Basic Math Examples

\frac{1}{\frac{2}{\frac{3}{\frac{4}{\frac{5}{\frac{6}{\frac{7}{\frac{8}{\frac{9}{\frac{10}{Z}}}}}}}}}} \cdot 26 = 64

$\frac{1}{\frac{2}{\frac{3}{\frac{4}{\frac{5}{\frac{6}{\frac{7}{\frac{8}{\frac{9}{\frac{10}{Z}}}}}}}}}} \cdot 26 = 64$

Step 1

Simplify

$\frac{1}{\frac{2}{\frac{3}{\frac{4}{\frac{5}{\frac{6}{\frac{7}{\frac{8}{\frac{9}{\frac{10}{Z}}}}}}}}}} \cdot 26$ .

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Step 1.1

Simplify the denominator.

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Step 1.1.1

Multiply the numerator by the reciprocal of the denominator.

$\frac{1}{\frac{2}{\frac{3}{\frac{4}{\frac{5}{\frac{6}{\frac{7}{\frac{8}{9 \frac{Z}{10}}}}}}}}} \cdot 26 = 64$

Step 1.1.2

Combine

$9$ and

$\frac{Z}{10}$ .

$\frac{1}{\frac{2}{\frac{3}{\frac{4}{\frac{5}{\frac{6}{\frac{7}{\frac{8}{\frac{9 Z}{10}}}}}}}}} \cdot 26 = 64$

Step 1.2

Simplify the denominator.

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Step 1.2.1

Multiply the numerator by the reciprocal of the denominator.

$\frac{1}{\frac{2}{\frac{3}{\frac{4}{\frac{5}{\frac{6}{\frac{7}{8 \frac{10}{9 Z}}}}}}}} \cdot 26 = 64$

Step 1.2.2

Multiply

$8 \frac{10}{9 Z}$ .

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Step 1.2.2.1

Combine

$8$ and

$\frac{10}{9 Z}$ .

$\frac{1}{\frac{2}{\frac{3}{\frac{4}{\frac{5}{\frac{6}{\frac{7}{\frac{8 \cdot 10}{9 Z}}}}}}}} \cdot 26 = 64$

Step 1.2.2.2

Multiply

$8$ by

$10$ .

$\frac{1}{\frac{2}{\frac{3}{\frac{4}{\frac{5}{\frac{6}{\frac{7}{\frac{80}{9 Z}}}}}}}} \cdot 26 = 64$

Step 1.3

Simplify the denominator.

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Step 1.3.1

Multiply the numerator by the reciprocal of the denominator.

$\frac{1}{\frac{2}{\frac{3}{\frac{4}{\frac{5}{\frac{6}{7 \frac{9 Z}{80}}}}}}} \cdot 26 = 64$

Step 1.3.2

Multiply

$7 \frac{9 Z}{80}$ .

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Step 1.3.2.1

Combine

$7$ and

$\frac{9 Z}{80}$ .

$\frac{1}{\frac{2}{\frac{3}{\frac{4}{\frac{5}{\frac{6}{\frac{7 (9 Z)}{80}}}}}}} \cdot 26 = 64$

Step 1.3.2.2

Multiply

$9$ by

$7$ .

$\frac{1}{\frac{2}{\frac{3}{\frac{4}{\frac{5}{\frac{6}{\frac{63 Z}{80}}}}}}} \cdot 26 = 64$

Step 1.4

Simplify the denominator.

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Step 1.4.1

Multiply the numerator by the reciprocal of the denominator.

$\frac{1}{\frac{2}{\frac{3}{\frac{4}{\frac{5}{6 \frac{80}{63 Z}}}}}} \cdot 26 = 64$

Step 1.4.2

Cancel the common factor of

$3$ .

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Step 1.4.2.1

Factor

$3$ out of

$6$ .

$\frac{1}{\frac{2}{\frac{3}{\frac{4}{\frac{5}{3 (2) \frac{80}{63 Z}}}}}} \cdot 26 = 64$

Step 1.4.2.2

Factor

$3$ out of

$63 Z$ .

$\frac{1}{\frac{2}{\frac{3}{\frac{4}{\frac{5}{3 (2) \frac{80}{3 (21 Z)}}}}}} \cdot 26 = 64$

Step 1.4.2.3

Cancel the common factor.

$\frac{1}{\frac{2}{\frac{3}{\frac{4}{\frac{5}{3 \cdot 2 \frac{80}{3 (21 Z)}}}}}} \cdot 26 = 64$

Step 1.4.2.4

Rewrite the expression.

$\frac{1}{\frac{2}{\frac{3}{\frac{4}{\frac{5}{2 \frac{80}{21 Z}}}}}} \cdot 26 = 64$

Step 1.4.3

Combine

$2$ and

$\frac{80}{21 Z}$ .

$\frac{1}{\frac{2}{\frac{3}{\frac{4}{\frac{5}{\frac{2 \cdot 80}{21 Z}}}}}} \cdot 26 = 64$

Step 1.4.4

Multiply

$2$ by

$80$ .

$\frac{1}{\frac{2}{\frac{3}{\frac{4}{\frac{5}{\frac{160}{21 Z}}}}}} \cdot 26 = 64$

Step 1.5

Simplify the denominator.

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Step 1.5.1

Multiply the numerator by the reciprocal of the denominator.

