# Khan/khan-exercises

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 Proportions 2
randVar() rand(2) randRange(2, 6) randRange(2, 12) DENOMINATOR2 * randRange(2, 6) randRangeNonZero(-12, 12) plus(X, CONSTANT) DENOMINATOR1 * NUMERATOR2 / DENOMINATOR2 - CONSTANT

Solve for X.

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

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

X = SOLUTION

Multiply both sides by \blue{DENOMINATOR1}.

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

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

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

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

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

EXPR = fractionReduce(DENOMINATOR1 * NUMERATOR2, DENOMINATOR2)

X = SOLUTION

randVar() rand(2) randRange(2, 6) randRange(2, 12) NUMERATOR2 * randRange(2, 6) randRangeNonZero(-12, 12) plus(X, CONSTANT) DENOMINATOR2 * NUMERATOR1 / NUMERATOR2 - CONSTANT

Solve for X.

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

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

X = SOLUTION

Multiply both sides by \blue{(EXPR)}.

\dfrac{NUMERATOR1}{EXPR} \times \blue{(EXPR)} = \dfrac{NUMERATOR2}{DENOMINATOR2} \times \blue{(EXPR)}

NUMERATOR1 = \dfrac{NUMERATOR2}{DENOMINATOR2}\blue{(EXPR)}

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

NUMERATOR1 \times \green{\dfrac{DENOMINATOR2}{NUMERATOR2}} = \dfrac{NUMERATOR2}{DENOMINATOR2} \blue{(EXPR)} \times \green{\dfrac{DENOMINATOR2}{NUMERATOR2}}

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

Multiply both sides by \blue{(EXPR)}.

\blue{(EXPR)} \times \dfrac{NUMERATOR2}{DENOMINATOR2} = \dfrac{NUMERATOR1}{EXPR} \times \blue{(EXPR)}

\dfrac{NUMERATOR2}{DENOMINATOR2}\blue{(EXPR)} = NUMERATOR1

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

\dfrac{NUMERATOR2}{DENOMINATOR2} \blue{(EXPR)} \times \green{\dfrac{DENOMINATOR2}{NUMERATOR2}} = NUMERATOR1 \times \green{\dfrac{DENOMINATOR2}{NUMERATOR2}}

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

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

EXPR = fractionReduce(DENOMINATOR2 * NUMERATOR1, NUMERATOR2)

X = SOLUTION