Basic Math Examples

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

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:

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