Basic Math Examples

$8 \frac{7}{8} - 2 \frac{1}{2} - \frac{3}{1} - 4 \frac{1}{8}$

Step 1

Convert $8 \frac{7}{8}$ to an improper fraction.

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Step 1.1

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

$8 + \frac{7}{8} - 2 \frac{1}{2} - \frac{3}{1} - 4 \frac{1}{8}$

Step 1.2

Add $8$ and $\frac{7}{8}$ .

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Step 1.2.1

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

$8 \cdot \frac{8}{8} + \frac{7}{8} - 2 \frac{1}{2} - \frac{3}{1} - 4 \frac{1}{8}$

Step 1.2.2

Combine $8$ and $\frac{8}{8}$ .

$\frac{8 \cdot 8}{8} + \frac{7}{8} - 2 \frac{1}{2} - \frac{3}{1} - 4 \frac{1}{8}$

Step 1.2.3

Combine the numerators over the common denominator.

$\frac{8 \cdot 8 + 7}{8} - 2 \frac{1}{2} - \frac{3}{1} - 4 \frac{1}{8}$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply $8$ by $8$ .

$\frac{64 + 7}{8} - 2 \frac{1}{2} - \frac{3}{1} - 4 \frac{1}{8}$

Step 1.2.4.2

Add $64$ and $7$ .

$\frac{71}{8} - 2 \frac{1}{2} - \frac{3}{1} - 4 \frac{1}{8}$

Step 2

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

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Step 2.1

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

$\frac{71}{8} - (2 + \frac{1}{2}) - \frac{3}{1} - 4 \frac{1}{8}$

Step 2.2

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

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Step 2.2.1

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

$\frac{71}{8} - (2 \cdot \frac{2}{2} + \frac{1}{2}) - \frac{3}{1} - 4 \frac{1}{8}$

Step 2.2.2

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

$\frac{71}{8} - (\frac{2 \cdot 2}{2} + \frac{1}{2}) - \frac{3}{1} - 4 \frac{1}{8}$

Step 2.2.3

Combine the numerators over the common denominator.

$\frac{71}{8} - \frac{2 \cdot 2 + 1}{2} - \frac{3}{1} - 4 \frac{1}{8}$

Step 2.2.4

Simplify the numerator.

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Step 2.2.4.1

Multiply $2$ by $2$ .

$\frac{71}{8} - \frac{4 + 1}{2} - \frac{3}{1} - 4 \frac{1}{8}$

Step 2.2.4.2

Add $4$ and $1$ .

$\frac{71}{8} - \frac{5}{2} - \frac{3}{1} - 4 \frac{1}{8}$

Step 3

Convert $4 \frac{1}{8}$ to an improper fraction.

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Step 3.1

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

$\frac{71}{8} - \frac{5}{2} - \frac{3}{1} - (4 + \frac{1}{8})$

Step 3.2

Add $4$ and $\frac{1}{8}$ .

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Step 3.2.1

To write $4$ as a fraction with a common denominator, multiply by $\frac{8}{8}$ .

$\frac{71}{8} - \frac{5}{2} - \frac{3}{1} - (4 \cdot \frac{8}{8} + \frac{1}{8})$

Step 3.2.2

Combine $4$ and $\frac{8}{8}$ .

$\frac{71}{8} - \frac{5}{2} - \frac{3}{1} - (\frac{4 \cdot 8}{8} + \frac{1}{8})$

Step 3.2.3

Combine the numerators over the common denominator.

$\frac{71}{8} - \frac{5}{2} - \frac{3}{1} - \frac{4 \cdot 8 + 1}{8}$

Step 3.2.4

Simplify the numerator.

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Step 3.2.4.1

Multiply $4$ by $8$ .

$\frac{71}{8} - \frac{5}{2} - \frac{3}{1} - \frac{32 + 1}{8}$

Step 3.2.4.2

Add $32$ and $1$ .

$\frac{71}{8} - \frac{5}{2} - \frac{3}{1} - \frac{33}{8}$

Step 4

Combine the numerators over the common denominator.

$\frac{71 - 33}{8} + \frac{- 5}{2} + \frac{- 3}{1}$

Step 5

Subtract $33$ from $71$ .

$\frac{38}{8} + \frac{- 5}{2} + \frac{- 3}{1}$

Step 6

Find the common denominator.

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Step 6.1

Multiply $\frac{- 5}{2}$ by $\frac{4}{4}$ .

$\frac{38}{8} + \frac{- 5}{2} \cdot \frac{4}{4} + \frac{- 3}{1}$

Step 6.2

Multiply $\frac{- 5}{2}$ by $\frac{4}{4}$ .

$\frac{38}{8} + \frac{- 5 \cdot 4}{2 \cdot 4} + \frac{- 3}{1}$

Step 6.3

Multiply $\frac{- 3}{1}$ by $\frac{8}{8}$ .

$\frac{38}{8} + \frac{- 5 \cdot 4}{2 \cdot 4} + \frac{- 3}{1} \cdot \frac{8}{8}$

Step 6.4

Multiply $\frac{- 3}{1}$ by $\frac{8}{8}$ .

$\frac{38}{8} + \frac{- 5 \cdot 4}{2 \cdot 4} + \frac{- 3 \cdot 8}{8}$

Step 6.5

Multiply $2$ by $4$ .

$\frac{38}{8} + \frac{- 5 \cdot 4}{8} + \frac{- 3 \cdot 8}{8}$

Step 7

Combine the numerators over the common denominator.

$\frac{38 - 5 \cdot 4 - 3 \cdot 8}{8}$

Step 8

Simplify each term.

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Step 8.1

Multiply $- 5$ by $4$ .

$\frac{38 - 20 - 3 \cdot 8}{8}$

Step 8.2

Multiply $- 3$ by $8$ .

$\frac{38 - 20 - 24}{8}$

Step 9

Reduce the expression by cancelling the common factors.

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Step 9.1

Subtract $20$ from $38$ .

$\frac{18 - 24}{8}$

Step 9.2

Subtract $24$ from $18$ .

$\frac{- 6}{8}$

Step 9.3

Cancel the common factor of $- 6$ and $8$ .

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Step 9.3.1

Factor $2$ out of $- 6$ .

$\frac{2 (- 3)}{8}$

Step 9.3.2

Cancel the common factors.

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Step 9.3.2.1

Factor $2$ out of $8$ .

$\frac{2 \cdot - 3}{2 \cdot 4}$

Step 9.3.2.2

Cancel the common factor.

$\frac{2 \cdot - 3}{2 \cdot 4}$

Step 9.3.2.3

Rewrite the expression.

$\frac{- 3}{4}$

Step 9.4

Move the negative in front of the fraction.

$- \frac{3}{4}$

Step 10

The result can be shown in multiple forms.

Exact Form:

$- \frac{3}{4}$

Decimal Form:

$- 0.75$