Copyright © 2012, 2009, 2005, 2002 Pearson Education, Inc. Chapter 2 Fractions

Copyright © 2012, 2009, 2005, 2002 Pearson Education, Inc. Simplifying Fractions 2.2

Copyright © 2012, 2009, 2005, 2002 Pearson Education, Inc. Prime Numbers A prime number is a whole number greater than 1 that cannot be evenly divided except by 1 and itself. 2, 3, 5, 7, 11, 13, 17, 19, 23, 29 The first 10 prime numbers A composite number is a whole number greater than 1 that can be evenly divided by whole numbers other than 1 and itself. 24 = 2  1224 = 3  824 = 4  6

Copyright © 2012, 2009, 2005, 2002 Pearson Education, Inc. Divisibility Tests 1.A number is divisible by 2 if the last digit is 0, 2, 4, 6, or 8. 2.A number is divisible by 3 if the sum of the digits is divisible by 3. 3.A number is divisible by 5 if the last digit is 0 or 5. Example: The number 450 is divisible by 2. (It ends in 0.) The number 450 is divisible by 3. ( = 9 and 9 is divisible by 3.) The number 450 is divisible by 5. (It ends in 0.)

Copyright © 2012, 2009, 2005, 2002 Pearson Education, Inc. Prime Factorization Example: Write the number 24 as a product of primes. Write 24 as the product of any two factors. 24 = 4  6 If the factors are not prime, they must be factored. 2  22  3 When all of the factors are prime, the number has been completely factored. 24 = 2  2  2  3 Instead of writing 2  2  2  3, we can also write 2 3  3.

Copyright © 2012, 2009, 2005, 2002 Pearson Education, Inc. The Fundamental Theorem of Arithmetic 24 = 4  6 2  22  3 The order of the prime factors is not important because multiplication is commutative. The Fundamental Theorem of Arithmetic Every composite number can be written in exactly one way as a product of primes. 24 = 3  8 2  4 2  2 24 = 2  2  2  324 = 3  2  2  2

Copyright © 2012, 2009, 2005, 2002 Pearson Education, Inc. Equivalent Fractions Equivalent fractions can be written in more than one way. The value of the fractions is the same. is shaded. Equivalent fractions

Copyright © 2012, 2009, 2005, 2002 Pearson Education, Inc. Simplest Form Any nonzero number divided by itself is equal to 1. A fraction is in simplest form when the numerator and denominator have no common factors. are equivalent fractions.

Copyright © 2012, 2009, 2005, 2002 Pearson Education, Inc. Common Factors When a fraction is not in simplest form, it can be reduced. 5 is the common factor. To reduce a fraction, find a common factor in the numerator and the denominator and divide it out. A fraction is called simplified, reduced, or in lowest terms if the numerator and the denominator only have 1 as a common factor.

Copyright © 2012, 2009, 2005, 2002 Pearson Education, Inc. Equal Fractions If two fractions are equivalent, their diagonal products or cross products will be equal. Equality Test for Fractions For any two fractions where a, b, c and d are whole numbers and b  0, d  0, if then a  d = b  c. =