# Khan/khan-exercises

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 Proportions 1
randVar() rand(2) randRange(3, 12) randRange(3, 12) randRange(3, 12) DENOMINATOR1 * NUMERATOR2 / DENOMINATOR2

Solve for X.

\dfrac{X}{DENOMINATOR1} = \dfrac{NUMERATOR2}{DENOMINATOR2}

\dfrac{NUMERATOR2}{DENOMINATOR2} = \dfrac{X}{DENOMINATOR1}

X = SOLUTION

Multiply both sides by \blue{DENOMINATOR1}.

\blue{DENOMINATOR1} \times \dfrac{X}{DENOMINATOR1} = \dfrac{NUMERATOR2}{DENOMINATOR2} \times \blue{DENOMINATOR1}

\blue{DENOMINATOR1} \times \dfrac{NUMERATOR2}{DENOMINATOR2} = \dfrac{X}{DENOMINATOR1} \times \blue{DENOMINATOR1}

X = \dfrac{\blue{DENOMINATOR1} \times NUMERATOR2}{DENOMINATOR2}

\dfrac{\blue{DENOMINATOR1} \times NUMERATOR2}{DENOMINATOR2} = X

X = \dfrac{DENOMINATOR1 * NUMERATOR2}{DENOMINATOR2}

randVar() rand(2) randRange(3, 12) randRange(3, 12) randRange(3, 12) DENOMINATOR2 * NUMERATOR1 / NUMERATOR2

Solve for X.

\dfrac{NUMERATOR1}{X} = \dfrac{NUMERATOR2}{DENOMINATOR2}

\dfrac{NUMERATOR2}{DENOMINATOR2} = \dfrac{NUMERATOR1}{X}

X = SOLUTION

Multiply both sides by \blue{X}.

\blue{X} \times \dfrac{NUMERATOR1}{X} = \dfrac{NUMERATOR2}{DENOMINATOR2} \times \blue{X}

NUMERATOR1 = \dfrac{NUMERATOR2}{DENOMINATOR2}\blue{X}

Multiply both sides by \green{\dfrac{DENOMINATOR2}{NUMERATOR2}}.

NUMERATOR1 \times \green{\dfrac{DENOMINATOR2}{NUMERATOR2}} = \dfrac{NUMERATOR2}{DENOMINATOR2} \blue{X} \times \green{\dfrac{DENOMINATOR2}{NUMERATOR2}}

\dfrac{NUMERATOR1 \times \green{DENOMINATOR2}}{\green{NUMERATOR2}} = \blue{X}

Multiply both sides by \blue{X}.

\blue{X} \times \dfrac{NUMERATOR2}{DENOMINATOR2} = \dfrac{NUMERATOR1}{X} \times \blue{X}

\dfrac{NUMERATOR2}{DENOMINATOR2}\blue{X} = NUMERATOR1

Multiply both sides by \green{\dfrac{DENOMINATOR2}{NUMERATOR2}}.

\dfrac{NUMERATOR2}{DENOMINATOR2} \blue{X} \times \green{\dfrac{DENOMINATOR2}{NUMERATOR2}} = NUMERATOR1 \times \green{\dfrac{DENOMINATOR2}{NUMERATOR2}}

\blue{X} = \dfrac{NUMERATOR1 \times \green{DENOMINATOR2}}{\green{NUMERATOR2}}

X = \dfrac{DENOMINATOR2 * NUMERATOR1}{NUMERATOR2}