exercises/changing_fractions_to_percents.html

<!DOCTYPE html>
<html data-require="math math-format graphie graphie-helpers">
<head>
	<title>Changing fractions to percents</title>
	<script src="../khan-exercise.js"></script>

	<script type="text/javascript">
	function decimalLength( n ) {
		return ( ( n + "" ).split( "." )[1] || "" ).length;
	}

	</script>
</head>

<body>
	<div class="exercise">
		<div class="problems">
			<div>
				<div class="vars">

					<div data-ensure="decimalLength( DEC ) <= 4">
						<var id="_D">randFromArray([ 4, 5, 8, 10, 16, 20, 25, 40, 50, 100 ])</var>
						<var id="_N">randRange( 1, _D - 1 )</var>
						<var id="DEC">_N / _D</var>
					</div>

					<var id="GCD">getGCD( _N, _D )</var>
					<var id="N">round( _N / GCD )</var>
					<var id="D">round( _D / GCD )</var>

				</div>

				<p class="question">Express <code><var>fraction( _N, _D )</var></code> as a percent.</p>

				<div class="solution" data-type="multiple">
					<span class="sol" data-type="decimal"><var>100 * DEC</var></span> %
				</div>

				<div class="hints">
					<div data-if="_D === 100" data-unwrap>
						<p>When the denominator is 100, you can simply take the numerator and apply the % sign:</p>
						<p><code><var>fraction( _N, _D )</var></code> = <var>100 * DEC</var>%</p>
					</div>
					<div data-else data-unwrap>
						<p data-if="GCD > 1"><code><var>fraction( _N, _D )</var></code> reduces to <code><var>fraction( N, D )</var></code>.</p>
						<p>To turn a fraction into a percent, turn the fraction into a decimal and then multiply the decimal by 100.</p>
						<p data-if="D === 10">Denominators of 10 are an easy case: The decimal form is just the numerator with the decimal place moved left by the number of 0s in the denominator - in this case 1 place.</p>
						<p data-else>To turn <code><var>fraction( N, D )</var></code> into a decimal, perform long division, dividing <code><var>D</var></code> into <code><var>N</var></code> (if you need help with this, try practicing some Division exercises or watching some related videos).</p>
						<p><code><var>N</var> \div <var>D</var> = <var>DEC</var></code></p>
						<p>To convert this decimal into a percent, we need to multiply it by 100.</p>
						<p><code><var>DEC</var> = (100 \cdot <var>DEC</var>) \% = <var>roundTo( 2, 100 * DEC )</var>\%</code></p>
					</div>
				</div>
			</div>
		</div>
	</div>
</body>
</html>