Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
History of logarithms wikipedia , lookup
Positional notation wikipedia , lookup
Mathematics of radio engineering wikipedia , lookup
Factorization wikipedia , lookup
Proofs of Fermat's little theorem wikipedia , lookup
Vincent's theorem wikipedia , lookup
Elementary arithmetic wikipedia , lookup
Working with Fractions ADDITION/SUBTRACTION LCD It is necessary to find a Least Common Denominator (LCD) when adding or subtracting fractions. The Least Common Multiple (LCM) of the denominators is called the LCD. Example: Add 3 8 1 . 6 Finding the LCD Method 1 List the multiples of each denominator and find the smallest one common to both lists. Multiples of 8: 8, 16, 24, 32… Multiples of 6: 6, 12, 18, 24, 30… Method 2 LCD = 24 Find the prime factorization* of each denominator. Compare and list each prime factor without duplicating or leaving any out. Multiply to obtain the LCD. 8 2 6 2 2 2 3 2 6=2 3 8 = 2 2 2=23 Use a chart to compare factors without duplicating or leaving any out: 8= 2 2 2 6 = 2 3 2 2 2 3 = 24 LCD = 24 *The Fundamental Theorem of Arithmetic states that every positive integer greater than 1 can be written as a unique product of prime numbers. Using the LCD to Add Fractions 3 1 8 6 24 24 1) Write two equivalent fractions with the LCD. 3 3 1 4 9 8 3 6 4 24 More Examples 1. 1 2 1 3 3 6 1 3 2. 3. 2 5 4. 2 3 2 6 4 24 5 6 2 3 1 4 2) Find the number each original denominator needs to multiply to equal the LCD. Multiply the numerator by the same number. 3 3 8 20 1 9 13 24 1 8 5 20 6 9 1 9 5 3 20 20 7 9 MULTIPLICATION/DIVISION No LCD is needed when multiplying and dividing fractions. Multiply straight across and simplify if possible. Multiplication 1 1 2 3 Examples: 1 6 2 5 3 2 5 3 1 3 8 4 9 1 10 3 3 82 93 14 1 2 1 3 2 3 Division (Multiplication by Reciprocal) Change division to multiplication by “flipping” the second fraction. (Multiply the first fraction by the reciprocal of the second). 3 8 Examples: 2 3 2 5 3 5 8 2 3 4 2 3 15 16 4 3 8 9 LSC-Montgomery Learning Center: Working With Fractions Updated April 7, 2011 Page 2