Übung: Verhältnisse und Proportionen #2

randRangeNonZero(3, 12)*randRangeNonZero(-1,1) "x + " + xConstant randRange( 0, 3 ) insertionIndex > 1 ? false : true insertionIndex % 2 !== 0 ? false: true (function() { var numbers = randRangeUnique( 5, 12, 3 ); numbers.splice( insertionIndex, 0, xExpression ); return numbers; })() (function() { if ( numerator1 === xExpression ) { return [ numerator2 * denominator1, denominator2 ]; } else if ( numerator2 === xExpression ) { return [ numerator1 * denominator2, denominator1 ]; } else if ( denominator1 === xExpression ) { return [ numerator1 * denominator2, numerator2 ]; } else { return [ numerator2 * denominator1, numerator1 ]; } })() (solutionNumerator/solutionDenominator) - xConstant (function() { if ( numerator1 === xExpression ) { return denominator1; } else if ( numerator2 === xExpression ) { return denominator2; } else { return xExpression; } })() (function() { var hint1Product = function( numerator, denominator ) { if ( denominator === hint1Multiplier ) { return numerator; } else if ( hint1Multiplier === xExpression ) { return "\\dfrac{" + numerator + "}{" + denominator + "}(" + xExpression + ")"; } else { return "\\dfrac{" + hint1Multiplier * numerator + "}{" + denominator + "}"; } } return [ hint1Product( numerator1, denominator1 ), hint1Product( numerator2, denominator2 ) ]; })() (function() { if ( denominator1 === xExpression ) { return "\\dfrac{" + denominator2 + "}{" + numerator2 + "}"; } else if ( denominator2 === xExpression ) { return "\\dfrac{" + denominator1 + "}{" + numerator1 + "}"; } else { return hint1Multiplier; } })() (function() { if ( denominator1 === xExpression ) { return [ "\\dfrac{" + solutionNumerator + "}{" + solutionDenominator + "}", "(" + xExpression + ")" ]; } else if ( denominator2 === xExpression ) { return [ "(" + xExpression + ")", "\\dfrac{" + solutionNumerator + "}{" + solutionDenominator + "}" ]; } else { return [hint1Product1, hint1Product2]; } })() (function() { if (inLHS && inDenominator || !inLHS && !inDenominator) { return [ "\\cancel {\\dfrac{" + solutionNumerator + "}{" + solutionDenominator + "}}{" + solutionNumerator / solutionDenominator + "} - " + xConstant, "x" ]; } else { return [ "x", "\\cancel {\\dfrac{" + solutionNumerator + "}{" + solutionDenominator + "}}{" + solutionNumerator / solutionDenominator + "} - " + xConstant ]; } })()

Multipliziere
beide Seiten mit hint1Multiplier

\color{red}{ (hint1Multiplier) \times } \dfrac{numerator1}{denominator1} = \dfrac{numerator2}{denominator2} \color{red}{ \times (hint1Multiplier) }
↓
hint1Product1 = hint1Product2

Multipliziere
beide Seiten mit hint2Multiplier

\color{red}{ hint2Multiplier \times } hint1Product1 = hint1Product2 \color{red}{ \times hint2Multiplier }
↓
hint2Product1 = hint2Product2

Addiere abs(xConstant) zuSubtrahiere abs(xConstant) zuvon beiden Seiten und vereinfache um x zu isolieren

hint2Product1 \color{red}{+ -xConstant} = hint2Product2 \color{red}{+ -xConstant}
↓
hint3Product1 = hint3Product2

x ist

= SOLUTION.

Löse nach x auf.

\large\dfrac{numerator1}{denominator1} = \large\dfrac{numerator2}{denominator2}

SOLUTION