# Khan/khan-exercises

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 Comparing improper fractions and mixed numbers
randRange(1, 5) WHOLE randRangeWeighted(2, 5, 2, 0.4) randFromArray([[4, 6, 8, 10, 12], [6, 12], [8, 12], [10]][DENOM1 - 2]) DENOM2 / DENOM1 randRange(0, 1) ORDER ? DENOM1 : DENOM2 ORDER ? DENOM2 : DENOM1 randRange(1, M_DENOM - 1) randRange(1, I_DENOM - 1) WHOLE * I_DENOM + I_NUM2 (function() { var n1 = WHOLE2 + M_NUM / M_DENOM; var n2 = I_NUM / I_DENOM; if (n1 - n2 > 1e-9) { return [">", i18n._("is more than")]; } else if (abs(n1 - n2) < 1e-9) { return ["=", i18n._("is equal to")]; } else { return ["<", i18n._("is less than")]; } })()

Fill in the blank to compare the mixed number and the fraction.

WHOLE2\dfrac{M_NUM}{M_DENOM} ____\space \dfrac{I_NUM}{I_DENOM}

SOLUTION

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\dfrac{I_DENOM * WHOLE}{I_DENOM} = WHOLE

So \dfrac{I_NUM}{I_DENOM} is \dfrac{I_NUM2}{I_DENOM} more than WHOLE

WHOLE2\dfrac{M_NUM}{M_DENOM} is \dfrac{M_NUM}{M_DENOM} more than WHOLE2

Which is bigger, \dfrac{M_NUM}{M_DENOM} or \dfrac{I_NUM2}{I_DENOM} ?

\dfrac{M_NUM}{M_DENOM} is the same thing as \dfrac{M_NUM * F}{M_DENOM * F}

init({ range: [[-0.1, 1], [0, 2.5]], scale: [400, 50] }); rectchart([M_NUM * F, (M_DENOM - M_NUM) * F], ["#e00", "#999"], 1.5); rectchart([I_NUM2, I_DENOM - I_NUM2], ["#e00", "#999"], 0); label([0, 2], "\\dfrac{" + (M_NUM * F) + "}{" + (M_DENOM * F) + "}", "left"); label([0, 0.5], "\\dfrac{" + I_NUM2 + "}{" + I_DENOM + "}", "left");

\dfrac{I_NUM2}{I_DENOM} is the same thing as \dfrac{I_NUM2 * F}{I_DENOM * F}

init({ range: [[-0.1, 1], [0, 2.5]], scale: [400, 50] }); rectchart([M_NUM, M_DENOM - M_NUM], ["#e00", "#999"], 1.5); rectchart([I_NUM2 * F, (I_DENOM - I_NUM2) * F], ["#e00", "#999"], 0); label([0, 2], "\\dfrac{" + M_NUM + "}{" + M_DENOM + "}", "left"); label([0, 0.5], "\\dfrac{" + (I_NUM2 * F) + "}{" + (I_DENOM * F) + "}", "left");

\dfrac{M_NUM * F}{M_DENOM * F} COMPARISON \dfrac{I_NUM2}{I_DENOM}.

\dfrac{M_NUM}{M_DENOM} COMPARISON \dfrac{I_NUM2 * F}{I_DENOM * F}.

Therefore \dfrac{M_NUM}{M_DENOM} COMPARISON \dfrac{I_NUM2}{I_DENOM}.

Therefore WHOLE2\dfrac{M_NUM}{M_DENOM} SOLUTION \dfrac{I_NUM}{I_DENOM}

randRange(1, 5)

\dfrac{I_DENOM * WHOLE}{I_DENOM} = WHOLE

So \dfrac{I_NUM}{I_DENOM} is \dfrac{I_NUM2}{I_DENOM} more than WHOLE

WHOLE2\dfrac{M_NUM}{M_DENOM} is \dfrac{M_NUM}{M_DENOM} more than WHOLE2

Therefore WHOLE2\dfrac{M_NUM}{M_DENOM} SOLUTION \dfrac{I_NUM}{I_DENOM}