Thanks for the explanation I guess I understood right 

<h2>Understanding the Meaning of Fractions</h2>
<p>Andy and Bobby love pizza. On Monday night, they share a pizza equally. How much of the pizza does each one get? Are you thinking that each boy gets half of the pizza? That’s right. There is one whole pizza, evenly divided into two parts, so each boy gets one of the two equal parts.</p>
<p>In math, we write \(\frac{1}{2}\) to mean one out of two parts.</p>
<p><img alt="An image of a round pizza sliced vertically down the center, creating two equal pieces. Each piece is labeled as one half." src="https://data.ulearngo.com/assets/f44c40a7-4dd1-4c46-82fe-d2d857edb5ca"/></p>
<p>On Tuesday, Andy and Bobby share a pizza with their parents, Fred and Christy, with each person getting an equal amount of the whole pizza. How much of the pizza does each person get? There is one whole pizza, divided evenly into four equal parts. Each person has one of the four equal parts, so each has \(\frac{1}{4}\) of the pizza.</p>
<p><img alt="An image of a round pizza sliced vertically and horizontally, creating four equal pieces. Each piece is labeled as one fourth." src="https://data.ulearngo.com/assets/d03b1f02-df5a-4b93-ad46-04a88583d5ef"/></p>
<p>On Wednesday, the family invites some friends over for a pizza dinner. There are a total of \(12\) people. If they share the pizza equally, each person would get \(\frac{1}{12}\) of the pizza.</p>
<p><img alt="An image of a round pizza sliced into twelve equal wedges. Each piece is labeled as one twelfth." src="https://data.ulearngo.com/assets/1e925ab5-d679-4e2e-bd78-536377535266"/></p>
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<h3>Fractions</h3>
<p>A fraction is written \(\frac{a}{b},\) where \(a\) and \(b\) are integers and \(b\ne 0.\) In a fraction, \(a\) is called the numerator and \(b\) is called the denominator.</p>
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<p>A fraction is a way to represent parts of a whole. The denominator \(b\) represents the number of equal parts the whole has been divided into, and the numerator \(a\) represents how many parts are included. The denominator, \(b,\) cannot equal zero because division by zero is undefined.</p>
<p>In the figure below, the circle has been divided into three parts of equal size. Each part represents \(\frac{1}{3}\) of the circle. This type of model is called a fraction circle. Other shapes, such as rectangles, can also be used to model fractions.</p>
<p><img alt="A circle is divided into three equal wedges. Each piece is labeled as one third." src="https://data.ulearngo.com/assets/581c57b8-2b21-4ade-aabe-f8724cf3f70f"/></p>
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<p>What does the fraction \(\frac{2}{3}\) represent? The fraction \(\frac{2}{3}\) means two of three equal parts.</p>
<img alt="A circle is divided into three equal wedges. Two of the wedges are shaded." src="https://data.ulearngo.com/assets/2fb37045-991d-4868-975a-6ddbfcdde9c4"/>
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<h2>Example</h2>
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<p>Name the <strong>fraction</strong> of the shape that is shaded in each of the figures.</p>
<img alt="In part “a”, a circle is divided into eight equal wedges. Five of the wedges are shaded. In part “b”, a square is divided into nine equal pieces. Two of the pieces are shaded." src="https://data.ulearngo.com/assets/9713994f-72f8-46fd-8ac2-84f2bcad1106"/></div>
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<h3>Solution</h3>
<p>We need to ask two questions. First, how many equal parts are there? This will be the <strong>denominator</strong>. Second, of these equal parts, how many are shaded? This will be the <strong>numerator</strong>.</p>
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\(\begin{array}{cccc}\text{How many equal parts are there?}\hfill &amp; &amp; &amp; \text{There are eight equal parts}\text{.}\hfill \\ \text{How many are shaded?}\hfill &amp; &amp; &amp; \text{Five parts are shaded}\text{.}\hfill \end{array}\)

<p>Five out of eight parts are shaded. Therefore, the fraction of the circle that is shaded is \(\frac{5}{8}.\)</p>
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\(\begin{array}{cccc}\text{How many equal parts are there?}\hfill &amp; &amp; &amp; \text{There are nine equal parts}\text{.}\hfill \\ \text{How many are shaded?}\hfill &amp; &amp; &amp; \text{Two parts are shaded}\text{.}\hfill \end{array}\)

