Chapter 1 Section 1 Slide 2 Copyright 2012, 2008, 2004 Pearson
Education, Inc. 1 1.1 Fractions Objectives Learn the definition of
factor. Write fractions in lowest terms. Multiply and divide
fractions. Add and subtract fractions. Solve applied problems that
involve fractions. Interpret data in a circle graph. 2 3 4 5 6
Slide 3 Copyright 2012, 2008, 2004 Pearson Education, Inc. Natural
numbers: 1, 2, 3, 4,,, Numerator Fraction Bar Denominator Example:
The improper fraction can be written, a mixed number. Whole
numbers: 0, 1, 2, 3, 4,, Fractions: Proper fraction: Numerator is
less than denominator and the value is less than 1. Improper
fraction: Numerator is greater than or equal to denominator and the
value is greater than or equal to 1. Mixed number: A combination of
a natural number and a proper fraction. Slide 1.1-3 Definitions
Slide 4 Copyright 2012, 2008, 2004 Pearson Education, Inc.
Objective 1 Learn the definition of factor. Slide 1.1-4 Slide 5
Copyright 2012, 2008, 2004 Pearson Education, Inc. Learn the
definition of factor. In the statement 3 6 = 18, the numbers 3 and
6 are called factors of 18. Other factors of 18 include 1, 2, 9,
and 18. The number 18 in this statement is called the product. The
number 18 is factored by writing it as a product of two or more
numbers. Examples: 6 3, 18 1, (2)(9),2(3)(3) Slide 1.1-5 A raised
dot is often used instead of the symbol to indicate multiplication
because may be confused with the letter x. Slide 6 Copyright 2012,
2008, 2004 Pearson Education, Inc. Learn the definition of factor.
(contd) A natural number greater than 1 is prime if its factors
include only 1 and itself. Examples: 2, 3, 5, 7, 11, 13, 17, 19,
23, 29, 31, 37 A natural number greater than 1 that is not prime is
called a composite number. Examples: 4, 6, 8, 9, 10, 12, 14, 15,
16, 18, 20, 21 Slide 1.1-6 Slide 7 Copyright 2012, 2008, 2004
Pearson Education, Inc. EXAMPLE 1 Write 90 as the product of prime
factors. Starting with the least prime factor is not necessary. No
matter which prime factor we start with, the same prime
factorization will always be obtained. Solution: Factoring Numbers
Slide 1.1-7 Slide 8 Copyright 2012, 2008, 2004 Pearson Education,
Inc. Objective 2 Write fractions in lowest terms. Slide 1.1-8 Slide
9 Copyright 2012, 2008, 2004 Pearson Education, Inc. A fraction is
in lowest terms when the numerator and denominator have no common
factors other than 1. Write fractions in lowest terms. Slide 1.1-9
Basic Principle of Fractions If the numerator and denominator of a
fraction are multiplied or divided by the same nonzero number, the
value of the fraction remains unchanged. Slide 10 Copyright 2012,
2008, 2004 Pearson Education, Inc. Writing a Fraction in Lowest
Terms Step 1:Write the numerator and the denominator as the product
of prime factors. Write fractions in lowest terms. (contd) Step 2:
Divide the numerator and the denominator by the greatest common
factor, the product of all factors common to both. Slide 1.1-10
Slide 11 Copyright 2012, 2008, 2004 Pearson Education, Inc. EXAMPLE
2 Write in lowest terms. When writing fractions in lowest terms, be
sure to include the factor 1 in the numerator or an error may
result. Solution: = Writing Fractions in Lowest Terms Slide 1.1-11
Slide 12 Copyright 2012, 2008, 2004 Pearson Education, Inc.
