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
Positional notation wikipedia , lookup
Bra–ket notation wikipedia , lookup
Georg Cantor's first set theory article wikipedia , lookup
Large numbers wikipedia , lookup
Location arithmetic wikipedia , lookup
Proofs of Fermat's little theorem wikipedia , lookup
Real number wikipedia , lookup
P-adic number wikipedia , lookup
Multiplying Rational Numbers 5 20 5 13 12 1 112 high 1 ; low 11 Page 76 – 77 #18 – 58 even (#36 & #56 bonus) (19 problems – 19 points) Multiplying Rational Numbers Multiplication is repeated addition. So, 3 7 7 7 7 21 By the Commutative Property of Multiplication, 3 7 73 This example suggests the following rule: Multiplying Rational Numbers Multiplying Two Numbers with Different Signs The product of two numbers with different signs is negative. Examples: 4 3 12 34 12 Multiplying Rational Numbers The product of two positive integers is positive. What is the sign of the product of two negative integers? Use the pattern to find (– 4)(– 1). One positive and one negative factor: Negative product Two negative factors: Positive product 42 8 41 4 40 0 4 1 4 4 2 8 4 4 4 4 Each product is 4 more than the previous product. Multiplying Rational Numbers This example suggests the following rule. Multiplying Two Numbers with the Same Sign The product of two numbers with the same sign is positive. Examples: 43 12 3 4 12 Multiplying Integers Find (–8)(–6). same signs positive product Answer: 48 Multiplying Integers Find (10)(–11). different signs negative product Answer: –110 Multiplying Integers Find each product. a. (–4)(8) Answer: –32 b. (–6)(–12) Answer: 72 You can simplify expressions by applying the rules of multiplication. Simplify Expressions Simplify the expression Associative Property () Substitution Distributive Property Answer: Simplify. Simplify Expressions Simplify the expression Answer: 3x Multiplying rational numbers is similar to multiplying integers. Multiply Rational Numbers Find same signs positive product Answer: Multiply Rational Numbers Find Answer: Multiply Rational Numbers to Solve a Problem Stocks The value of a company’s stock dropped by $1.25 per share. By what amount did the total value of the company’s stock change if the company has issued 500,000 shares of stock? To find the change in the total value of the company’s stock, multiply the price lost per share by the number of shares. different signs negative product Answer: The total value of the company’s stock changed by –$625,000. Multiply Rational Numbers to Solve a Problem Construction A construction project is stopped by a winter storm. For every day that they are unable to work, the company loses $35,000. If the storm keeps them from working for 4 days, how much money do they lose? Answer: –$140,000 You can evaluate expressions that contain rational numbers. Evaluate Expressions Substitution Answer: same signs positive product Evaluate Expressions Answer: Multiplying Rational Numbers Multiplicative Property of – 1 The product of any number and – 1 is its additive inverse. Examples: 1a a 1 a 14 4 1 4 1 2.3 2.3 1 2.3