$\frac{1}{\frac{2}{\frac{3}{\frac{4}{5 \frac{21 Z}{160}}}}} \cdot 26 = 64$

Step 1.5.2

Cancel the common factor of

$5$ .

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Step 1.5.2.1

Factor

$5$ out of

$160$ .

$\frac{1}{\frac{2}{\frac{3}{\frac{4}{5 \frac{21 Z}{5 (32)}}}}} \cdot 26 = 64$

Step 1.5.2.2

Cancel the common factor.

$\frac{1}{\frac{2}{\frac{3}{\frac{4}{5 \frac{21 Z}{5 \cdot 32}}}}} \cdot 26 = 64$

Step 1.5.2.3

Rewrite the expression.

$\frac{1}{\frac{2}{\frac{3}{\frac{4}{\frac{21 Z}{32}}}}} \cdot 26 = 64$

Step 1.6

Simplify the denominator.

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Step 1.6.1

Multiply the numerator by the reciprocal of the denominator.

$\frac{1}{\frac{2}{\frac{3}{4 \frac{32}{21 Z}}}} \cdot 26 = 64$

Step 1.6.2

Multiply

$4 \frac{32}{21 Z}$ .

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Step 1.6.2.1

Combine

$4$ and

$\frac{32}{21 Z}$ .

$\frac{1}{\frac{2}{\frac{3}{\frac{4 \cdot 32}{21 Z}}}} \cdot 26 = 64$

Step 1.6.2.2

Multiply

$4$ by

$32$ .

$\frac{1}{\frac{2}{\frac{3}{\frac{128}{21 Z}}}} \cdot 26 = 64$

Step 1.7

Simplify the denominator.

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Step 1.7.1

Multiply the numerator by the reciprocal of the denominator.

$\frac{1}{\frac{2}{3 \frac{21 Z}{128}}} \cdot 26 = 64$

Step 1.7.2

Multiply

$3 \frac{21 Z}{128}$ .

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Step 1.7.2.1

Combine

$3$ and

$\frac{21 Z}{128}$ .

$\frac{1}{\frac{2}{\frac{3 (21 Z)}{128}}} \cdot 26 = 64$

Step 1.7.2.2

Multiply

$21$ by

$3$ .

$\frac{1}{\frac{2}{\frac{63 Z}{128}}} \cdot 26 = 64$

Step 1.8

Simplify the denominator.

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Step 1.8.1

Multiply the numerator by the reciprocal of the denominator.

$\frac{1}{2 \frac{128}{63 Z}} \cdot 26 = 64$

Step 1.8.2

Multiply

$2 \frac{128}{63 Z}$ .

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Step 1.8.2.1

Combine

$2$ and

$\frac{128}{63 Z}$ .

$\frac{1}{\frac{2 \cdot 128}{63 Z}} \cdot 26 = 64$

Step 1.8.2.2

Multiply

$2$ by

$128$ .

$\frac{1}{\frac{256}{63 Z}} \cdot 26 = 64$

Step 1.9

Multiply the numerator by the reciprocal of the denominator.

$1 \frac{63 Z}{256} \cdot 26 = 64$

Step 1.10

Multiply

$\frac{63 Z}{256}$ by

$1$ .

$\frac{63 Z}{256} \cdot 26 = 64$

Step 1.11

Cancel the common factor of

$2$ .

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Step 1.11.1

Factor

$2$ out of

$256$ .

$\frac{63 Z}{2 (128)} \cdot 26 = 64$

Step 1.11.2

Factor

$2$ out of

$26$ .

$\frac{63 Z}{2 \cdot 128} \cdot (2 \cdot 13) = 64$

Step 1.11.3

Cancel the common factor.

$\frac{63 Z}{2 \cdot 128} \cdot (2 \cdot 13) = 64$

Step 1.11.4

Rewrite the expression.

$\frac{63 Z}{128} \cdot 13 = 64$

Step 1.12

Combine

$\frac{63 Z}{128}$ and

$13$ .

$\frac{63 Z \cdot 13}{128} = 64$

Step 1.13

Multiply

$13$ by

$63$ .

$\frac{819 Z}{128} = 64$

Step 2

Find the LCD of the terms in the equation.

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Step 2.1

Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.

$128, 1$

Step 2.2

The LCM of one and any expression is the expression.

$128$

Step 3

Multiply each term in

$\frac{819 Z}{128} = 64$ by

$128$ to eliminate the fractions.

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Step 3.1

Multiply each term in

$\frac{819 Z}{128} = 64$ by

$128$ .

$\frac{819 Z}{128} \cdot 128 = 64 \cdot 128$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of

$128$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{819 Z}{128} \cdot 128 = 64 \cdot 128$

Step 3.2.1.2

Rewrite the expression.

$819 Z = 64 \cdot 128$

Step 3.3

Simplify the right side.

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Step 3.3.1

Multiply

$64$ by

$128$ .

$819 Z = 8192$

Step 4

Divide each term in

$819 Z = 8192$ by

$819$ and simplify.

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Step 4.1

Divide each term in

$819 Z = 8192$ by

$819$ .

$\frac{819 Z}{819} = \frac{8192}{819}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of

$819$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{819 Z}{819} = \frac{8192}{819}$

Step 4.2.1.2

Divide

$Z$ by

$1$ .

$Z = \frac{8192}{819}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$Z = \frac{8192}{819}$

Decimal Form:

$Z = 10.00244200 \dots$

Mixed Number Form:

$Z = 10 \frac{2}{819}$