Basic Math Examples

\frac{78}{174} = \frac{65}{145} \cdot (p o r p o r t i o n)

$\frac{78}{174} = \frac{65}{145} \cdot (p o r p o r t i o n)$

Step 1

Rewrite the equation as

$\frac{65}{145} \cdot (p o r p o r t i o n) = \frac{78}{174}$ .

$\frac{65}{145} \cdot (p o r p o r t i o n) = \frac{78}{174}$

Step 2

Multiply both sides of the equation by

$\frac{1}{\frac{65}{145} i}$ .

$\frac{1}{\frac{65}{145} i} (\frac{65}{145} \cdot (p o r p o r t i o n)) = \frac{1}{\frac{65}{145} i} \cdot \frac{78}{174}$

Step 3

Simplify both sides of the equation.

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Step 3.1

Simplify the left side.

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Step 3.1.1

Simplify

$\frac{1}{\frac{65}{145} i} (\frac{65}{145} \cdot (p o r p o r t i o n))$ .

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Step 3.1.1.1

Multiply

$p$ by

$p$ by adding the exponents.

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Step 3.1.1.1.1

Move

$p$ .

$\frac{1}{\frac{65}{145} i} (\frac{65}{145} \cdot (p \cdot p o r o r t i o n)) = \frac{1}{\frac{65}{145} i} \cdot \frac{78}{174}$

Step 3.1.1.1.2

Multiply

$p$ by

$p$ .

$\frac{1}{\frac{65}{145} i} (\frac{65}{145} \cdot (p^{2} o r o r t i o n)) = \frac{1}{\frac{65}{145} i} \cdot \frac{78}{174}$

Step 3.1.1.2

Multiply

$o$ by

$o$ by adding the exponents.

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Step 3.1.1.2.1

Move

$o$ .

$\frac{1}{\frac{65}{145} i} (\frac{65}{145} \cdot (p^{2} (o \cdot o) r \cdot r t i o n)) = \frac{1}{\frac{65}{145} i} \cdot \frac{78}{174}$

Step 3.1.1.2.2

Multiply

$o$ by

$o$ .

$\frac{1}{\frac{65}{145} i} (\frac{65}{145} \cdot (p^{2} o^{2} r \cdot r t i o n)) = \frac{1}{\frac{65}{145} i} \cdot \frac{78}{174}$

Step 3.1.1.3

Multiply

$o^{2}$ by

$o$ by adding the exponents.

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Step 3.1.1.3.1

Move

$o$ .

$\frac{1}{\frac{65}{145} i} (\frac{65}{145} \cdot (p^{2} (o \cdot o^{2}) r \cdot r t i n)) = \frac{1}{\frac{65}{145} i} \cdot \frac{78}{174}$

Step 3.1.1.3.2

Multiply

$o$ by

$o^{2}$ .

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Step 3.1.1.3.2.1

Raise

$o$ to the power of

$1$ .

$\frac{1}{\frac{65}{145} i} (\frac{65}{145} \cdot (p^{2} (o^{1} o^{2}) r \cdot r t i n)) = \frac{1}{\frac{65}{145} i} \cdot \frac{78}{174}$

Step 3.1.1.3.2.2

Use the power rule

$a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{1}{\frac{65}{145} i} (\frac{65}{145} \cdot (p^{2} o^{1 + 2} r \cdot r t i n)) = \frac{1}{\frac{65}{145} i} \cdot \frac{78}{174}$

Step 3.1.1.3.3

Add

$1$ and

$2$ .

$\frac{1}{\frac{65}{145} i} (\frac{65}{145} \cdot (p^{2} o^{3} r \cdot r t i n)) = \frac{1}{\frac{65}{145} i} \cdot \frac{78}{174}$

Step 3.1.1.4

Multiply

$r$ by

$r$ by adding the exponents.

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Step 3.1.1.4.1

Move

$r$ .

$\frac{1}{\frac{65}{145} i} (\frac{65}{145} \cdot (p^{2} o^{3} (r \cdot r) t i n)) = \frac{1}{\frac{65}{145} i} \cdot \frac{78}{174}$

Step 3.1.1.4.2

Multiply

$r$ by

$r$ .

$\frac{1}{\frac{65}{145} i} (\frac{65}{145} \cdot (p^{2} o^{3} r^{2} t i n)) = \frac{1}{\frac{65}{145} i} \cdot \frac{78}{174}$

Step 3.1.1.5

Cancel the common factor of

$\frac{65 i}{145}$ .

