Basic Math Examples

$(37653 - 535 \cdot 5495 \div 574 + 165)$

Step 1

Simplify each term.

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Step 1.1

Rewrite the division as a fraction.

$37653 - \frac{535 \cdot 5495}{574} + 165$

Step 1.2

Cancel the common factor of $5495$ and $574$ .

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Step 1.2.1

Factor $7$ out of $535 \cdot 5495$ .

$37653 - \frac{7 (535 \cdot 785)}{574} + 165$

Step 1.2.2

Cancel the common factors.

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Step 1.2.2.1

Factor $7$ out of $574$ .

$37653 - \frac{7 (535 \cdot 785)}{7 (82)} + 165$

Step 1.2.2.2

Cancel the common factor.

$37653 - \frac{7 (535 \cdot 785)}{7 \cdot 82} + 165$

Step 1.2.2.3

Rewrite the expression.

$37653 - \frac{535 \cdot 785}{82} + 165$

Step 1.3

Multiply $535$ by $785$ .

$37653 - \frac{419975}{82} + 165$

Step 2

Find the common denominator.

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Step 2.1

Write $37653$ as a fraction with denominator $1$ .

$\frac{37653}{1} - \frac{419975}{82} + 165$

Step 2.2

Multiply $\frac{37653}{1}$ by $\frac{82}{82}$ .

$\frac{37653}{1} \cdot \frac{82}{82} - \frac{419975}{82} + 165$

Step 2.3

Multiply $\frac{37653}{1}$ by $\frac{82}{82}$ .

$\frac{37653 \cdot 82}{82} - \frac{419975}{82} + 165$

Step 2.4

Write $165$ as a fraction with denominator $1$ .

$\frac{37653 \cdot 82}{82} - \frac{419975}{82} + \frac{165}{1}$

Step 2.5

Multiply $\frac{165}{1}$ by $\frac{82}{82}$ .

$\frac{37653 \cdot 82}{82} - \frac{419975}{82} + \frac{165}{1} \cdot \frac{82}{82}$

Step 2.6

Multiply $\frac{165}{1}$ by $\frac{82}{82}$ .

$\frac{37653 \cdot 82}{82} - \frac{419975}{82} + \frac{165 \cdot 82}{82}$

Step 3

Combine the numerators over the common denominator.

$\frac{37653 \cdot 82 - 419975 + 165 \cdot 82}{82}$

Step 4

Simplify each term.

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Step 4.1

Multiply $37653$ by $82$ .

$\frac{3087546 - 419975 + 165 \cdot 82}{82}$

Step 4.2

Multiply $165$ by $82$ .

$\frac{3087546 - 419975 + 13530}{82}$

Step 5

Simplify by adding and subtracting.

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Step 5.1

Subtract $419975$ from $3087546$ .

$\frac{2667571 + 13530}{82}$

Step 5.2

Add $2667571$ and $13530$ .

$\frac{2681101}{82}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{2681101}{82}$

Decimal Form:

$32696.35365853 \dots$

Mixed Number Form:

$32696 \frac{29}{82}$