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In Unit 6, we delve into the addition of common fractions, emphasizing longhand methods over calculators for a solid understanding of fractions. This unit explains how fractions consist of two parts and outlines the importance of having a common denominator for addition. You'll learn how to identify common denominators, create equivalent fractions, and reduce fractions to their lowest terms. Example problems illustrate these concepts, aiding in grasping addition techniques and ensuring accuracy with fractions.
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Unit 6 Addition of Common Fractions
Fraction problems are best worked longhand. • Some fractions do have exact decimal equivalents and can be converted to numbers that can be worked with on the calculator. • Not all fractions have exact decimal equivalents, it is best to learn how to solve problems involving fractions without the use of the calculator.
Each fraction is made up of two numbers When adding fractions, arrange them either in vertical form as whole numbers or in linear form. Fractions cannot be added unless they have the same denominator. If the fractions have the same denominators, add the numerators and put the sum over the denominator. Example 2: Example 1:
If the fractions have different denominators, equivalent fractions with a common denominator must be created. To find the common denominator, take the largest denominator and then make multiples of the number until you have a number that each of the denominators can be divided into evenly. Example 3: Once the fractions have the common denominator, add the numerators.
The last step of each problem is to see if the fraction can be reduced. Many times it cannot be reduced. There are two ways that fractions can be reduced. Example 4: Add 7/18 and 5/18 In this example, the same factor, 6, can be divided evenly into the numerator and denominator.
Example 5: Find the sum of 3/5, 19/20, and 9/10 This answer has a fraction with the numerator larger than the denominator. Taking multiples of the denominator out of the numerator allows them to be written as whole numbers. The remainder is left as a fraction.
A second way of working with mixed numbers is to convert the numbers to fractions, add, and then convert the answer back to a mixed number.
Guidelines when adding common fractions: • Find the lowest common denominator. • Make equivalent fractions with lowest common denominators. • Reduce the answer to lowest terms.