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Step 3.1.1.5.1

Factor

$\frac{65 i}{145}$ out of

$\frac{65}{145} i$ .

$\frac{1}{\frac{65 i}{145} (- i i)} (\frac{65}{145} \cdot (p^{2} o^{3} r^{2} t i n)) = \frac{1}{\frac{65}{145} i} \cdot \frac{78}{174}$

Step 3.1.1.5.2

Factor

$\frac{65 i}{145}$ out of

$\frac{65}{145} \cdot (p^{2} o^{3} r^{2} t i n)$ .

$\frac{1}{\frac{65 i}{145} (- i i)} (\frac{65 i}{145} (- i \cdot (p^{2} o^{3} r^{2} t i n))) = \frac{1}{\frac{65}{145} i} \cdot \frac{78}{174}$

Step 3.1.1.5.3

Cancel the common factor.

$\frac{1}{\frac{65 i}{145} (- i i)} (\frac{65 i}{145} (- i \cdot (p^{2} o^{3} r^{2} t i n))) = \frac{1}{\frac{65}{145} i} \cdot \frac{78}{174}$

Step 3.1.1.5.4

Rewrite the expression.

$\frac{1}{- i i} (- i \cdot (p^{2} o^{3} r^{2} t i n)) = \frac{1}{\frac{65}{145} i} \cdot \frac{78}{174}$

Step 3.1.1.6

Raise

$i$ to the power of

$1$ .

$\frac{1}{- (i^{1} i)} (- i \cdot (p^{2} o^{3} r^{2} t i n)) = \frac{1}{\frac{65}{145} i} \cdot \frac{78}{174}$

Step 3.1.1.7

Raise

$i$ to the power of

$1$ .

$\frac{1}{- (i^{1} i^{1})} (- i \cdot (p^{2} o^{3} r^{2} t i n)) = \frac{1}{\frac{65}{145} i} \cdot \frac{78}{174}$

Step 3.1.1.8

Use the power rule

$a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{1}{- i^{1 + 1}} (- i \cdot (p^{2} o^{3} r^{2} t i n)) = \frac{1}{\frac{65}{145} i} \cdot \frac{78}{174}$

Step 3.1.1.9

Add

$1$ and

$1$ .

$\frac{1}{- i^{2}} (- i \cdot (p^{2} o^{3} r^{2} t i n)) = \frac{1}{\frac{65}{145} i} \cdot \frac{78}{174}$

Step 3.1.1.10

Raise

$i$ to the power of

$1$ .

$\frac{1}{- i^{2}} (- 1 \cdot (p^{2} o^{3} r^{2} t (i^{1} i) n)) = \frac{1}{\frac{65}{145} i} \cdot \frac{78}{174}$

Step 3.1.1.11

Raise

$i$ to the power of

$1$ .

$\frac{1}{- i^{2}} (- 1 \cdot (p^{2} o^{3} r^{2} t (i^{1} i^{1}) n)) = \frac{1}{\frac{65}{145} i} \cdot \frac{78}{174}$

Step 3.1.1.12

Use the power rule

$a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{1}{- i^{2}} (- 1 \cdot (p^{2} o^{3} r^{2} t i^{1 + 1} n)) = \frac{1}{\frac{65}{145} i} \cdot \frac{78}{174}$

Step 3.1.1.13

Combine fractions.

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Step 3.1.1.13.1

Add

$1$ and

$1$ .

$\frac{1}{- i^{2}} (- 1 \cdot (p^{2} o^{3} r^{2} t i^{2} n)) = \frac{1}{\frac{65}{145} i} \cdot \frac{78}{174}$

Step 3.1.1.13.2

Combine

$\frac{1}{- i^{2}}$ and

$p^{2}$ .

$- 1 \cdot (\frac{p^{2}}{- i^{2}} o^{3} r^{2} t i^{2} n) = \frac{1}{\frac{65}{145} i} \cdot \frac{78}{174}$

Step 3.1.1.13.3

Combine

$\frac{p^{2}}{- i^{2}}$ and

$o^{3}$ .

$- 1 \cdot (\frac{p^{2} o^{3}}{- i^{2}} r^{2} t i^{2} n) = \frac{1}{\frac{65}{145} i} \cdot \frac{78}{174}$

Step 3.1.1.13.4

Combine

$\frac{p^{2} o^{3}}{- i^{2}}$ and

$r^{2}$ .

