Basic Math Examples

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

Step 1

Simplify each term.

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Step 1.1

Cancel the common factor of $3$ .

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Step 1.1.1

Cancel the common factor.

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

Step 1.1.2

Rewrite the expression.

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

Step 1.2

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

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

Step 1.3

Multiply the numerator by the reciprocal of the denominator.

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

Step 1.4

Multiply $\frac{1}{4} \cdot \frac{5}{4}$ .

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Step 1.4.1

Multiply $\frac{1}{4}$ by $\frac{5}{4}$ .

$\frac{1}{4} + \frac{4}{5} - \frac{5}{4 \cdot 4}$

Step 1.4.2

Multiply $4$ by $4$ .

$\frac{1}{4} + \frac{4}{5} - \frac{5}{16}$

Step 2

Find the common denominator.

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Step 2.1

Multiply $\frac{1}{4}$ by $\frac{20}{20}$ .

$\frac{1}{4} \cdot \frac{20}{20} + \frac{4}{5} - \frac{5}{16}$

Step 2.2

Multiply $\frac{1}{4}$ by $\frac{20}{20}$ .

$\frac{20}{4 \cdot 20} + \frac{4}{5} - \frac{5}{16}$

Step 2.3

Multiply $\frac{4}{5}$ by $\frac{16}{16}$ .

$\frac{20}{4 \cdot 20} + \frac{4}{5} \cdot \frac{16}{16} - \frac{5}{16}$

Step 2.4

Multiply $\frac{4}{5}$ by $\frac{16}{16}$ .

$\frac{20}{4 \cdot 20} + \frac{4 \cdot 16}{5 \cdot 16} - \frac{5}{16}$

Step 2.5

Multiply $\frac{5}{16}$ by $\frac{5}{5}$ .

$\frac{20}{4 \cdot 20} + \frac{4 \cdot 16}{5 \cdot 16} - (\frac{5}{16} \cdot \frac{5}{5})$

Step 2.6

Multiply $\frac{5}{16}$ by $\frac{5}{5}$ .

$\frac{20}{4 \cdot 20} + \frac{4 \cdot 16}{5 \cdot 16} - \frac{5 \cdot 5}{16 \cdot 5}$

Step 2.7

Multiply $4$ by $20$ .

$\frac{20}{80} + \frac{4 \cdot 16}{5 \cdot 16} - \frac{5 \cdot 5}{16 \cdot 5}$

Step 2.8

Multiply $5$ by $16$ .

$\frac{20}{80} + \frac{4 \cdot 16}{80} - \frac{5 \cdot 5}{16 \cdot 5}$

Step 2.9

Reorder the factors of $16 \cdot 5$ .

$\frac{20}{80} + \frac{4 \cdot 16}{80} - \frac{5 \cdot 5}{5 \cdot 16}$

Step 2.10

Multiply $5$ by $16$ .

$\frac{20}{80} + \frac{4 \cdot 16}{80} - \frac{5 \cdot 5}{80}$

Step 3

Combine the numerators over the common denominator.

$\frac{20 + 4 \cdot 16 - 5 \cdot 5}{80}$

Step 4

Simplify each term.

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Step 4.1

Multiply $4$ by $16$ .

$\frac{20 + 64 - 5 \cdot 5}{80}$

Step 4.2

Multiply $- 5$ by $5$ .

$\frac{20 + 64 - 25}{80}$

Step 5

Simplify by adding and subtracting.

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Step 5.1

Add $20$ and $64$ .

$\frac{84 - 25}{80}$

Step 5.2

Subtract $25$ from $84$ .

$\frac{59}{80}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{59}{80}$

Decimal Form:

$0.7375$