randFromArray([2, 3, 4, 6, 8]) randRange(1, DEN_1 * 2) ceil(NUM_1 / DEN_1) NUM_1 - (WHOLES - 1) * DEN_1 "\\blue{\\dfrac{1}{" + DEN_1 + "}}"

This circle represents one whole.

init({ range: [[0, 6], [-2.1, 2.1]], scale: 25 }); piechart([0, DEN_1], [BLUE, GRAY20], 2, false, 3, 0);

What fraction is shaded blue below?

init({ range: [[0, 6 * WHOLES], [-2.1, 2.1]], scale: 25 }); for (var i = 0; i < WHOLES; i++) { if (i === 0) { piechart([FINAL, DEN_1 - FINAL], [BLUE, GRAY20], 2, false, (i + 1) * 3, 0); } else { piechart([DEN_1, 0], [BLUE, GRAY20], 2, false, i * 6 + 3, 0); } }

NUM_1 / DEN_1

Each blue slice is FRACTION of the whole.

Only one slice is shaded blue.

\pink{NUM_1} slices are shaded blue, so we add FRACTION a total of \pink{NUM_1} times.

_.times(NUM_1, function() { return FRACTION; }).join(" + ") = ?

The fraction shaded blue is \dfrac{NUM_1}{DEN_1}.

This rectangle represents one whole.

init({ range: [[0, 1], [0, 1]], scale: [250, 25] }); rectchart([0, DEN_1], [BLUE, GRAY20], 0);

What fraction is shaded blue below?

init({ range: [[0, 1], [0, 2 * WHOLES - 1]], scale: [250, 25] }); for (var i = 0; i < WHOLES; i++) { if (i === 0) { rectchart([FINAL, DEN_1 - FINAL], [BLUE, GRAY20], i * 2); } else { rectchart([DEN_1, 0], [BLUE, GRAY20], i * 2); } }

NUM_1 / DEN_1

Each blue piece is FRACTION of the whole.

Only one piece is shaded blue.

\pink{NUM_1} piece are shaded blue, so we add FRACTION a total of \pink{NUM_1} times.

_.times(NUM_1, function() { return FRACTION; }).join(" + ") = ?

The fraction shaded blue is \dfrac{NUM_1}{DEN_1}.