THANK YOU FOR SUPPORTING US BUT I NEED MORE EXPLAINTION OF PROPER FRACTION AND IMPROPER FRACTION THHANK YOU SO MUCH

<h2>Modeling Improper Fractions and Mixed Numbers</h2>
<p>In an example in the previous lesson, you were given eight equal fifth pieces. You used five of them to make one whole, and you had three fifths left over. Let us use fraction notation to show what happened. You had eight pieces, each of them one fifth, \(\frac{1}{5},\) so altogether you had eight fifths, which we can write as \(\frac{8}{5}.\) The fraction \(\frac{8}{5}\) is one whole, \(1,\) plus three fifths, \(\frac{3}{5},\) or \(1\frac{3}{5},\) which is read as <em>one and three-fifths</em>.</p>
<p>The number \(1\frac{3}{5}\) is called a mixed number. A mixed number consists of a whole number and a fraction.</p>
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<h3>Mixed Numbers</h3>
<p>A <strong>mixed number</strong> consists of a whole number \(a\) and a fraction \(\frac{b}{c}\) where \(c\ne 0.\) It is written as follows.</p>
<p>\(a\frac{b}{c}\phantom{\rule{2em}{0ex}}c\ne 0\)</p>
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<p>Fractions such as \(\frac{5}{4},\frac{3}{2},\frac{5}{5},\) and \(\frac{7}{3}\) are called improper fractions. In an improper fraction, the <strong>numerator</strong> is greater than or equal to the <strong>denominator</strong>, so its value is greater than or equal to one. When a fraction has a numerator that is smaller than the denominator, it is called a proper fraction, and its value is less than one. Fractions such as \(\frac{1}{2},\frac{3}{7},\) and \(\frac{11}{18}\) are proper fractions.</p>
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<h3>Proper and Improper Fractions</h3>
<p>The fraction \(\frac{a}{b}\) is a <strong>proper fraction</strong> if \(a&lt;b\) and an <strong>improper fraction</strong> if \(a\ge b.\)</p>
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<h2>Example</h2>
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<p>Name the improper fraction modeled. Then write the improper fraction as a mixed number.</p>
<img alt="Two circles are shown, both divided into three equal pieces. The circle on the left has all three pieces shaded. The circle on the right has one piece shaded." src="https://data.ulearngo.com/assets/da065ec4-572a-4c1b-a207-966c25ce5ea5"/></div>
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<h3>Solution</h3>
<p>Each circle is divided into three pieces, so each piece is \(\frac{1}{3}\) of the circle. There are four pieces shaded, so there are four thirds or \(\frac{4}{3}.\) The figure shows that we also have one whole circle and one third, which is \(1\frac{1}{3}.\) So, \(\frac{4}{3}=1\frac{1}{3}.\)</p>
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<h2>Example</h2>
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<p>Draw a figure to model \(\frac{11}{8}.\)</p>
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<h3>Solution</h3>
<p>The denominator of the improper fraction is \(8.\) Draw a circle divided into eight pieces and shade all of them. This takes care of eight eighths, but we have \(11\) eighths. We must shade three of the eight parts of another circle.</p>
<img alt="Two circles are shown, both divided into eight equal pieces. The circle on the left has all eight pieces shaded and is labeled as eight eighths. The circle on the right has three pieces shaded and is labeled as three eighths. The diagram indicates that eight eighths plus three eighths is one plus three eighths." src="https://data.ulearngo.com/assets/6225c205-4129-4e4a-a21a-08f9294479be"/>
<p>So, \(\frac{11}{8}=1\frac{3}{8}.\)</p>
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<h2>Example</h2>
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<p>Use a model to rewrite the improper fraction \(\frac{11}{6}\) as a mixed number. </p>
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<h3>Solution</h3>
<p>We start with \(11\) sixths \(\left(\frac{11}{6}\right).\) We know that six sixths makes one whole.</p>
<div data-label="">\(\frac{6}{6}=1\)</div>
<p>That leaves us with five more sixths, which is</p>

\(\frac{5}{6}\phantom{\rule{0.2em}{0ex}}\left(11\phantom{\rule{0.2em}{0ex}}\text{sixths minus}\phantom{\rule{0.2em}{0ex}}6\phantom{\rule{0.2em}{0ex}}\text{sixths is}\phantom{\rule{0.2em}{0ex}}5\phantom{\rule{0.2em}{0ex}}\text{sixths}\right).\)

<p>So, \(\frac{11}{6}=1\frac{5}{6}.\)</p>
<img alt="Two circles are shown, both divided into six equal pieces. The circle on the left has all six pieces shaded and is labeled as six sixths. The circle on the right has five pieces shaded and is labeled as five sixths. Below the circles, it says one plus five sixths, then six sixths plus five sixths equals eleven sixths, and one plus five sixths equals one and five sixths. It then says that eleven sixths equals one and five sixths." src="https://data.ulearngo.com/assets/4d1a18bc-69cb-49f8-a825-bae735967af8"/></div>
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<h2>Example</h2>
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<p>Use a model to rewrite the mixed number \(1\frac{4}{5}\) as an improper fraction.</p>
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<h3>Solution</h3>
<p>The mixed number \(1\frac{4}{5}\) means one whole plus four fifths. The denominator is \(5,\) so the whole is \(\frac{5}{5}.\) Together five fifths and four fifths equals nine fifths.</p>
<p>So, \(1\frac{4}{5}=\frac{9}{5}.\)</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 5 fifths. The circle on the right has four pieces shaded and is labeled as 4 fifths. It then says that 5 fifths plus 4 fifths equals 9 fifths and that 9 fifths is equal to one plus 4 fifths." src="https://data.ulearngo.com/assets/3ff886ae-e882-40c4-9de7-38e037e6768a"/></div>
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<h3>Optional Video: Identify Fractions Using Pattern Blocks</h3>
<p><iframe allowfullscreen="allowfullscreen" frameborder="0" height="386" src="https://www.youtube.com/embed/VCqk_Vzy6ug?rel=0&amp;modestbranding=1&amp;cc_lang_pref=en&amp;cc_load_policy=1" width="686"><span class="mce_SELRES_start" data-mce-type="bookmark" style="display: inline-block; width: 0px; overflow: hidden; line-height: 0;">﻿</span></iframe></p>

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Modeling Improper Fractions and Mixed Numbers

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.


Modeling Improper Fractions and Mixed Numbers

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