$- 1 \cdot (\frac{p^{2} o^{3} r^{2}}{- i^{2}} t i^{2} n) = \frac{1}{\frac{65}{145} i} \cdot \frac{78}{174}$

Step 3.1.1.13.5

Combine

$\frac{p^{2} o^{3} r^{2}}{- i^{2}}$ and

$t$ .

$- 1 \cdot (\frac{p^{2} o^{3} r^{2} t}{- i^{2}} i^{2} n) = \frac{1}{\frac{65}{145} i} \cdot \frac{78}{174}$

Step 3.1.1.13.6

Combine

$\frac{p^{2} o^{3} r^{2} t}{- i^{2}}$ and

$i^{2}$ .

$- 1 \cdot (\frac{p^{2} o^{3} r^{2} t i^{2}}{- i^{2}} n) = \frac{1}{\frac{65}{145} i} \cdot \frac{78}{174}$

Step 3.1.1.13.7

Combine

$\frac{p^{2} o^{3} r^{2} t i^{2}}{- i^{2}}$ and

$n$ .

$- 1 \cdot \frac{p^{2} o^{3} r^{2} t i^{2} n}{- i^{2}} = \frac{1}{\frac{65}{145} i} \cdot \frac{78}{174}$

Step 3.1.1.14

Simplify the numerator.

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Step 3.1.1.14.1

Rewrite

$i^{2}$ as

$- 1$ .

$- 1 \cdot \frac{p^{2} o^{3} r^{2} t \cdot - 1 n}{- i^{2}} = \frac{1}{\frac{65}{145} i} \cdot \frac{78}{174}$

Step 3.1.1.14.2

Factor out negative.

$- 1 \cdot \frac{- p^{2} o^{3} r^{2} t n}{- i^{2}} = \frac{1}{\frac{65}{145} i} \cdot \frac{78}{174}$

Step 3.1.1.15

Rewrite

$i^{2}$ as

$- 1$ .

$- 1 \cdot \frac{- p^{2} o^{3} r^{2} t n}{- - 1} = \frac{1}{\frac{65}{145} i} \cdot \frac{78}{174}$

Step 3.1.1.16

Multiply

$- 1$ by

$- 1$ .

$- 1 \cdot \frac{- p^{2} o^{3} r^{2} t n}{1} = \frac{1}{\frac{65}{145} i} \cdot \frac{78}{174}$

Step 3.1.1.17

Divide

$- p^{2} o^{3} r^{2} t n$ by

$1$ .

$- 1 \cdot (- p^{2} o^{3} r^{2} t n) = \frac{1}{\frac{65}{145} i} \cdot \frac{78}{174}$

Step 3.1.1.18

Multiply

$- 1 (- p^{2} o^{3} r^{2} t n)$ .

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Step 3.1.1.18.1

Multiply

$- 1$ by

$- 1$ .

$1 (p^{2} o^{3} r^{2} t n) = \frac{1}{\frac{65}{145} i} \cdot \frac{78}{174}$

Step 3.1.1.18.2

Multiply

$p^{2}$ by

$1$ .

$p^{2} (o^{3} r^{2} t n) = \frac{1}{\frac{65}{145} i} \cdot \frac{78}{174}$

$p^{2} o^{3} r^{2} t n = \frac{1}{\frac{65}{145} i} \cdot \frac{78}{174}$

Step 3.2

Simplify the right side.

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Step 3.2.1

Simplify

$\frac{1}{\frac{65}{145} i} \cdot \frac{78}{174}$ .

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Step 3.2.1.1

Cancel the common factor of

$65$ and

$145$ .

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Step 3.2.1.1.1

Factor

$5$ out of

$65$ .

$p^{2} o^{3} r^{2} t n = \frac{1}{\frac{5 (13)}{145} i} \cdot \frac{78}{174}$

Step 3.2.1.1.2

Cancel the common factors.

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Step 3.2.1.1.2.1

Factor

$5$ out of

$145$ .

$p^{2} o^{3} r^{2} t n = \frac{1}{\frac{5 \cdot 13}{5 \cdot 29} i} \cdot \frac{78}{174}$

Step 3.2.1.1.2.2

Cancel the common factor.

$p^{2} o^{3} r^{2} t n = \frac{1}{\frac{5 \cdot 13}{5 \cdot 29} i} \cdot \frac{78}{174}$

Step 3.2.1.1.2.3

Rewrite the expression.

