Basic Math Examples

$\frac{3}{4} + 1^{3} - \frac{5}{6} \div 1 \frac{4}{5}$

Step 1

Convert $1 \frac{4}{5}$ to an improper fraction.

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Step 1.1

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

$\frac{3}{4} + 1^{3} - \frac{5}{6} \div (1 + \frac{4}{5})$

Step 1.2

Add $1$ and $\frac{4}{5}$ .

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Step 1.2.1

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

$\frac{3}{4} + 1^{3} - \frac{5}{6} \div (\frac{5}{5} + \frac{4}{5})$

Step 1.2.2

Combine the numerators over the common denominator.

$\frac{3}{4} + 1^{3} - \frac{5}{6} \div \frac{5 + 4}{5}$

Step 1.2.3

Add $5$ and $4$ .

$\frac{3}{4} + 1^{3} - \frac{5}{6} \div \frac{9}{5}$

Step 2

Simplify each term.

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Step 2.1

One to any power is one.

$\frac{3}{4} + 1 - \frac{5}{6} \div \frac{9}{5}$

Step 2.2

To divide by a fraction, multiply by its reciprocal.

$\frac{3}{4} + 1 - (\frac{5}{6} \cdot \frac{5}{9})$

Step 2.3

Multiply $\frac{5}{6} \cdot \frac{5}{9}$ .

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Step 2.3.1

Multiply $\frac{5}{6}$ by $\frac{5}{9}$ .

$\frac{3}{4} + 1 - \frac{5 \cdot 5}{6 \cdot 9}$

Step 2.3.2

Multiply $5$ by $5$ .

$\frac{3}{4} + 1 - \frac{25}{6 \cdot 9}$

Step 2.3.3

Multiply $6$ by $9$ .

$\frac{3}{4} + 1 - \frac{25}{54}$

Step 3

Find the common denominator.

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Step 3.1

Multiply $\frac{3}{4}$ by $\frac{27}{27}$ .

$\frac{3}{4} \cdot \frac{27}{27} + 1 - \frac{25}{54}$

Step 3.2

Multiply $\frac{3}{4}$ by $\frac{27}{27}$ .

$\frac{3 \cdot 27}{4 \cdot 27} + 1 - \frac{25}{54}$

Step 3.3

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

$\frac{3 \cdot 27}{4 \cdot 27} + \frac{1}{1} - \frac{25}{54}$

Step 3.4

Multiply $\frac{1}{1}$ by $\frac{108}{108}$ .

$\frac{3 \cdot 27}{4 \cdot 27} + \frac{1}{1} \cdot \frac{108}{108} - \frac{25}{54}$

Step 3.5

Multiply $\frac{1}{1}$ by $\frac{108}{108}$ .

$\frac{3 \cdot 27}{4 \cdot 27} + \frac{108}{108} - \frac{25}{54}$

Step 3.6

Multiply $\frac{25}{54}$ by $\frac{2}{2}$ .

$\frac{3 \cdot 27}{4 \cdot 27} + \frac{108}{108} - (\frac{25}{54} \cdot \frac{2}{2})$

Step 3.7

Multiply $\frac{25}{54}$ by $\frac{2}{2}$ .

$\frac{3 \cdot 27}{4 \cdot 27} + \frac{108}{108} - \frac{25 \cdot 2}{54 \cdot 2}$

Step 3.8

Multiply $4$ by $27$ .

$\frac{3 \cdot 27}{108} + \frac{108}{108} - \frac{25 \cdot 2}{54 \cdot 2}$

Step 3.9

Reorder the factors of $54 \cdot 2$ .

$\frac{3 \cdot 27}{108} + \frac{108}{108} - \frac{25 \cdot 2}{2 \cdot 54}$

Step 3.10

Multiply $2$ by $54$ .

$\frac{3 \cdot 27}{108} + \frac{108}{108} - \frac{25 \cdot 2}{108}$

Step 4

Combine the numerators over the common denominator.

$\frac{3 \cdot 27 + 108 - 25 \cdot 2}{108}$

Step 5

Simplify each term.

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Step 5.1

Multiply $3$ by $27$ .

$\frac{81 + 108 - 25 \cdot 2}{108}$

Step 5.2

Multiply $- 25$ by $2$ .

$\frac{81 + 108 - 50}{108}$

Step 6

Simplify by adding and subtracting.

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Step 6.1

Add $81$ and $108$ .

$\frac{189 - 50}{108}$

Step 6.2

Subtract $50$ from $189$ .

$\frac{139}{108}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{139}{108}$

Decimal Form:

$1.28\overline{703}$

Mixed Number Form:

$1 \frac{31}{108}$