Math "Multiplying and Reducing Fractions"
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1 Math "Multiplying and Reducing Fractions" Objectives * Know that rational number is the technical term for fraction. * Learn how to multiply fractions. * Learn how to build and reduce fractions. Preliminaries So far we have learned how to multiply and divide whole numbers and integers. In this section we will study a new collection of numbers and develop ways to multiply them. De nition "Rational Number" A rational number is any number that can be written as Examples Question Non-examples Is a whole number a rational number? What about an integer? De nition "Proper Fraction" and "Improper Fraction" A proper fraction is a fraction in which the numerator is less than the denominator. An improper fraction is a fractions in which the numerator is greater than the denominator. Rational Numbers Example (Describing fractions) Describe the following fractions as equal parts of a whole. 5 8 Example 2 (Describing fractions) Describe each fraction as a Division. [Numerator divided by denominator] Page
2 Page 2 Rule for the placement of negative signs If a and b are integers then Question In the rule above can we have b = 0? Example (Alternate forms of a fraction) 9 Write two alternate forms of 80 Multiplying Rational Numbers (Fractions) To Multiply Fractions. Multiply the numerators. 2. Multiply the denominators. Example (Multiplying fractions). Find the following values. The product of 2 and c) Find 0 of 6 d) 5 7 Commutative Property of Multiplication If a b and c d are rational numbers, then Associative Property of Multiplication If a b, c d and e f are rational numbers, then Example 5 State the property of multiplication that is being illustrated Then nd the product. 9 = 9 2 = 2
3 Page Raising Factors to Higher Terms and Reducing Fractions Recall that from integers we have a = a. For fractions we have the following Multiplicative Identity. For any rational number a b ; we have a 2. b = a b = a b = NOTE The above identity will allow us to perform the following operations. Raise a fraction to higher terms (e.g. nd an equal fraction with bigger denominator). 2. Reduce a fraction to lower terms (e.g. nd an equal fraction with smaller denominator). Example 6 (Raising fractions to higher terms) Raise each fraction to higher terms as indicated. 2 =? x 2 6y =? 80y 2 c) 7xy 0 =? 00xy To Reduce a Fraction to Lower Terms. Factor the numerator and denominator into prime factorizations. 2. Use = and "divide out" common factors. NOTE If both numerator and denominator have a factor of, then we "divide out" and treat the fraction as positive since = Example 7 (Reducing fractions) Reduce the following fractions to lowest terms y 2
4 Page c) 5x 9x 2 d) 2a 2 b 00a o Shortcut We don t have to write down the number when reducing the form. We can use cancel mars to indicate "dividing out" common factors n Example 8 (Reducing fractions using the shortcut) Reduce the following fractions to lowest terms Multiplying and Reducing at the Same Time Example 9 (Multiplying and reducing fractions at the same time) Multiply and reduce to lowest terms. 2x 52xy 27 22x 9 7n 8m 5mn n 8 5 m2
5 Page 5 NOTE There s another method for multiplying and reducing fractions which is to divide the numerator and denominator by a common factor. Example 0 (Multiplying and reducing fractions using an alternate method) 8 Multiply and reduce to lowest term Example (Word problem) If you had $25 and you spent $5 to buy computer diss, what fraction of your money did you spend on computer diss? What fraction do you still have? Example 2 (Word Problem) Suppose that a ball is dropped from a height of 0 feet and that each time the ball bounces it bounces bac to 2 it dropped. How high will the ball bounce on its second bounce? On its third bounce? the height
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5.6 Solving Percent Problems percent of a number? How can you use mental math to find the I have a secret way for finding 2% of 80. 0% is 8, and % is 0.8. So, 2% is 8 + 8 + 0.8 = 6.8. ACTIVITY: Finding
Algebra. Chapter 8: Factoring Polynomials. Name: Teacher: Pd:
Algebra Chapter 8: Factoring Polynomials Name: Teacher: Pd: Table of Contents o Day 1: SWBAT: Factor polynomials by using the GCF. Pgs: 1-6 HW: Pages 7-8 o Day 2: SWBAT: Factor quadratic trinomials of