This repository has been archived by the owner on May 11, 2021. It is now read-only.
/
equivalent_fractions_2.html
367 lines (309 loc) · 16.8 KB
/
equivalent_fractions_2.html
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
<!DOCTYPE html>
<html data-require="math graphie graphie-helpers word-problems math-format">
<head>
<meta http-equiv="Content-Type" content="text/html; charset=UTF-8">
<title>Equivalent fractions 2</title>
<script data-main="../local-only/main.js" src="../local-only/require.js"></script>
</head>
<body>
<div class="exercise">
<div class="vars">
<var id="A">randRange(1, 10)</var>
<var id="Bf">randRange(2, 9)</var>
<var id="B">Bf + (Bf >= A ? 1 : 0)</var>
<var id="M">randRange(3, 9)</var>
<var id="C">A * M</var>
<var id="D">B * M</var>
<var id="N">ceil(A / B)</var>
<var id="SYMBOL">randVar()</var>
<var id="FILLED">1</var>
</div>
<div class="problems">
<div>
<p class="question">What number could replace <code><var>SYMBOL</var></code> below?</p>
<p><code>\dfrac{<var>A</var>}{<var>B</var>} = \dfrac{<var>C</var>}{<var>SYMBOL</var>}</code></p>
<div class="solution" data-forms="integer"><var>D</var></div>
<div class="hints">
<div>
<p>
The fraction on the left represents dividing some rectangular <var>pizza(1).plural(2)</var> into <var>B</var> slices,
then taking <var>A</var> slices.
</p>
<div class="graphie">
init({ range: [[0, 1], [0, N * 1.25]], scale: [475, 25] });
FILLED = A % B;
if (FILLED === 0) {
FILLED = B;
}
for (var i = 0; i < N; i++) {
if (i === 0) {
rectchart([FILLED, B - FILLED], [RED, GRAY], i * 1.25);
} else {
rectchart([B], [RED], i * 1.25);
}
}
</div>
</div>
<div>
<p>
How many slices would we need to cut each <var>pizza(1)</var> into so that <var>C</var>
slices would give us the same amount of <var>pizza(1)</var>?
</p>
<div class="graphie">
init({ range: [[0, 1], [0, N * 1.25]], scale: [475, 25] });
FILLED *= M;
for (var i = 0; i < N; i++) {
if (i === 0) {
rectchart([FILLED, D - FILLED], [RED, _BACKGROUND], i * 1.25);
} else {
rectchart([D], [RED], i * 1.25);
}
}
</div>
</div>
<div>
<p>
Each of the original <var>A</var> slices must be divided into <var>M</var>
slices to get <var>C</var> slices in total.
</p>
<div class="graphie">
init({ range: [[0, 1], [0, 1]], scale: [475, 25] });
rectchart([M, M * B - M], [RED, _BACKGROUND]);
</div>
</div>
<div>
<p>
If we divide all the original slices into <var>M</var> slices, then one
<var>pizza(1)</var> will have a total of <var>D</var> slices.
</p>
<div class="graphie">
init({ range: [[0, 1], [0, 1]], scale: [475, 25] });
rectchart([M, M * B - M], [RED, GRAY]);
</div>
</div>
<p><code>\dfrac{<var>A</var>}{<var>B</var>} = \dfrac{<var>C</var>}{<var>D</var>}</code> and so the answer is <code><var>D</var></code>.</p>
<div>
<p>Another way to get the answer is to multiply by <code>\dfrac{<var>M</var>}{<var>M</var>}</code>.</p>
<p><code>\dfrac{<var>M</var>}{<var>M</var>} = \dfrac{1}{1} = 1</code> so really we are multiplying by 1.</p>
</div>
<p>
The final equation is: <code>\dfrac{<var>A</var>}{<var>B</var>} \times \dfrac{<var>M</var>}{<var>M</var>} =
\dfrac{<var>C</var>}{<var>D</var>} </code> so our answer is <code><var>D</var></code>.
</p>
</div>
</div>
<div>
<p class="question">What number could replace <code><var>SYMBOL</var></code> below?</p>
<p><code>\dfrac{<var>A</var>}{<var>B</var>} = \dfrac{<var>SYMBOL</var>}{<var>D</var>}</code></p>
<div class="solution" data-forms="integer"><var>C</var></div>
<div class="hints">
<div>
<p>
The fraction on the left represents dividing some rectangular <var>pizza(1).plural(2)</var> into <var>B</var> slices,
then taking <var>A</var> slices.
