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 [">", $._("is more than")]; } else if (abs(n1 - n2) < 1e-9) { return ["=", $._("is equal to")]; } else { return ["<", $._("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`

- `<`
- `>`
- `=`

`\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}`