5.1 for student to learn mathematics.pptx

lecture

1. 5-1 Multiplication and Division of Rational Numbers Multiplication of Rational Numbers Properties of Multiplication of Rational Numbers Multiplication with Mixed Numbers Division of Rational Numbers Estimation and Mental Math with Rational Numbers Extending the Notion of Exponents Copyright © 2013, 2010, and 2007, Pearson Education, Inc.

2. Multiplication of Rational Numbers Multiplication as repeated addition Multiplication as part of an area Copyright © 2013, 2010, and 2007, Pearson Education, Inc.

3. If are any rational numbers, then Multiplication of Rational Numbers Copyright © 2013, 2010, and 2007, Pearson Education, Inc.

4. Example 1 If of the population of a certain city are college graduates and of the city’s college graduates are female, what fraction of the population of that city is female college graduates? of the population is female college graduates. Copyright © 2013, 2010, and 2007, Pearson Education, Inc.

5. Multiplicative Identity The number 1 is the unique number such that for every rational number Properties of Multiplication of Rational Numbers Copyright © 2013, 2010, and 2007, Pearson Education, Inc.

6. Multiplicative Inverse ( Reciprocal ) For any nonzero rational number , is the unique rational number such that Properties of Multiplication of Rational Numbers Copyright © 2013, 2010, and 2007, Pearson Education, Inc.

7. Properties of Multiplication of Rational Numbers If are any rational numbers, then Distributive Property of Multiplication Over Addition Copyright © 2013, 2010, and 2007, Pearson Education, Inc.

8. Multiplication Property of Equality If are any rational numbers such that , and if is any rational number, then Properties of Multiplication of Rational Numbers Copyright © 2013, 2010, and 2007, Pearson Education, Inc.

9. Multiplication Property of Inequality Properties of Multiplication of Rational Numbers Copyright © 2013, 2010, and 2007, Pearson Education, Inc.

10. Multiplication Property of Zero Properties of Multiplication of Rational Numbers If is any rational number, then Copyright © 2013, 2010, and 2007, Pearson Education, Inc.

11. A bicycle is on sale at of its original price. If the sale price is $330, what was the original price? Example 2 Let x = the original price. Then the sale price. The original price was $440. Copyright © 2013, 2010, and 2007, Pearson Education, Inc.

12. Multiplication with Mixed Numbers Using the Distributive Property Using Improper Fractions Copyright © 2013, 2010, and 2007, Pearson Education, Inc.

13. Operations on Decimals Multiplying Decimals Scientific Notation Dividing Decimals Mental Computation Rounding Decimals Estimating Decimal Computations Using Rounding Round-off Errors Copyright © 2013, 2010, and 2007, Pearson Education, Inc.

14. Add 2.16 and 1.73. Adding Decimals Copyright © 2013, 2010, and 2007, Pearson Education, Inc.

15. Adding Decimals We can change the problem to one we already know how to solve, that is, to a sum involving fractions. Copyright © 2013, 2010, and 2007, Pearson Education, Inc.

16. If there are n digits to the right of the decimal point in one number and m digits to the right of the decimal point in the second number, multiply the two numbers ignoring the decimals, and then place the decimal point so that there are m + n digits to the right of the decimal point in the product. Multiplying Decimals Copyright © 2013, 2010, and 2007, Pearson Education, Inc.

17. Example 3 Compute each of the following: a. (6.2)(1.43) b. (0.02)(0.013) Copyright © 2013, 2010, and 2007, Pearson Education, Inc.

18. Example 3 ( cont ) Compute each of the following: c. (1000)(3.6) Copyright © 2013, 2010, and 2007, Pearson Education, Inc.