Basic Math Examples

$(5 \frac{1}{8} - \frac{3}{4}) \div (- 1 \frac{1}{3})$

Step 1

Convert $5 \frac{1}{8}$ to an improper fraction.

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Step 1.1

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

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

Step 1.2

Add $5$ and $\frac{1}{8}$ .

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Step 1.2.1

To write $5$ as a fraction with a common denominator, multiply by $\frac{8}{8}$ .

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

Step 1.2.2

Combine $5$ and $\frac{8}{8}$ .

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

Step 1.2.3

Combine the numerators over the common denominator.

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

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply $5$ by $8$ .

$(\frac{40 + 1}{8} - \frac{3}{4}) \div (- 1 \frac{1}{3})$

Step 1.2.4.2

Add $40$ and $1$ .

$(\frac{41}{8} - \frac{3}{4}) \div (- 1 \frac{1}{3})$

Step 2

Convert $1 \frac{1}{3}$ to an improper fraction.

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Step 2.1

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

$(\frac{41}{8} - \frac{3}{4}) \div (- (1 + \frac{1}{3}))$

Step 2.2

Add $1$ and $\frac{1}{3}$ .

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Step 2.2.1

Write $1$ as a fraction with a common denominator.

$(\frac{41}{8} - \frac{3}{4}) \div (- (\frac{3}{3} + \frac{1}{3}))$

Step 2.2.2

Combine the numerators over the common denominator.

$(\frac{41}{8} - \frac{3}{4}) \div (- \frac{3 + 1}{3})$

Step 2.2.3

Add $3$ and $1$ .

$(\frac{41}{8} - \frac{3}{4}) \div (- \frac{4}{3})$

Step 3

To divide by a fraction, multiply by its reciprocal.

$(\frac{41}{8} - \frac{3}{4}) (- \frac{3}{4})$

Step 4

To write $- \frac{3}{4}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$(\frac{41}{8} - \frac{3}{4} \cdot \frac{2}{2}) (- \frac{3}{4})$

Step 5

Write each expression with a common denominator of $8$ , by multiplying each by an appropriate factor of $1$ .

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Step 5.1

Multiply $\frac{3}{4}$ by $\frac{2}{2}$ .

$(\frac{41}{8} - \frac{3 \cdot 2}{4 \cdot 2}) (- \frac{3}{4})$

Step 5.2

Multiply $4$ by $2$ .

$(\frac{41}{8} - \frac{3 \cdot 2}{8}) (- \frac{3}{4})$

Step 6

Combine the numerators over the common denominator.

$\frac{41 - 3 \cdot 2}{8} (- \frac{3}{4})$

Step 7

Simplify the numerator.

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Step 7.1

Multiply $- 3$ by $2$ .

$\frac{41 - 6}{8} (- \frac{3}{4})$

Step 7.2

Subtract $6$ from $41$ .

$\frac{35}{8} (- \frac{3}{4})$

Step 8

Multiply $\frac{35}{8} (- \frac{3}{4})$ .

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Step 8.1

Multiply $\frac{35}{8}$ by $\frac{3}{4}$ .

$- \frac{35 \cdot 3}{8 \cdot 4}$

Step 8.2

Multiply $35$ by $3$ .

$- \frac{105}{8 \cdot 4}$

Step 8.3

Multiply $8$ by $4$ .

$- \frac{105}{32}$

Step 9

The result can be shown in multiple forms.

Exact Form:

$- \frac{105}{32}$

Decimal Form:

$- 3.28125$

Mixed Number Form:

$- 3 \frac{9}{32}$