<h2>Determining Whether a Fraction is a Solution of an Equation</h2>
<p>As we saw in <a data-page="11" href="https://app.ulearngo.com/tutorial/mathematics-102/">Mathematics 102</a> and <a data-page="19" href="https://app.ulearngo.com/tutorial/mathematics-103/">Mathematics 103</a>, a solution of an equation is a value that makes a true statement when substituted for the variable in the equation. In those sections, we found whole number and integer solutions to equations. Now that we have worked with fractions, we are ready to find fraction solutions to equations.</p>
<p>The steps we take to determine whether a number is a solution to an equation are the same whether the solution is a whole number, an integer, or a fraction.</p>
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<h3>Determining Whether a Fraction is a Solution of an Equation</h3>
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<li>Substitute the number for the variable in the equation.</li>
<li>Simplify the expressions on both sides of the equation.</li>
<li>Determine whether the resulting equation is true. If it is true, the number is a solution. If it is not true, the number is not a solution.</li>
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<h2>Example</h2>
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<p>Determine whether each of the following is a solution of \(x-\frac{3}{10}=\frac{1}{2}.\)</p>
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<li>\(x=1\)</li>
<li>\(x=\frac{4}{5}\)</li>
<li>\(x=-\frac{4}{5}\)</li>
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<h3>Solution</h3>
<table data-label="" summary="The first line says x minus 3 tenths equals one half. The next line says substitute 1 for x and shows 1 minus 3 tenths followed by an equal sign with a question mark and 1 half. The next line says, “Change to fractions with a LCD of 10,” and shows a red 10 tenths minus 3 tenths followed by an equal sign with a question mark and 5 tenths. The last step says to subtract and shows that 7 tenths does not equal 5 tenths. The last line says, “Since x equals 1 does not result in a true equation, 1 is not a solution to the equation.">
<tbody>
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<td> </td>
<td> </td>
</tr>
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<td> </td>
<td><img alt="." src="https://data.ulearngo.com/assets/b5e72c81-e400-4ed5-98a4-8f2d7e130057"/></td>
</tr>
<tr>
<td><img alt="." src="https://data.ulearngo.com/assets/95fd6b8a-a050-4e8a-9b2f-d4be93889864"/></td>
<td><img alt="." src="https://data.ulearngo.com/assets/8217384b-b6db-4289-a1ba-9807b333ea94"/></td>
</tr>
<tr>
<td>Change to fractions with a LCD of 10.</td>
<td><img alt="." src="https://data.ulearngo.com/assets/a9501de9-db9b-406e-9720-279ce79c52bd"/></td>
</tr>
<tr>
<td>Subtract.</td>
<td><img alt="." src="https://data.ulearngo.com/assets/98658d04-7c49-43fa-9b44-104de9280f1a"/></td>
</tr>
</tbody>
</table>
<p>Since \(x=1\) does not result in a true equation, \(1\) is not a solution to the equation.</p>
<table data-label="" summary="The first line says x minus 3 tenths equals 1 half. The next line says substitute 4 fifths for x and shows a red 4 fifths minus 3 tenths followed by an equal sign with a question mark and 1 half. The next line shows a red 8 tenths minus 3 tenths followed by an equal sign with a question mark and 5 tenths. The last step says to subtract and shows that 5 tenths equals 5 tenths followed by a check mark.">
<tbody>
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<td> </td>
<td> </td>
</tr>
<tr>
<td> </td>
<td><img alt="." src="https://data.ulearngo.com/assets/27c825f5-1d1d-4658-b640-66ad1afdbb53"/></td>
</tr>
<tr>
<td><img alt="." src="https://data.ulearngo.com/assets/2630ed2b-5ea9-4ab4-a44a-8dd32bb74ebc"/></td>
<td><img alt="." src="https://data.ulearngo.com/assets/db66d1d6-7375-40a8-bbbd-a890b60f780a"/></td>
</tr>
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<td> </td>
<td><img alt="." src="https://data.ulearngo.com/assets/1aacd672-f65b-4b41-88fd-0be9a29bc7ec"/></td>
</tr>
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<td>Subtract.</td>
<td><img alt="." src="https://data.ulearngo.com/assets/b93c0f39-179c-49cc-ac39-d0dadaee48db"/></td>
</tr>
</tbody>
</table>
<p>Since \(x=\frac{4}{5}\) results in a true equation, \(\frac{4}{5}\) is a solution to the equation \(x-\frac{3}{10}=\frac{1}{2}.\)</p>
<table data-label="" summary="The first line says x minus 3 tenths equals 1 half. The next line says substitute negative 4 fifths for x and shows a red negative 4 fifths minus 3 tenths followed by an equal sign with a question mark and 1 half. The next line says to simplify and shows a red negative 8 tenths minus 3 tenths followed by an equal sign with a question mark and 5 tenths. The last step says to subtract and shows that negative 11 tenths does not equal 5 tenths.">
<tbody>
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<td> </td>
<td> </td>
</tr>
<tr>
<td> </td>
<td><img alt="." src="https://data.ulearngo.com/assets/35035953-5412-4b4a-9dc0-7ae9bcfffa40"/></td>
</tr>
<tr>
<td><img alt="." src="https://data.ulearngo.com/assets/ea8ea466-a215-4934-a115-f0f47b13622f"/></td>
<td><img alt="." src="https://data.ulearngo.com/assets/1f4bc989-60e6-43bc-b998-6fa885a0ea0e"/></td>
</tr>
<tr>
<td> </td>
<td><img alt="." src="https://data.ulearngo.com/assets/3cc3bb64-4f04-444f-ad20-ffbcdd245a52"/></td>
</tr>
<tr>
<td>Subtract.</td>
<td><img alt="." src="https://data.ulearngo.com/assets/14239ba1-e6fd-44a8-8f4a-e1c25f0c59fc"/></td>
</tr>
</tbody>
</table>
<p>Since \(x=-\frac{4}{5}\) does not result in a true equation, \(-\frac{4}{5}\) is not a solution to the equation.</p>
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<h3>Optional Video: Solve One Step Equations With Fractions</h3>
<p><iframe allowfullscreen="allowfullscreen" frameborder="0" height="337" src="https://www.youtube.com/embed/COdQd39TTmU" width="599"></iframe></p>

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Determining Whether a Fraction is a Solution of an Equation

Mathematics studies measurement, relationships, and properties of quantities and sets, using numbers and symbols. Arithmetic, algebra, geometry, and calculus are popular topics in mathematics.

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Discover how to model fractions, simplify them, find equivalent fractions, and perform operations such as addition, subtraction, multiplication, and division with both fractions and mixed numbers, as well as solving equations that involve fractions.


Determining Whether a Fraction is a Solution of an Equation

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