</p>
<div class="graphie">
init({ range: [[0, 1], [0, N * 1.25]], scale: [475, 25] });
FILLED = A % B;
if (FILLED === 0) {
FILLED = B;
}
for (var i = 0; i < N; i++) {
if (i === 0) {
rectchart([FILLED, B - FILLED], [RED, GRAY], i * 1.25);
} else {
rectchart([B], [RED], i * 1.25);
}
}
</div>
</div>
<div>
<p>What if we cut each <var>pizza(1)</var> into <var>D</var> slices instead?</p>
<div class="graphie">
init({ range: [[0, 1], [0, N * 1.25]], scale: [475, 25] });
FILLED *= M;
for (var i = 0; i < N; i++) {
if (i === 0) {
rectchart([FILLED, D - FILLED], [RED, GRAY], i * 1.25);
} else {
rectchart([D], [RED], i * 1.25);
}
}
</div>
</div>
<div>
<p>
In order to take the same amount of <var>pizza(1)</var> as before,
we now need to take <var>C</var> slices.
</p>
<div class="graphie">
init({ range: [[0, 1], [0, N * 1.25]], scale: [475, 25] });
for (var i = 0; i < N; i++) {
if (i === 0) {
rectchart([FILLED, D - FILLED], [RED, _BACKGROUND], i * 1.25);
} else {
rectchart([D], [RED], i * 1.25);
}
}
</div>
</div>
<p><code>\dfrac{<var>A</var>}{<var>B</var>} = \dfrac{<var>C</var>}{<var>D</var>}</code> and so the answer is <code><var>C</var></code>.</p>
<div>
<p>Another way to get the answer is to multiply by <code>\dfrac{<var>M</var>}{<var>M</var>}</code>.</p>
<p><code>\dfrac{<var>M</var>}{<var>M</var>} = \dfrac{1}{1} = 1</code> so really we are multiplying by 1.</p>
</div>
<p>
The final equation is: <code>\dfrac{<var>A</var>}{<var>B</var>} \times \dfrac{<var>M</var>}{<var>M</var>} =
\dfrac{<var>C</var>}{<var>D</var>} </code> so our answer is <code><var>C</var></code>.
</p>
</div>
</div>
<div>
<p class="question">What number could replace <code><var>SYMBOL</var></code> below?</p>
<p><code>\dfrac{<var>C</var>}{<var>D</var>} = \dfrac{<var>A</var>}{<var>SYMBOL</var>}</code></p>
<div class="solution" data-forms="integer"><var>B</var></div>
<div class="hints">
<div>
<p>
The fraction on the left represents dividing some rectangular <var>pizza(1).plural(2)</var> into <var>D</var> slices,
then taking <var>C</var> slices.
</p>
<div class="graphie">
init({ range: [[0, 1], [0, N * 1.25]], scale: [475, 25] });
FILLED = C % D;
if (FILLED === 0) {
FILLED = D;
}
for (var i = 0; i < N; i++) {
if (i === 0) {
rectchart([FILLED, D - FILLED], [RED, GRAY], i * 1.25);
} else {
rectchart([D], [RED], i * 1.25);
}
}
</div>
</div>
<div>
<p data-if="isSingular(A)">
If we share those <var>C</var> slices equally between <var>A</var> person,
how many slices does each person get?
</p><p data-else="">
If we share those <var>C</var> slices equally between <var>A</var> people,
how many slices does each person get?
</p>
<div class="graphie">
init({ range: [[0, 1], [0, N * 1.25]], scale: [475, 25] });
FILLED /= M;
for (var i = 0; i < N; i++) {
if (i === 0) {
rectchart([FILLED, B - FILLED], [RED, _BACKGROUND], i * 1.25);
} else {
rectchart([B], [RED], i * 1.25);
}
}
</div>
</div>
<div>
<p data-if="isSingular(A)">
Sharing <var>C</var> slices equally between <var>A</var> person means each person gets <var>M</var> slices.
</p><p data-else="">
Sharing <var>C</var> slices equally between <var>A</var> people means each person gets <var>M</var> slices.
