Basic Math Examples

$\frac{1}{\frac{43}{10} + \frac{25}{100}} + \frac{4}{1}$

Step 1

Simplify each term.

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Step 1.1

Cancel the common factor of $25$ and $100$ .

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Step 1.1.1

Factor $25$ out of $25$ .

$\frac{1}{\frac{43}{10} + \frac{25 (1)}{100}} + \frac{4}{1}$

Step 1.1.2

Cancel the common factors.

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Step 1.1.2.1

Factor $25$ out of $100$ .

$\frac{1}{\frac{43}{10} + \frac{25 \cdot 1}{25 \cdot 4}} + \frac{4}{1}$

Step 1.1.2.2

Cancel the common factor.

$\frac{1}{\frac{43}{10} + \frac{25 \cdot 1}{25 \cdot 4}} + \frac{4}{1}$

Step 1.1.2.3

Rewrite the expression.

$\frac{1}{\frac{43}{10} + \frac{1}{4}} + \frac{4}{1}$

Step 1.2

Simplify the denominator.

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Step 1.2.1

To write $\frac{43}{10}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{1}{\frac{43}{10} \cdot \frac{2}{2} + \frac{1}{4}} + \frac{4}{1}$

Step 1.2.2

To write $\frac{1}{4}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{1}{\frac{43}{10} \cdot \frac{2}{2} + \frac{1}{4} \cdot \frac{5}{5}} + \frac{4}{1}$

Step 1.2.3

Write each expression with a common denominator of $20$ , by multiplying each by an appropriate factor of $1$ .

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Step 1.2.3.1

Multiply $\frac{43}{10}$ by $\frac{2}{2}$ .

$\frac{1}{\frac{43 \cdot 2}{10 \cdot 2} + \frac{1}{4} \cdot \frac{5}{5}} + \frac{4}{1}$

Step 1.2.3.2

Multiply $10$ by $2$ .

$\frac{1}{\frac{43 \cdot 2}{20} + \frac{1}{4} \cdot \frac{5}{5}} + \frac{4}{1}$

Step 1.2.3.3

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

$\frac{1}{\frac{43 \cdot 2}{20} + \frac{5}{4 \cdot 5}} + \frac{4}{1}$

Step 1.2.3.4

Multiply $4$ by $5$ .

$\frac{1}{\frac{43 \cdot 2}{20} + \frac{5}{20}} + \frac{4}{1}$

Step 1.2.4

Combine the numerators over the common denominator.

$\frac{1}{\frac{43 \cdot 2 + 5}{20}} + \frac{4}{1}$

Step 1.2.5

Simplify the numerator.

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Step 1.2.5.1

Multiply $43$ by $2$ .

$\frac{1}{\frac{86 + 5}{20}} + \frac{4}{1}$

Step 1.2.5.2

Add $86$ and $5$ .

$\frac{1}{\frac{91}{20}} + \frac{4}{1}$

Step 1.3

Multiply the numerator by the reciprocal of the denominator.

$1 (\frac{20}{91}) + \frac{4}{1}$

Step 1.4

Multiply $\frac{20}{91}$ by $1$ .

$\frac{20}{91} + \frac{4}{1}$

Step 1.5

Divide $4$ by $1$ .

$\frac{20}{91} + 4$

Step 2

To write $4$ as a fraction with a common denominator, multiply by $\frac{91}{91}$ .

$\frac{20}{91} + 4 \cdot \frac{91}{91}$

Step 3

Combine $4$ and $\frac{91}{91}$ .

$\frac{20}{91} + \frac{4 \cdot 91}{91}$

Step 4

Combine the numerators over the common denominator.

$\frac{20 + 4 \cdot 91}{91}$

Step 5

Simplify the numerator.

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Step 5.1

Multiply $4$ by $91$ .

$\frac{20 + 364}{91}$

Step 5.2

Add $20$ and $364$ .

$\frac{384}{91}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{384}{91}$

Decimal Form:

$4.\overline{219780}$

Mixed Number Form:

$4 \frac{20}{91}$