Basic Math Examples

$\frac{8}{- 7} - - \frac{5}{2}$

Step 1

Replace all occurrences of $-$ $-$ with a single $+$ . Two consecutive minus signs have the same mathematical meaning as a single plus sign because $- 1 \cdot - 1 = 1$

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

Step 2

Move the negative in front of the fraction.

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

Step 3

To write $- \frac{8}{7}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$- \frac{8}{7} \cdot \frac{2}{2} + \frac{5}{2}$

Step 4

To write $\frac{5}{2}$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$- \frac{8}{7} \cdot \frac{2}{2} + \frac{5}{2} \cdot \frac{7}{7}$

Step 5

Write each expression with a common denominator of $14$ , by multiplying each by an appropriate factor of $1$ .

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Step 5.1

Multiply $\frac{8}{7}$ by $\frac{2}{2}$ .

$- \frac{8 \cdot 2}{7 \cdot 2} + \frac{5}{2} \cdot \frac{7}{7}$

Step 5.2

Multiply $7$ by $2$ .

$- \frac{8 \cdot 2}{14} + \frac{5}{2} \cdot \frac{7}{7}$

Step 5.3

Multiply $\frac{5}{2}$ by $\frac{7}{7}$ .

$- \frac{8 \cdot 2}{14} + \frac{5 \cdot 7}{2 \cdot 7}$

Step 5.4

Multiply $2$ by $7$ .

$- \frac{8 \cdot 2}{14} + \frac{5 \cdot 7}{14}$

Step 6

Combine the numerators over the common denominator.

$\frac{- 8 \cdot 2 + 5 \cdot 7}{14}$

Step 7

Simplify the numerator.

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Step 7.1

Multiply $- 8$ by $2$ .

$\frac{- 16 + 5 \cdot 7}{14}$

Step 7.2

Multiply $5$ by $7$ .

$\frac{- 16 + 35}{14}$

Step 7.3

Add $- 16$ and $35$ .

$\frac{19}{14}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$\frac{19}{14}$

Decimal Form:

$1.35714285 \dots$

Mixed Number Form:

$1 \frac{5}{14}$