</p>
<div class="graphie">
init({ range: [[0, 1], [0, 1]], scale: [475, 25] });
rectchart([M, D - M], [RED, _BACKGROUND]);
</div>
<p>If we give each person <var>M</var> slices, how many people can we feed with one <var>pizza(1)</var>?</p>
</div>
<div>
<div class="graphie">
init({ range: [[0, 1], [0, 1]], scale: [475, 25] });
var filled = A % B;
rectchart([FILLED, B - FILLED], [RED, GRAY]);
</div>
<p>
One <var>pizza(1)</var> has <var>D</var> slices, so if we give each person
<var>M</var> slices, we could feed <var>B</var> people.
</p>
</div>
<p><code>\dfrac{<var>C</var>}{<var>D</var>} = \dfrac{<var>A</var>}{<var>B</var>}</code> and so the answer is <code><var>B</var></code>.</p>
<div>
<p>Another way to get the answer is to divide by <code>\dfrac{<var>M</var>}{<var>M</var>}</code>.</p>
<p><code>\dfrac{<var>M</var>}{<var>M</var>} = \dfrac{1}{1} = 1</code> so really we are dividing by 1.</p>
</div>
<p>
The final equation is: <code>\dfrac{<var>C</var>}{<var>D</var>} \div \dfrac{<var>M</var>}{<var>M</var>} =
\dfrac{<var>A</var>}{<var>B</var>}</code> so our answer is <code><var>B</var></code>.
</p>
</div>
</div>
<div>
<p class="question">What number could replace <code><var>SYMBOL</var></code> below?</p>
<p><code>\dfrac{<var>C</var>}{<var>D</var>} = \dfrac{<var>SYMBOL</var>}{<var>B</var>}</code></p>
<div class="solution" data-forms="integer"><var>A</var></div>
<div class="hints">
<div>
<p>
The fraction on the left represents dividing some rectangular <var>pizza(1).plural(2)</var> into <var>D</var> slices,
then taking <var>C</var> slices.
</p>
<div class="graphie">
init({ range: [[0, 1], [0, N * 1.25]], scale: [475, 25] });
FILLED = C % D;
if (FILLED === 0) {
FILLED = D;
}
for (var i = 0; i < N; i++) {
if (i === 0) {
rectchart([FILLED, D - FILLED], [RED, GRAY], i * 1.25);
} else {
rectchart([D], [RED], i * 1.25);
}
}
</div>
</div>
<div>
<p>What if we cut each <var>pizza(1)</var> into <var>B</var> slices instead?</p>
<div class="graphie">
init({ range: [[0, 1], [0, N * 1.25]], scale: [475, 25] });
FILLED /= M;
for (var i = 0; i < N; i++) {
if (i === 0) {
rectchart([FILLED, B - FILLED], [RED, GRAY], i * 1.25);
} else {
rectchart([B], [RED], i * 1.25);
}
}
</div>
</div>
<div>
<p>
In order to take the same amount of <var>pizza(1)</var> as before,
we now need to take only <var>A</var> slices.
</p>
<div class="graphie">
init({ range: [[0, 1], [0, N * 1.25]], scale: [475, 25] });
for (var i = 0; i < N; i++) {
if (i === 0) {
rectchart([FILLED, B - FILLED], [RED, _BACKGROUND], i * 1.25);
} else {
rectchart([B], [RED], i * 1.25);
}
}
</div>
</div>
<p><code>\dfrac{<var>C</var>}{<var>D</var>} = \dfrac{<var>A</var>}{<var>B</var>}</code> and so the answer is <code><var>A</var></code>.</p>
<div>
<p>Another way to get the answer is to divide by <code>\dfrac{<var>M</var>}{<var>M</var>}</code>.</p>
<p><code>\dfrac{<var>M</var>}{<var>M</var>} = \dfrac{1}{1} = 1</code> so really we are dividing by 1.</p>
</div>
<p>
The final equation is: <code>\dfrac{<var>C</var>}{<var>D</var>} \div \dfrac{<var>M</var>}{<var>M</var>} =
\dfrac{<var>A</var>}{<var>B</var>}</code> so our answer is <code><var>A</var></code>.
</p>
</div>
</div>
</div>
</div>
</body>
</html>