Multiply and Divide Rational Numbers, Writing Verbal Expressions Algebraically Objective: To multiply and divide rational numbers. To write verbal expressions for algebraic expressions and to write algebraic expressions for verbal expressions.

Sign Rules The product or quotient of two rational numbers having the same sign is positive. The product or quotient of two rational numbers having different signs is negative.

Example 1 Find each product or quotient. -5.4(0.05) = ÷ (-2.4) = 2.85

Multiplying Fractions To multiply fractions, multiply the numerators and multiply the denominators. If the numerators and denominators have common factors, you can simplify before you multiply by canceling.

Example 2 Find each product

Example 3 Find 1 5

Dividing Fractions Two numbers whose product is 1 are called multiplicative inverses or reciprocals. To divide one fraction by another fraction, multiply the dividend by the reciprocal of the divisor. – First fraction times reciprocal of second fraction.

Example 4 Name the reciprocal of each number.

Example 5 Find each quotient

Writing Verbal Expressions An algebraic expression consists of sums and/or products of numbers and variables. In the algebraic expression 0.10d, the letter d is called a variable. In algebra, variables are symbols used to represent unspecified numbers or values. Any letter may be used as a variable.

Writing Verbal Expressions Examples: 0.10d, 2x + 4, 3 +, p q, 4cd ÷ 3mn A term of an expression may be a number, a variable, or a product or quotient of numbers and variables. A variable term is a term that contains a variable. A constant term is a term that only has a number. 1 term 2 terms 1 term

Writing Verbal Expressions In a multiplication expression, the quantities being multiplied are factors, and the result is the product. An expression like x n is called a power. The exponent indicates the number of times the base is used as a factor. xnxn exponent base

Example 6 Write a verbal expression for each algebraic expression. 8x 2 Eight times x squared. y 5 – 16y Y to the fifth power minus the product of 16 and y.

Check Your Progress Choose the correct answer for the following. Write a verbal expression for 7a 4. A.7 times a B.7 times the product of 4 and a C.7 times a to the fourth power D.4 times a to the seventh power

Check Your Progress Choose the correct answer for the following. Write a verbal expression for x A.The sum of 3 and x B.The product of x squared and 3 C.The sum of x and 3 squared D.The sum of x squared and 3

Write Algebraic Expressions In order to write algebraic expressions, you will need to be able to translate words into symbols. OperationVerbal Phrases Addition Subtraction Multiplication Division Sum, Plus, More than, Increased by, Added to Difference, Minus, Less than, Decreased by, Subtracted from Times, Product of, Multiplied by, Of Quotient of, Divided by

Example 7 Write an algebraic expression for each verbal expression. 5 less than a number c. c – 5 9 plus the product of 2 and d d Two fifths of the area a.

Check Your Progress Choose the correct answer for the following. Write an algebraic expression for nine more than a number h. A.9 – h B.9h C.9 + h D.h – 9

Check Your Progress Choose the correct answer for the following. Write an algebraic expression for the difference of 6 and 4 times a number x. A.6 – 4x B.(6 – 4) + x C.6 + 4x D.6x – 4

Check Your Progress Choose the correct answer for the following. Write an algebraic expression for one half the size of the original perimeter p. A.2p B.½ p C.p 2 D.p ½

Real-World Problems Variables can represent quantities that are known and quantities that are unknown. They are also used in formulas, expressions, and equations.

Example 8 Mr. Nehru bought two adult tickets and three student tickets for the planetarium show. Write an algebraic expression that represents the cost of the tickets. – Let a = adult tickets. – Let s = student tickets. 2a + 3s

Check Your Progress Choose the correct answer for the following. Lorenzo bought a bag of peanuts that cost p dollars and he gave the cashier a $20 bill. Write an expression for the amount of change that he will receive. A.20 – p B.p – 20 C.20 + p D.20 ÷ p