Basic Math Examples

$\frac{2}{5} + \frac{- 3}{8} + \frac{4}{5} + \frac{7}{8} - \frac{2}{3} - 2$

Step 1

Combine the numerators over the common denominator.

$- 2 + \frac{2 + 4}{5} + \frac{- 3 + 7}{8} + \frac{- 2}{3}$

Step 2

Simplify by adding numbers.

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Step 2.1

Add $2$ and $4$ .

$- 2 + \frac{6}{5} + \frac{- 3 + 7}{8} + \frac{- 2}{3}$

Step 2.2

Add $- 3$ and $7$ .

$- 2 + \frac{6}{5} + \frac{4}{8} + \frac{- 2}{3}$

Step 3

Find the common denominator.

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Step 3.1

Write $- 2$ as a fraction with denominator $1$ .

$\frac{- 2}{1} + \frac{6}{5} + \frac{4}{8} + \frac{- 2}{3}$

Step 3.2

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

$\frac{- 2}{1} \cdot \frac{120}{120} + \frac{6}{5} + \frac{4}{8} + \frac{- 2}{3}$

Step 3.3

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

$\frac{- 2 \cdot 120}{120} + \frac{6}{5} + \frac{4}{8} + \frac{- 2}{3}$

Step 3.4

Multiply $\frac{6}{5}$ by $\frac{24}{24}$ .

$\frac{- 2 \cdot 120}{120} + \frac{6}{5} \cdot \frac{24}{24} + \frac{4}{8} + \frac{- 2}{3}$

Step 3.5

Multiply $\frac{6}{5}$ by $\frac{24}{24}$ .

$\frac{- 2 \cdot 120}{120} + \frac{6 \cdot 24}{5 \cdot 24} + \frac{4}{8} + \frac{- 2}{3}$

Step 3.6

Multiply $\frac{4}{8}$ by $\frac{15}{15}$ .

$\frac{- 2 \cdot 120}{120} + \frac{6 \cdot 24}{5 \cdot 24} + \frac{4}{8} \cdot \frac{15}{15} + \frac{- 2}{3}$

Step 3.7

Multiply $\frac{4}{8}$ by $\frac{15}{15}$ .

$\frac{- 2 \cdot 120}{120} + \frac{6 \cdot 24}{5 \cdot 24} + \frac{4 \cdot 15}{8 \cdot 15} + \frac{- 2}{3}$

Step 3.8

Multiply $\frac{- 2}{3}$ by $\frac{40}{40}$ .

$\frac{- 2 \cdot 120}{120} + \frac{6 \cdot 24}{5 \cdot 24} + \frac{4 \cdot 15}{8 \cdot 15} + \frac{- 2}{3} \cdot \frac{40}{40}$

Step 3.9

Multiply $\frac{- 2}{3}$ by $\frac{40}{40}$ .

$\frac{- 2 \cdot 120}{120} + \frac{6 \cdot 24}{5 \cdot 24} + \frac{4 \cdot 15}{8 \cdot 15} + \frac{- 2 \cdot 40}{3 \cdot 40}$

Step 3.10

Multiply $5$ by $24$ .

$\frac{- 2 \cdot 120}{120} + \frac{6 \cdot 24}{120} + \frac{4 \cdot 15}{8 \cdot 15} + \frac{- 2 \cdot 40}{3 \cdot 40}$

Step 3.11

Multiply $8$ by $15$ .

$\frac{- 2 \cdot 120}{120} + \frac{6 \cdot 24}{120} + \frac{4 \cdot 15}{120} + \frac{- 2 \cdot 40}{3 \cdot 40}$

Step 3.12

Multiply $3$ by $40$ .

$\frac{- 2 \cdot 120}{120} + \frac{6 \cdot 24}{120} + \frac{4 \cdot 15}{120} + \frac{- 2 \cdot 40}{120}$

Step 4

Combine the numerators over the common denominator.

$\frac{- 2 \cdot 120 + 6 \cdot 24 + 4 \cdot 15 - 2 \cdot 40}{120}$

Step 5

Simplify each term.

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Step 5.1

Multiply $- 2$ by $120$ .

$\frac{- 240 + 6 \cdot 24 + 4 \cdot 15 - 2 \cdot 40}{120}$

Step 5.2

Multiply $6$ by $24$ .

$\frac{- 240 + 144 + 4 \cdot 15 - 2 \cdot 40}{120}$

Step 5.3

Multiply $4$ by $15$ .

$\frac{- 240 + 144 + 60 - 2 \cdot 40}{120}$

Step 5.4

Multiply $- 2$ by $40$ .

$\frac{- 240 + 144 + 60 - 80}{120}$

Step 6

Reduce the expression by cancelling the common factors.

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Step 6.1

Add $- 240$ and $144$ .

$\frac{- 96 + 60 - 80}{120}$

Step 6.2

Simplify by adding and subtracting.

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Step 6.2.1

Add $- 96$ and $60$ .

$\frac{- 36 - 80}{120}$

Step 6.2.2

Subtract $80$ from $- 36$ .

$\frac{- 116}{120}$

Step 6.3

Cancel the common factor of $- 116$ and $120$ .

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Step 6.3.1

Factor $4$ out of $- 116$ .

$\frac{4 (- 29)}{120}$

Step 6.3.2

Cancel the common factors.

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Step 6.3.2.1

Factor $4$ out of $120$ .

$\frac{4 \cdot - 29}{4 \cdot 30}$

Step 6.3.2.2

Cancel the common factor.

$\frac{4 \cdot - 29}{4 \cdot 30}$

Step 6.3.2.3

Rewrite the expression.

$\frac{- 29}{30}$

Step 6.4

Move the negative in front of the fraction.

$- \frac{29}{30}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$- \frac{29}{30}$

Decimal Form:

$- 0.9\overline{6}$