Common fractions - Adding fractions with the same denominator - Lesson 3
mathematics·@apteacher·
0.000 HBDCommon fractions - Adding fractions with the same denominator - Lesson 3
<html> <h1>Addition of fractions:</h1> <p><img src="https://imgoat.com/uploads/613985ec49/89963.png" width="680" height="380"/></p> <p><a href="https://imgoat.com/uploads/613985ec49/89963.png">Source</a></p> <p>Knowing how to get the LCM of the denominator is very important when adding fractions.</p> <p>In this lesson we are going to look at fractions with the same denominator.</p> <p>Tomorrow we will add fractions with different denominators.</p> <p><br></p> <h3>Prior knowledge learners should have:</h3> <ul> <li>Converting from an improper fraction to a mixed fraction.</li> </ul> <blockquote>An improper fraction is a fraction in which the numerator (top number) is greater than or equal to the denominator (bottom number). </blockquote> <p><a href="https://www.google.co.za/url?sa=t&rct=j&q=&esrc=s&source=web&cd=3&cad=rja&uact=8&ved=0ahUKEwien9-xu83ZAhWBJcAKHe9YCIoQFgguMAI&url=https%3A%2F%2Fwww.varsitytutors.com%2Fhotmath%2Fhotmath_help%2Ftopics%2Fimproper-fractions&usg=AOvVaw0oW6xQCDAcZcxyoLez71Ti">Source</a></p> <p>Given the fraction:</p> <p><img src="https://imgoat.com/uploads/613985ec49/89941.png" width="378" height="184"/></p> <h3>The circled numbers are the steps to follow:</h3> <ol> <li>Divide the denominator into the numerator ( 4 can go into 10 two times)</li> <li>Write the answer as 2 wholes</li> <li>Multiply the whole with the denominator</li> <li>Subtract this answer from the numerator (What is left after 4 goes into 10 two times)</li> <li>Write the answer as a fraction. (Remember that we are busy with quarters, so the denominator stays 4)</li> <li>Simplify your answer if necessary. (Whatever you do at the top, you must do at the bottom too)</li> </ol> <h3>Converting from a mixed fraction to an improper fraction.</h3> <blockquote>A mixed fraction is a whole number and a fraction combined into one "mixed" number. Example: 1½ (one and a half) is a mixed fraction. (Also called a Mixed Number) .</blockquote> <p><a href="https://www.google.co.za/url?sa=t&rct=j&q=&esrc=s&source=web&cd=3&cad=rja&uact=8&ved=0ahUKEwiipfu7ls7ZAhVsCMAKHWT9Db0QFgguMAI&url=https%3A%2F%2Fwww.mathsisfun.com%2Fdefinitions%2Fmixed-fraction.html&usg=AOvVaw2IwePdexyLGefNg4A9-b_Q">Source</a></p> <p><img src="https://imgoat.com/uploads/613985ec49/89943.png" width="258" height="164"/></p> <p>The easier conversion of the two.</p> <h3>Follow the following steps:</h3> <ol> <li>Multiply the whole with the denominator (3x6 =18)</li> <li>Add the numerator to the previous answer (18 + 2 = 20)</li> <li>Write the answer over the denominator given. (The fraction started over 6, so it stays a denominator of 6)</li> </ol> <p><br></p> <h1>Adding fractions with the same denominator:</h1> <p>When adding fractions, always make sure that your denominators are the same:</p> <p>In the examples below, the denominators are the same, so learners may add the fractions together.</p> <p>1. <img src="https://imgoat.com/uploads/613985ec49/89950.png" width="296" height="109"/></p> <ul> <li>Only numerators are added together.</li> <li>NEVER add the denominators, as you are busy with thirds.</li> <li>Explain this by asking your learners, if you have half of a pizza and you add another half you get 1 whole and not a quarter.</li> </ul> <p><img src="https://imgoat.com/uploads/613985ec49/89954.png" width="692" height="331"/></p> <p><a href="https://imgoat.com/uploads/613985ec49/89954.png">Source</a></p> <p>2. <img src="https://imgoat.com/uploads/613985ec49/89955.png" width="511" height="376"/></p> <p>Looking at the two examples above:</p> <p>The example on the left takes longer but gets to the same answer. </p> <ol> <li>First we convert the mixed fraction into an improper fraction.</li> <li>Add the two fractions together (Remember the denominators stay the same)</li> <li>Calculating the answer, you will see that now, you have an improper fraction.</li> <li>Convert this improper fraction to a mixed fraction again and simplify if possible.</li> </ol> <p><br></p> <p>The example on the right is quite shorter and also gets the same answer.</p> <ol> <li>Add the two wholes together as well as the fractions.</li> <li>Simplify your answer.</li> </ol> <p><br></p> <p><img src="https://imgoat.com/uploads/613985ec49/89958.png" width="236" height="280"/></p> <h1>Conclusion:</h1> <ul> <li>When the denominators of the fractions are the same, fractions may be added together.</li> <li>Remind your learners not to add the denominators, as the denominator is the part of the fraction you are working with .</li> <li>Only numerators are added together.</li> <li>Simplify your answer if possible.</li> </ul> <p><br></p> <p><img src="https://imgoat.com/uploads/613985ec49/89964.gif" width="562" height="141"/></p> </html>
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