$p^{2} o^{3} r^{2} t n = \frac{1}{\frac{13}{29} i} \cdot \frac{78}{174}$

Step 3.2.1.2

Multiply the numerator and denominator of

$\frac{1}{0.44827586 i}$ by the conjugate of

$0.44827586 i$ to make the denominator real.

$p^{2} o^{3} r^{2} t n = \frac{1}{0.44827586 i} \cdot \frac{i}{i} \frac{78}{174}$

Step 3.2.1.3

Multiply.

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Step 3.2.1.3.1

Combine.

$p^{2} o^{3} r^{2} t n = \frac{1 i}{0.44827586 i i} \cdot \frac{78}{174}$

Step 3.2.1.3.2

Multiply

$i$ by

$1$ .

$p^{2} o^{3} r^{2} t n = \frac{i}{0.44827586 i i} \cdot \frac{78}{174}$

Step 3.2.1.3.3

Simplify the denominator.

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Step 3.2.1.3.3.1

Add parentheses.

$p^{2} o^{3} r^{2} t n = \frac{i}{0.44827586 (i i)} \cdot \frac{78}{174}$

Step 3.2.1.3.3.2

Raise

$i$ to the power of

$1$ .

$p^{2} o^{3} r^{2} t n = \frac{i}{0.44827586 (i^{1} i)} \cdot \frac{78}{174}$

Step 3.2.1.3.3.3

Raise

$i$ to the power of

$1$ .

$p^{2} o^{3} r^{2} t n = \frac{i}{0.44827586 (i^{1} i^{1})} \cdot \frac{78}{174}$

Step 3.2.1.3.3.4

Use the power rule

$a^{m} a^{n} = a^{m + n}$ to combine exponents.

$p^{2} o^{3} r^{2} t n = \frac{i}{0.44827586 i^{1 + 1}} \cdot \frac{78}{174}$

Step 3.2.1.3.3.5

Add

$1$ and

$1$ .

$p^{2} o^{3} r^{2} t n = \frac{i}{0.44827586 i^{2}} \cdot \frac{78}{174}$

Step 3.2.1.3.3.6

Rewrite

$i^{2}$ as

$- 1$ .

$p^{2} o^{3} r^{2} t n = \frac{i}{0.44827586 \cdot - 1} \cdot \frac{78}{174}$

Step 3.2.1.4

Multiply

$0.44827586$ by

$- 1$ .

$p^{2} o^{3} r^{2} t n = \frac{i}{- 0.44827586} \cdot \frac{78}{174}$

Step 3.2.1.5

Move the negative in front of the fraction.

$p^{2} o^{3} r^{2} t n = - \frac{i}{0.44827586} \cdot \frac{78}{174}$

Step 3.2.1.6

Multiply by

$1$ .

$p^{2} o^{3} r^{2} t n = - \frac{1 i}{0.44827586} \cdot \frac{78}{174}$

Step 3.2.1.7

Factor

$0.44827586$ out of

$0.44827586$ .

$p^{2} o^{3} r^{2} t n = - \frac{1 i}{0.44827586 (1)} \cdot \frac{78}{174}$

Step 3.2.1.8

Separate fractions.

$p^{2} o^{3} r^{2} t n = - (\frac{1}{0.44827586} \cdot \frac{i}{1}) \frac{78}{174}$

Step 3.2.1.9

Simplify the expression.

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Step 3.2.1.9.1

Divide

$1$ by

$0.44827586$ .

$p^{2} o^{3} r^{2} t n = - (2.\overline{230769} \frac{i}{1}) \frac{78}{174}$

Step 3.2.1.9.2

Divide

$i$ by

$1$ .

$p^{2} o^{3} r^{2} t n = - (2.\overline{230769} i) \frac{78}{174}$

Step 3.2.1.9.3

Multiply

$2.\overline{230769}$ by

$- 1$ .

$p^{2} o^{3} r^{2} t n = - 2.\overline{230769} i \frac{78}{174}$

Step 3.2.1.10

Cancel the common factor of

$78$ and

$174$ .

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Step 3.2.1.10.1

Factor

$6$ out of

$78$ .

$p^{2} o^{3} r^{2} t n = - 2.\overline{230769} i \frac{6 (13)}{174}$

Step 3.2.1.10.2

Cancel the common factors.

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Step 3.2.1.10.2.1

Factor

$6$ out of

$174$ .

$p^{2} o^{3} r^{2} t n = - 2.\overline{230769} i \frac{6 \cdot 13}{6 \cdot 29}$

Step 3.2.1.10.2.2

Cancel the common factor.