<p>Two out of nine parts are shaded. Therefore, the fraction of the square that is shaded is \(\frac{2}{9}.\)</p>
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<h2>Example</h2>
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<p>Shade \(\frac{3}{4}\) of the circle.</p>
<img alt="An image of a circle." src="https://data.ulearngo.com/assets/7091f708-4c45-4658-bdc7-4c8cf178948c"/></div>
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<h3>Solution</h3>
<p>The denominator is \(4,\) so we divide the circle into four equal parts .</p>
<p>The numerator is \(3,\) so we shade three of the four parts .</p>
<img alt="In “a”, a circle is shown divided into four equal pieces. An arrow points from “a” to “b”. In “b”, the same image is shown with three of the pieces shaded." src="https://data.ulearngo.com/assets/f8718691-30b2-475e-8ab9-706bb7fc7829"/>
<p>\(\frac{3}{4}\) of the circle is shaded.</p>
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<p>In the examples above, we used circles and rectangles to model fractions. Fractions can also be modeled as manipulatives called fraction tiles, as shown in the figure below. Here, the whole is modeled as one long, undivided rectangular tile. Beneath it are tiles of equal length divided into different numbers of equally sized parts.</p>
<p><img alt="One long, undivided rectangular tile is shown, labeled “1”. Below it is a rectangular tile of the same size and shape that has been divided vertically into two equal pieces, each labeled as one half. Below that is another rectangular tile that has been divided into three equal pieces, each labeled as one third. Below that is another rectangular tile that has been divided into four equal pieces, each labeled as one fourth. Below that is another rectangular tile that has been divided into six pieces, each labeled as one sixth." src="https://data.ulearngo.com/assets/7a91fb23-c220-4c3f-aff0-46b586db015f"/></p>
<p>We’ll be using <strong>fraction tiles</strong> to discover some basic facts about fractions. Get familiar with the figure above to answer the following questions:</p>
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<td>How many \(\frac{1}{2}\) tiles does it take to make one whole tile?</td>
<td>It takes two halves to make a whole, so two out of two is \(\frac{2}{2}=1.\)</td>
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<td>How many \(\frac{1}{3}\) tiles does it take to make one whole tile?</td>
<td>It takes three thirds, so three out of three is \(\frac{3}{3}=1.\)</td>
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<td>How many \(\frac{1}{4}\) tiles does it take to make one whole tile?</td>
<td>It takes four fourths, so four out of four is \(\frac{4}{4}=1.\)</td>
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<td>How many \(\frac{1}{6}\) tiles does it take to make one whole tile?</td>
<td>It takes six sixths, so six out of six is \(\frac{6}{6}=1.\)</td>
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<td>What if the whole were divided into \(24\) equal parts? (We have not shown fraction tiles to represent this, but try to visualize it in your mind.) How many \(\frac{1}{24}\) tiles does it take to make one whole tile?</td>
<td>It takes \(24\) twenty-fourths, so \(\frac{24}{24}=1.\)</td>
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<p>It takes \(24\) twenty-fourths, so \(\frac{24}{24}=1.\)</p>
<p>This leads us to the <em>Property of One</em>.</p>
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<h3>Property of One</h3>
<p>Any number, except zero, divided by itself is one.</p>
<p>\(\frac{a}{a}=1\phantom{\rule{4em}{0ex}}\left(a\ne 0\right)\)</p>
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<h2>Example</h2>
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<p>Use fraction circles to make wholes using the following pieces:</p>
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<li>\(4\) fourths</li>
<li>\(5\) fifths</li>
<li>\(6\) sixths</li>
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<h3>Solution</h3>
<img alt="Three circles are shown. The circle on the left is divided into four equal pieces. The circle in the middle is divided into five equal pieces. The circle on the right is divided into six equal pieces. Each circle says “Form 1 whole” beneath it." src="https://data.ulearngo.com/assets/034d06dd-98c2-4c26-9538-0ef354936494"/></div>
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<p>What if we have more fraction pieces than we need for \(1\) whole? We’ll look at this in the next example.</p>
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<h2>Example</h2>
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<p>Use fraction circles to make wholes using the following pieces:</p>
<ol type="1">
<li>\(3\) halves</li>
<li>\(8\) fifths</li>
<li>\(7\) thirds</li>
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<h3>Solution</h3>
<p>\(3\) halves make \(1\) whole with \(1\) half left over.</p>
<img alt="Two circles are shown, both divided into two equal pieces. The circle on the left has both pieces shaded and is labeled as “1”. The circle on the right has one piece shaded and is labeled as one half." src="https://data.ulearngo.com/assets/2cbf5770-c1da-4f6b-977f-aa9f4e8ceed3"/>
<p>\(8\) fifths make \(1\) whole with \(3\) fifths left over.</p>
<img alt="Two circles are shown, both divided into five equal pieces. The circle on the left has all five pieces shaded and is labeled as “1”. The circle on the right has three pieces shaded and is labeled as three fifths." src="https://data.ulearngo.com/assets/ca16e84f-be10-445a-9342-9bfac61e80d7"/>
<p>\(7\) thirds make \(2\) wholes with \(1\) third left over.</p>
<img alt="Three circles are shown, all divided into three equal pieces. The two circles on the left have all three pieces shaded and are labeled with ones. The circle on the right has one piece shaded and is labeled as one third." src="https://data.ulearngo.com/assets/92257036-1fa5-4010-9696-ccf3dd563f56"/></div>
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<h3>Optional Video: Introduction to Fractions</h3>
<p><iframe allowfullscreen="allowfullscreen" frameborder="0" height="386" src="https://www.youtube.com/embed/y5zfVtGflIk?rel=0&amp;modestbranding=1&amp;cc_lang_pref=en&amp;cc_load_policy=1" width="686"></iframe></p>

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Understanding the Meaning of Fractions

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

Mathematics

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.


Understanding the Meaning of Fractions

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