3 [2, 3, 4, 6, 8] _.map(randRangeUnique(0, 4, NUM_ITEMS), function(el) { return ALLOWED_DENOMINATORS[el]; }) min.apply(null, DENOMINATORS) randRange(1, MIN_DENOM) DENOMINATORS.slice(0).sort().reverse() NUMS_SORTED.join(",") $.map(NUMS_SORTED, function(el) { return "\\dfrac{" + NUMERATOR + "}{" + el + "}"; }).join(",") createSorter() [["blue", BLUE], ["green", GREEN], ["purple", PURPLE]]

Order the following fractions from least to greatest.

- D `\dfrac{NUMERATOR}{D}`

SORTER.init("sortable")

Drag the fractions left and right so they are in order from least to greatest
SORTER.getContent()
if (SORTER.hasAttempted) { return guess.join(",") === SORTED_LIST; } else { return ""; }
SORTER.setContent(guess);

Each fraction has a numerator of `NUMERATOR`. So, each whole will have `NUMERATOR` shaded piece.

Each fraction has a numerator of `NUMERATOR`. So, each whole will have `NUMERATOR` shaded pieces.

`\COLORS[i][0]{\dfrac{NUMERATOR}{denom}}` shows `NUMERATOR` out of a total of `\COLORS[i][0]{denom}` pieces shaded.

init({ range: [[-1, 1], [-1,1]], scale: [50,50] }); piechart([NUMERATOR, denom - NUMERATOR], [COLORS[i][1], "#bbb"], 1);

We can see that when the whole is divided into more pieces, each piece is smaller.

The fractions from least to greatest are:

`ANSWER`.

randFromArray([2, 3, 4, 6, 8]) randFromArrayExclude([2, 3, 4, 6, 8], [DENOMINATOR_1]) randRange(1, min(DENOMINATOR_1, DENOMINATOR_2)) DENOMINATOR_1 > DENOMINATOR_2 ? "<" : ">"

Compare.

`\dfrac{NUMERATOR}{DENOMINATOR_1}` ____ `\dfrac{NUMERATOR}{DENOMINATOR_2}`

`SOLUTION`

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

Each fraction has a numerator of `NUMERATOR`. So, each whole will have `NUMERATOR` shaded piece.

Each fraction has a numerator of `NUMERATOR`. So, each whole will have `NUMERATOR` shaded pieces.

`\green{\dfrac{NUMERATOR}{DENOMINATOR_1}}` means `NUMERATOR` out of a total of `DENOMINATOR_1` pieces shaded.

init({ range: [[-1, 1], [-1,1]], scale: [50,50] }); piechart([NUMERATOR, DENOMINATOR_1 - NUMERATOR], [GREEN, "#bbb"], 1);

`\dfrac{\purple{NUMERATOR}}{\purple{DENOMINATOR_2}}` means `NUMERATOR` out of a total of `DENOMINATOR_2` pieces shaded.

init({ range: [[-1, 1], [-1,1]], scale: [50,50] }); piechart([NUMERATOR, DENOMINATOR_2 - NUMERATOR], [PURPLE, "#bbb"], 1);

We can see that `\green{\dfrac{NUMERATOR}{DENOMINATOR_1}}` is divided into fewer pieces. So, each piece in `\green{\dfrac{NUMERATOR}{DENOMINATOR_1}}` is larger than each piece in `\purple{\dfrac{NUMERATOR}{DENOMINATOR_2}}`.

We can see that `\purple{\dfrac{NUMERATOR}{DENOMINATOR_2}}` is divided into fewer pieces. So, each piece in `\purple{\dfrac{NUMERATOR}{DENOMINATOR_2}}` is larger than each piece in `\green{\dfrac{NUMERATOR}{DENOMINATOR_1}}`.

`\green{\dfrac{NUMERATOR}{DENOMINATOR_1}} SOLUTION \purple{\dfrac{NUMERATOR}{DENOMINATOR_2}}`

randRange(1, 9) randFromArray([2, 3, 4, 6, 8]) randFromArrayExclude([2, 3, 4, 6, 8], [DENOMINATOR_1]) ceil(NUMERATOR / min(DENOMINATOR_1, DENOMINATOR_2)) DENOMINATOR_1 > DENOMINATOR_2 ? "<" : ">" randFromArray(["A", "B"])

Which number line correctly shows `\dfrac{NUMERATOR}{DENOMINATOR_1}` and `\dfrac{NUMERATOR}{DENOMINATOR_2}`?

init({ range: [[-0.15, 1.1], [0, 7]], scale: [400, 25] }); var tick = 0.25; var labels = [ 0, "\\dfrac{" + NUMERATOR + "}{" + DENOMINATOR_1 + "}", "\\dfrac{" + NUMERATOR + "}{" + DENOMINATOR_2 + "}" ]; var drawNumberLine = function(y, name, numbers) { // Seems this only adds an arrow to one end line([-0.05, y], [1.05, y], { arrows: "<->" }); line([1.05, y], [-0.05, y], { arrows: "<->" }); label([-0.1, y], name); for (var i = 0; i < numbers.length; i++) { var x = numbers[i] === 0 ? 0 : NUMERATOR / numbers[i] / MAX_NUM; line([x, y - tick], [x, y + tick]); label([x, y - 0.2], labels[i], "below"); } }; if (SOLUTION === "A") { drawNumberLine(6, "A", [0, DENOMINATOR_1, DENOMINATOR_2]); drawNumberLine(2, "B", [0, DENOMINATOR_2, DENOMINATOR_1]); } else { drawNumberLine(6, "A", [0, DENOMINATOR_2, DENOMINATOR_1]); drawNumberLine(2, "B", [0, DENOMINATOR_1, DENOMINATOR_2]); }
Number line `SOLUTION`

