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<!DOCTYPE html>
<html data-require="math">
<meta http-equiv="Content-Type" content="text/html; charset=UTF-8">
<title>Properties of numbers 2</title>
<script src="../khan-exercise.js"></script>
<div class="exercise">
<div class="vars">
<var id="NUM">randRange( 1000, 9999 )</var>
<div class="problems">
<div id="multiplication-identity">
<p class="question"><code><var>NUM</var> \times 1 =</code></p>
<p class="solution"><var>NUM</var></p>
<div class="hints">
<p>Any real number multiplied by <code>1</code> equals itself.</p>
<p>Without performing any multiplication steps, we know that <code><var>NUM</var> \times 1 = <var>NUM</var></code>.</p>
<p>This fact about multiplying by <code>1</code> is known as the identity property of multiplication, and it is useful for finding equivalent fractions.</p>
<div id="addition-identity">
<p class="question"><code><var>NUM</var> + 0 =</code></p>
<p class="solution"><var>NUM</var></p>
<div class="hints">
<p>Any real number plus <code>0</code> equals itself.</p>
<p>Without performing any addition steps, we know that <code><var>NUM</var> + 0 = <var>NUM</var></code>.</p>
<p>This fact about adding by <code>0</code> is known as the identity property of addition.</p>
<div id="multiplicative-inverse">
<p class="question">By what number can we multiply <code><var>NUM</var></code> to get <code>1</code>?</p>
<p class="solution" data-forms="proper"><var>1 / NUM</var></p>
<div class="hints">
<p>Any real number <code>x</code> (except <code>0</code>) can be multipled by <code>\dfrac{1}{x}</code> to get <code>1</code>.</p>
<p>Without performing any multiplication or division, we know that <code><var>NUM</var> \times \dfrac{1}{<var>NUM</var>} = 1</code>.</p>
<p>Thus, the answer is <code>\dfrac{1}{<var>NUM</var>}</code>.</p>
<p>This fact about multiplying by <code>\dfrac{1}{x}</code> is known as the multiplicative inverse property.
<div id="additive-inverse">
<p class="question">What number can we add to <code><var>NUM</var></code> to get <code>0</code>?</p>
<p class="solution" data-forms="integer"><var>-1 * NUM</var></p>
<div class="hints">
<p>Adding the negative inverse of a number to that number equals <code>0</code>.</p>
<p>Without performing any addition or subtraction, we know that <code><var>NUM</var> +(<var>-1 * NUM</var>) = 0</code>.</p>
<p>Thus, the answer is <code><var>-1 * NUM</var></code>.</p>
<p>This fact about adding negative inverses is known as the additive inverse property.</p>
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