$p^{2} o^{3} r^{2} t n = - 2.\overline{230769} i \frac{6 \cdot 13}{6 \cdot 29}$

Step 3.2.1.10.2.3

Rewrite the expression.

$p^{2} o^{3} r^{2} t n = - 2.\overline{230769} i \frac{13}{29}$

Step 3.2.1.11

Multiply

$- 2.\overline{230769} i \frac{13}{29}$ .

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Step 3.2.1.11.1

Combine

$\frac{13}{29}$ and

$- 2.\overline{230769}$ .

$p^{2} o^{3} r^{2} t n = \frac{13 \cdot - 2.\overline{230769}}{29} i$

Step 3.2.1.11.2

Multiply

$13$ by

$- 2.\overline{230769}$ .

$p^{2} o^{3} r^{2} t n = \frac{- 29}{29} i$

Step 3.2.1.11.3

Combine

$\frac{- 29}{29}$ and

$i$ .

$p^{2} o^{3} r^{2} t n = \frac{- 29 i}{29}$

Step 3.2.1.12

Move the negative in front of the fraction.

$p^{2} o^{3} r^{2} t n = - \frac{29 i}{29}$

Step 3.2.1.13

Factor

$29$ out of

$29 i$ .

$p^{2} o^{3} r^{2} t n = - \frac{29 (i)}{29}$

Step 3.2.1.14

Factor

$29$ out of

$29$ .

$p^{2} o^{3} r^{2} t n = - \frac{29 (i)}{29 (1)}$

Step 3.2.1.15

Separate fractions.

$p^{2} o^{3} r^{2} t n = - (\frac{29}{29} \cdot \frac{i}{1})$

Step 3.2.1.16

Divide

$29$ by

$29$ .

$p^{2} o^{3} r^{2} t n = - (1 \frac{i}{1})$

Step 3.2.1.17

Divide

$i$ by

$1$ .

$p^{2} o^{3} r^{2} t n = - (1 i)$

Step 3.2.1.18

Multiply

$1$ by

$- 1$ .

$p^{2} o^{3} r^{2} t n = - 1 i$

Step 4

Divide each term in

$p^{2} o^{3} r^{2} t n = - 1 i$ by

$p^{2} o^{3} r^{2} n$ and simplify.

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Step 4.1

Divide each term in

$p^{2} o^{3} r^{2} t n = - 1 i$ by

$p^{2} o^{3} r^{2} n$ .

$\frac{p^{2} o^{3} r^{2} t n}{p^{2} o^{3} r^{2} n} = \frac{- 1 i}{p^{2} o^{3} r^{2} n}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of

$p^{2}$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{p^{2} o^{3} r^{2} t n}{p^{2} o^{3} r^{2} n} = \frac{- 1 i}{p^{2} o^{3} r^{2} n}$

Step 4.2.1.2

Rewrite the expression.

$\frac{o^{3} r^{2} t n}{o^{3} r^{2} n} = \frac{- 1 i}{p^{2} o^{3} r^{2} n}$

Step 4.2.2

Cancel the common factor of

$o^{3}$ .

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Step 4.2.2.1

Cancel the common factor.

$\frac{o^{3} r^{2} t n}{o^{3} r^{2} n} = \frac{- 1 i}{p^{2} o^{3} r^{2} n}$

Step 4.2.2.2

Rewrite the expression.

$\frac{r^{2} t n}{r^{2} n} = \frac{- 1 i}{p^{2} o^{3} r^{2} n}$

Step 4.2.3

Cancel the common factor of

$r^{2}$ .

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Step 4.2.3.1

Cancel the common factor.

$\frac{r^{2} t n}{r^{2} n} = \frac{- 1 i}{p^{2} o^{3} r^{2} n}$

Step 4.2.3.2

Rewrite the expression.

$\frac{t n}{n} = \frac{- 1 i}{p^{2} o^{3} r^{2} n}$

Step 4.2.4

Cancel the common factor of

$n$ .

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Step 4.2.4.1

Cancel the common factor.

$\frac{t n}{n} = \frac{- 1 i}{p^{2} o^{3} r^{2} n}$

Step 4.2.4.2

Divide

$t$ by

$1$ .

$t = \frac{- 1 i}{p^{2} o^{3} r^{2} n}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Move the negative in front of the fraction.

$t = - \frac{1 i}{p^{2} o^{3} r^{2} n}$