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Lesson 25 ADDING AND SUBTRACTING




"5 eighths + 2 eighths = 7 eighths." The denominator of a fraction has but one function, which is to name what we are counting. In this example, we are counting eighths.
Fractions with different denominators To add or subtract fractions, the denominators must be the same. Before continuing, then, the student should know how to convert one fraction 





We choose a common multiple of the denominators because we change a denominator by multiplying it. Lesson 22.
Solution. The lowest common multiple of 3 and 4 is their product, 12. (Lesson 22, Question 4.) We will convert each fraction to an equivalent fraction with denominator 12.
(is contained in) 12 four times. Four times 2 is 8." (In that way, we multiplied both 2 and 3 by the same number, namely 4. See Lesson 22, Question 3.)
times. Three times 1 is 3." (We multiplied both 1 and 4 by 3.) The fact that we say what we do shows again that arithmetic is a spoken skill. In practice, it is necessary to write the common denominator only once:
Solution. The LCM of 5 and 15 is 15. Therefore,
times. Three times 4 is 12."
denominator 15.
Solution. The LCM of 3, 6, and 12 is 12.
times. Four times 2 is 8."
times. Two times 1 is 2."
denominator 12.
dividing 17 by 12. (Lesson 20.) "12 goes into 17 one (1) time with remainder 5."
Solution. The LCM of 6 and 9 is 18.
Just as 1 is half of 2, so 2 is half of 4. Therefore,
The student should not have to write any problem in which one of
For example,
Example 8. In a recent exam, one eighth of the students got A, two fifths got B, and the rest got C. What fraction got C? Solution. Let 1 represent the whole number of students. Then the question is:
Now,


 
Therefore,
Solution. When the denominators are different, we may arrange the work vertically; although that is not necessary. To add the fractions, the denominators must be the same. The LCM
both terms by 2:
At this point, please "turn" the page and do some Problems. or Continue on to Section 2: Subtracting mixed numbers Introduction  Home  Table of Contents Copyright © 2021 Lawrence Spector Questions or comments? Email: [email protected] 