Unit 6 Addition of Common Fractions

A fraction is a part of a whole An inch can be divided into equal parts: –For example an inch may be divided into eight equal parts called eighths of an inch

Addition of Common Fractions The number of parts is called the numerator –Numerator → –Denominator → The whole is called the denominator

Addition of Common Fractions To add fractions, each fraction must share a common denominator A common denominator may always be found by multiplying all of the denominators in the problem –This may result in a large denominator

Addition of Common Fractions A least common denominator (LCD) is generally found by inspection If inspection is not obvious: –Factor every denominator into its smallest factors. –To find the LCD take the product of all different factors, using each factor the greatest number of times it is found in a single denominator –Multiply the original fraction by the factor of the LCD that is missing in the original denominator

Addition of Common Fractions Find the LCD of Factor the denominators into the smallest factors: 8 = 2 x 2 x 2 6 = 2 x 3 Find the LCD by multiplying the factors, using each factor the greatest number of times it is found in a single denominator: LCD = 2 x 2 x 2 x 3 = 24

Addition of Common Fractions Example: –Step 1: Find the LCD 6 = 2 x 3 9 = 3 x 3 LCD = 2 x 3 x 3 = 18

Addition of Common Fractions Example continued: –Step 2: Multiply the original fractions

Addition of Common Fractions Example continued: –Step 3: Add the numerators and express over the common denominator –Step 4: Change the improper fraction to a whole number and proper fraction

Practical Problem What is the total thickness of a tabletop made of ¾ inch particle board covered with 1 / 16 inch laminated plastic?

Practical Problem Add the fractions to find the thickness. The total thickness of the tabletop is 13 / 16 ”.