mirror of
https://github.com/HananoshikaYomaru/openfreebooks.git
synced 2026-11-13 21:15:54 +00:00
47 lines
1.6 KiB
HTML
47 lines
1.6 KiB
HTML
<div class="book-prose">
|
|
<p>
|
|
Ratios compare quantities. Rates compare quantities with different units. Both are essential
|
|
for scale, speed, and pricing.
|
|
</p>
|
|
|
|
<h2 id="ratio-meaning" class="book-prose__heading">Part-to-part and part-to-whole ratios</h2>
|
|
<p>
|
|
A ratio \(2:3\) means two equal parts compared with three equal parts. Total parts are \(2+3=5\).
|
|
</p>
|
|
<p>
|
|
If a class has 12 boys and 18 girls, boys:girls is \(12:18=2:3\), and boys:total is \(12:30=2:5\).
|
|
</p>
|
|
|
|
<h2 id="equivalent" class="book-prose__heading">Equivalent ratios</h2>
|
|
<p>
|
|
Multiply or divide both parts by the same nonzero number.
|
|
</p>
|
|
<p class="book-formula">
|
|
\(3:5 = 6:10 = 12:20\)
|
|
</p>
|
|
|
|
<h2 id="unit-rate" class="book-prose__heading">Unit rates</h2>
|
|
<p>
|
|
A unit rate is “per one.” If 180 km takes 3 hours, speed is \(180\div3=60\) km/h.
|
|
</p>
|
|
|
|
<h2 id="proportion-graph" class="book-prose__heading">Proportional relationships</h2>
|
|
<p>
|
|
For proportional relationships, \(y=kx\). Graphs are straight lines through the origin where
|
|
slope is the constant of proportionality \(k\).
|
|
</p>
|
|
|
|
<details class="book-question">
|
|
<summary class="book-question__prompt">Checkpoint: share 56 in ratio \(3:4\)</summary>
|
|
<div class="book-question__solution">
|
|
<p>Total parts \(=7\), one part \(=8\), shares are 24 and 32.</p>
|
|
</div>
|
|
</details>
|
|
|
|
<details class="book-question">
|
|
<summary class="book-question__prompt">Checkpoint: 45 dollars for 6 kg, find unit price</summary>
|
|
<div class="book-question__solution">
|
|
<p>\(45\div6=7.5\). Unit price is 7.5 dollars per kg.</p>
|
|
</div>
|
|
</details>
|
|
</div>
|