- Number line `A`
- Number line `B`

`\dfrac{NUMERATOR}{\blue{DENOMINATOR_1}}` means dividing each whole into `\blue{DENOMINATOR_1}` equal lengths, then measuring `NUMERATOR` of those lengths.

var yScale = 1 / 16; // Scaling so the arcs have reasonable proportions init({ range: [[-0.1, 1.1], [-2/8, 1.5 * yScale]], scale: [400, 25 / yScale] }); var y = 0; line([-0.05, y], [1.05, y], { arrows: "<->" }); line([1.05, y], [-0.05, y], { arrows: "<->" }); var tick = 0.25 * yScale; for (var i = 0; i <= MAX_NUM * DENOMINATOR_1; i++) { var x = i / DENOMINATOR_1 / MAX_NUM; if (i % DENOMINATOR_1 === 0) { label([x, y], roundTo(1, i / DENOMINATOR_1), "above"); line([x, y - tick], [x, y + tick], { strokeWidth: 3 }); } else { line([x, y - tick], [x, y + tick], { strokeWidth: 2 }); } } var r = 1 / DENOMINATOR_1 / MAX_NUM / 2; for (var i = 0; i < NUMERATOR; i++) { var x = (i + 0.5) * r * 2; if (i < NUMERATOR - 1) { arc([x, y], r, 180, 0, { stroke: BLUE }); } else { curvyArrow([x, y], r, "bottom", true, { stroke: BLUE }); } } // Fraction var x = NUMERATOR / DENOMINATOR_1 / MAX_NUM; label([x, y - 0.2 * yScale], "\\blue{\\dfrac{" + NUMERATOR + "}{" + DENOMINATOR_1 + "}}", "below");

`\dfrac{NUMERATOR}{\pink{DENOMINATOR_2}}` means dividing each whole into `\pink{DENOMINATOR_2}` equal lengths, then measuring `NUMERATOR` of those lengths.

var yScale = 1 / 16; // Scaling so the arcs have reasonable proportions init({ range: [[-0.1, 1.1], [-2/8, 1.5 * yScale]], scale: [400, 25 / yScale] }); var y = 0; line([-0.05, y], [1.05, y], { arrows: "<->" }); line([1.05, y], [-0.05, y], { arrows: "<->" }); var tick = 0.25 * yScale; for (var i = 0; i <= MAX_NUM * DENOMINATOR_2; i++) { var x = i / DENOMINATOR_2 / MAX_NUM; if (i % DENOMINATOR_2 === 0) { label([x, y], roundTo(1, i / DENOMINATOR_2), "above"); line([x, y - tick], [x, y + tick], { strokeWidth: 3 }); } else { line([x, y - tick], [x, y + tick], { strokeWidth: 2 }); } } var r = 1 / DENOMINATOR_2 / MAX_NUM / 2; for (var i = 0; i < NUMERATOR; i++) { var x = (i + 0.5) * r * 2; if (i < NUMERATOR - 1) { arc([x, y], r, 180, 0, { stroke: PINK }); } else { curvyArrow([x, y], r, "bottom", true, { stroke: PINK }); } } // Fraction var x = NUMERATOR / DENOMINATOR_2 / MAX_NUM; label([x, y - 0.5 * yScale], "\\pink{\\dfrac{" + NUMERATOR + "}{" + DENOMINATOR_2 + "}}", "below");

`\dfrac{NUMERATOR}{\blue{DENOMINATOR_1}}` means dividing `1` whole into `\blue{DENOMINATOR_1}` equal segments, then taking `NUMERATOR` copies of them.

var yScale = 1 / 16; // Scaling so the arcs have reasonable proportions init({ range: [[-0.1, 1.1], [-2/8, 1.5 * yScale]], scale: [400, 25 / yScale] }); var y = 0; line([-0.05, y], [1.05, y], { arrows: "<->" }); line([1.05, y], [-0.05, y], { arrows: "<->" }); var tick = 0.25 * yScale; var LCM = getLCM(DENOMINATOR_1, DENOMINATOR_2); for (var i = 0; i <= MAX_NUM * LCM; i++) { var x = i / LCM / MAX_NUM; if (i % LCM === 0) { label([x, y], roundTo(1, i / LCM), "above"); line([x, y - tick], [x, y + tick], { strokeWidth: 3 }); } else { line([x, y - tick], [x, y + tick], { strokeWidth: 2 }); } } // Fraction var x = NUMERATOR / DENOMINATOR_1 / MAX_NUM; label([x, y - 0.5 * yScale], "\\blue{\\dfrac{" + NUMERATOR + "}{" + DENOMINATOR_1 + "}}", "below"); line([x, y - tick], [x, y + tick], { strokeWidth: 3, stroke: BLUE }); var x = NUMERATOR / DENOMINATOR_2 / MAX_NUM; label([x, y - 0.5 * yScale], "\\pink{\\dfrac{" + NUMERATOR + "}{" + DENOMINATOR_2 + "}}", "below"); line([x, y - tick], [x, y + tick], { strokeWidth: 3, stroke: PINK });

Number line `SOLUTION` is correct.