by $\frac{15}{15}$ .

$\frac{120}{2 \cdot 120} + \frac{- 3 \cdot 80}{3 \cdot 80} + \frac{- 4 \cdot 48}{5 \cdot 48} + \frac{- 1 \cdot 15}{16 \cdot 15}$

Step 3.9

Multiply $2$ by $120$ .

$\frac{120}{240} + \frac{- 3 \cdot 80}{3 \cdot 80} + \frac{- 4 \cdot 48}{5 \cdot 48} + \frac{- 1 \cdot 15}{16 \cdot 15}$

Step 3.10

Multiply $3$ by $80$ .

$\frac{120}{240} + \frac{- 3 \cdot 80}{240} + \frac{- 4 \cdot 48}{5 \cdot 48} + \frac{- 1 \cdot 15}{16 \cdot 15}$

Step 3.11

Multiply $5$ by $48$ .

$\frac{120}{240} + \frac{- 3 \cdot 80}{240} + \frac{- 4 \cdot 48}{240} + \frac{- 1 \cdot 15}{16 \cdot 15}$

Step 3.12

Reorder the factors of $16 \cdot 15$ .

$\frac{120}{240} + \frac{- 3 \cdot 80}{240} + \frac{- 4 \cdot 48}{240} + \frac{- 1 \cdot 15}{15 \cdot 16}$

Step 3.13

Multiply $15$ by $16$ .

$\frac{120}{240} + \frac{- 3 \cdot 80}{240} + \frac{- 4 \cdot 48}{240} + \frac{- 1 \cdot 15}{240}$

Step 4

Combine the numerators over the common denominator.

$\frac{120 - 3 \cdot 80 - 4 \cdot 48 - 1 \cdot 15}{240}$

Step 5

Simplify each term.

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Step 5.1

Multiply $- 3$ by $80$ .

$\frac{120 - 240 - 4 \cdot 48 - 1 \cdot 15}{240}$

Step 5.2

Multiply $- 4$ by $48$ .

$\frac{120 - 240 - 192 - 1 \cdot 15}{240}$

Step 5.3

Multiply $- 1$ by $15$ .

$\frac{120 - 240 - 192 - 15}{240}$

Step 6

Reduce the expression by cancelling the common factors.

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Step 6.1

Subtract $240$ from $120$ .

$\frac{- 120 - 192 - 15}{240}$

Step 6.2

Simplify by subtracting numbers.

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Step 6.2.1

Subtract $192$ from $- 120$ .

$\frac{- 312 - 15}{240}$

Step 6.2.2

Subtract $15$ from $- 312$ .

$\frac{- 327}{240}$

Step 6.3

Cancel the common factor of $- 327$ and $240$ .

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Step 6.3.1

Factor $3$ out of $- 327$ .

$\frac{3 (- 109)}{240}$

Step 6.3.2

Cancel the common factors.

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Step 6.3.2.1

Factor $3$ out of $240$ .

$\frac{3 \cdot - 109}{3 \cdot 80}$

Step 6.3.2.2

Cancel the common factor.

$\frac{3 \cdot - 109}{3 \cdot 80}$

Step 6.3.2.3

Rewrite the expression.

$\frac{- 109}{80}$

Step 6.4

Move the negative in front of the fraction.

$- \frac{109}{80}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$- \frac{109}{80}$

Decimal Form:

$- 1.3625$

Mixed Number Form:

$- 1 \frac{29}{80}$