Objective 3 Multiply and divide fractions. Slide 1.1-12 Slide 13
Copyright 2012, 2008, 2004 Pearson Education, Inc. Multiply and
divide fractions. Multiplying Fractions If and are fractions, then
=. That is, to multiply two fractions, multiply their numerators
and then multiply their denominators. Slide 1.1-13 Some prefer to
factor and divide out any common factors before multiplying. Slide
14 Copyright 2012, 2008, 2004 Pearson Education, Inc. EXAMPLE 3
Find each product, and write it in lowest terms. Solution: or
Multiplying Fractions Slide 1.1-14 Slide 15 Copyright 2012, 2008,
2004 Pearson Education, Inc. Dividing Fractions If and are
fractions, then =. Multiply and divide fractions. (contd) That is,
to divide by a fraction, multiply by its reciprocal; the fraction
flipped upside down. Slide 1.1-15 Slide 16 Copyright 2012, 2008,
2004 Pearson Education, Inc. EXAMPLE 4 Find each quotient, and
write it in lowest terms. Solution: or Dividing Fractions Slide
1.1-16 Slide 17 Copyright 2012, 2008, 2004 Pearson Education, Inc.
Objective 4 Add and subtract fractions. Slide 1.1-17 Slide 18
Copyright 2012, 2008, 2004 Pearson Education, Inc. Add and subtract
fractions. Adding Fractions If and are fractions, then + =. To find
the sum of two fractions having the same denominator, add the
numerators and keep the same denominator. Slide 1.1-18 Slide 19
Copyright 2012, 2008, 2004 Pearson Education, Inc. EXAMPLE 5 Find
the sum, and write it in lowest terms. Solution: Adding Fractions
with the Same Denominator Slide 1.1-19 Slide 20 Copyright 2012,
2008, 2004 Pearson Education, Inc. Add and subtract fractions.
(contd) Finding the Least Common Denominator If the fractions do
not share a common denominator, the least common denominator (LCD)
must first be found as follows: Step 1: Factor each denominator.
Step 2: Use every factor that appears in any factored form. If a
factor is repeated, use the largest number of repeats in the LCD.
Slide 1.1-20 Slide 21 Copyright 2012, 2008, 2004 Pearson Education,
Inc. EXAMPLE 6 Find each sum, and write it in lowest terms. or
Adding Fractions with Different Denominators Solution: Slide 1.1-21
Slide 22 Copyright 2012, 2008, 2004 Pearson Education, Inc. Add and
subtract fractions. (contd) Subtracting Fractions If and are
fractions, then. If fractions have different denominators, find the
LCD using the same method as with adding fractions. To find the
difference between two fractions having the same denominator,
subtract the numerators and keep the same denominator. Slide 1.1-22
Slide 23 Copyright 2012, 2008, 2004 Pearson Education, Inc.
Subtracting Fractions Find each difference, and write it in lowest
terms. EXAMPLE 7 or Solution: Slide 1.1-23 Slide 24 Copyright 2012,
2008, 2004 Pearson Education, Inc. Objective 5 Solve applied
problems that involve fractions. Slide 1.1-24 Slide 25 Copyright
2012, 2008, 2004 Pearson Education, Inc. EXAMPLE 8 A gallon of
paint covers 500 ft 2. To paint his house, Tran needs enough paint
to cover 4200 ft 2. How many gallons of paint should he buy? Tran
needs to buy 9 gallons of paint. Solution: Adding Fractions to
Solve an Applied Problem Slide 1.1-25 Slide 26 Copyright 2012,
2008, 2004 Pearson Education, Inc. Objective 6 Interpret data in a
circle graph. Slide 1.1-26 Slide 27 Copyright 2012, 2008, 2004
Pearson Education, Inc. EXAMPLE 9 Recently there were about 970
million Internet users world wide. The circle graph below shows the
fractions of these users living in various regions of the world.
Using a Circle Graph to Interpret Information How many actual
Internet users were there in Europe? Estimate the number of
Internet users in Europe. Which region had the second-largest
number of Internet Users? Slide 1.1-27 Slide 28 Copyright 2012,
2008, 2004 Pearson Education, Inc. Solution: a) Europe EXAMPLE 9 b)
c) Slide 1.1-28 Using a Circle Graph to Interpret Information
(contd)
