Integers Multiplying and Dividing. EXAMPLE 1 Multiplying Integers a. –5 ( –7 ) The product of two integers with the same sign is positive. b. –8 ( 2 )

Slides:

Advertisements

Similar presentations

Chapter 1 Discovery 1 Evaluate each expression, and compare the results obtained in the left column with the corresponding results in the right column.

Advertisements

Example 1 Multiplying Integers a. 3 () 4 – Different signs, so product is negative. = 12 – b. () 3 – 6 – Same sign, so product is positive. = 18 c. ()

EXAMPLE 1 Multiplying Integers

Example 1 Dividing Integers Same sign, so quotient is positive. 5 = a. 8 – 40 – b. 14 – 2 = 7 – Different signs, so quotient is negative. c. 9 – 36 = 4.

Integers: Multiplication & Division

1.4-5: Multiplying Integers: Basic Rules. Ways to Express multiplication Remember: All of these mean the same thing: Five times four 5 × 4 5 · 4 5(4)

EXAMPLE 1 a. –5(–7) = 35 b. –8(2) = –16 c. –12(0) = 0

Objective: Learn to multiply and divide integers.

EXAMPLE 1 Same sign, so quotient is positive. = –7 Different signs, so quotient is negative. c. 36 –9 = –4 Different signs, so quotient is negative. =

Dividing Integers EXAMPLE 1 The quotient of two integers with different signs is negative. The quotient of two integers with the same sign is positive.

RATIONAL EXPONENTS Assignments Assignments Basic terminology

Algebra 2-4 Dividing Rational Numbers

Integers. Adding integers Both positive…add as usual Both negative…add as usual and answer is negative Positive and negative…subtract…take the sign of.

Integer Rules. Adding with the same sign Rules Rules Add like normal Add like normal Keep the sign Keep the sign Examples Examples = -22 (all.

ALGEBRA 1 Operations with Integers

Operations: Add, Subtract, Multiply, Divide

Section 1-6 Multiply and Divide Real Numbers SPI 12B: Identify the reciprocal of a real number Objectives: Apply properties of real numbers by multiplying.

Math Journal Find the perimeter of the trapezoid: 4x ft 3x ft 60x in.

A dding two negative integers: add the absolute values the answer is negative Adding a negative and a positive number: subtract the absolute values the.

Evaluate numerical expressions

Example 3 Dividing Mixed Numbers ÷ – 3 19 = 17 6 – Multiply by the reciprocal of 17 6 – 6 – = 3 () 6 – 19 Use rule for multiplying fractions.

Addition, Subtraction, Multiplication, and Division of Integers

Dividing Monomials: The Quotient Rule and Integer Exponents.

11-7 Multiplying Integers Warm Up Find each product ,600 14,000.

Chapter 2 Section 5 Multiplying Integers. Multiplying Two Integers with Different Signs Words: The product of two integers with different signs. Numbers:

Lesson 1.7 Dividing Integers Standards: NS 1.2 and AF 2.1 Objectives: Dividing Integers Evaluate variable expressions.

Integers All whole numbers and their opposites including the number 0.

Multiplying and Dividing Integers When you MULTIPLY: Two positives equal a positive Two negatives equal a positive One positive & one negative equal.

EXAMPLE 2 Finding a Mean Temperatures One of the coldest places on Earth is the Russian town of Verkhoyansk, located near the Arctic Circle. Find the mean.

Day Problems Simplify each expression – – (-8.4) 3. Evaluate each expression for a = -2, b = 3.5, and c = a – b + c5. |c + a + 5|

1-4 Multiplying and Dividing Integers Aim: How can we Aim: How can we Multiply and divide integers and to solve problems involving integers? CCSS: 7.NS.2.a.

Cougar Time. Adding Negative Numbers  What are the two rules for adding integers?  Same Signs = Add and keep the sign  Different Signs = Find the absolute.

MULTIPLYING RATIONAL NUMBERS IF THE SIGNS ARE THE SAME, MULTIPLY THEIR ABSOLUTE VALUES AND THE ANSWER IS POSITIVE. (+4)(+5) = (-4)(-5) = (3)(6) = (-10)(-4)

Notes Over 2.8 Rules for Dividing Negative Numbers. ( Same as Multiplying ) If there is an even number of negative numbers, then the answer is Positive.

INTEGERS – Product & Quotient. Multiplying Integers - remember our changing sign table ? + + changes to changes to changes to changes.

2-5 HW = Pg #6-50 e, HW Continued 56.) C57.) B.

Multiplication and Division of Integers Multiplying! / Steps: / Ignore signs and multiply / Determine the sign / Positive times a Positive = Positive.

MULTIPLYING INTEGERS LESSON 2-4, P. 83. RULES When multiplying integers with like (the same) signs, the product (answer) will be positive. EX.) negative.

Copyright © 2014, 2010, and 2006 Pearson Education, Inc. Chapter 4 Polynomials.

LAWS OF EXPONENTS.

MULTIPLICATION & DIVISION OF INTEGERS 1-9 RULES FOR MULTIPLYING INTEGERS The product of two integers with the SAME SIGN is positive. The product of two.

Quick Review Find each sum: (-3) + (-3) + (-3) Answers:

Addition Multiplication Subtraction Division. 1.If the signs are the same, add the numbers and keep the same sign = = If the.

Dividing Rational Numbers Rational Numbers ~. Dividing Rational Numbers RULES: RULES: 1. When multiplying or dividing integers with the same signs, the.

Definitions Add & Subtract Multiply & Divide ExponentsMixed.

2.3 Multiplying Rational Numbers The product of numbers having the same sign is positive. The product of numbers having different signs is negative.

EXAMPLE 1 Find multiplicative inverses of numbers a. The multiplicative inverse of 1 5 – is – 5 because b. The multiplicative inverse of 6 7 – is 7 6 –

Notes 2.1 Order of Operations PEMDAS If an expression has only numbers and symbols, it is a numerical expression. If it has a variable it is a variable.

Location of Exponent An exponent is the small number high and to the right of a regular or base number. 3 4 Base Exponent.

Lesson 1-6 Multiplying and Dividing Real Numbers Pages

1.8 Dividing Real Numbers Objectives To Divide Real Numbers To evaluate algebraic expressions involving multiplication and division.

Interesting Integers – Part Dos

Integers Rules of Operation.

Multiplying and Dividing Decimals

Multiply and divide integers

Solving 1-Step Integer Equations

Multiplying Integers.

Lesson 2.4 – 2.5 Multiplying and Dividing Integers

Exponential Functions

Title of Notes: Multiplying and Dividing Integers pg. 9 RS

Multiplying and Dividing Integers

ALGEBRA I - SECTION 1-6 (Multiplying and Dividing Real Numbers)

Multiplying and Dividing Integers

DIRECTED NUMBERS.

Division Rules for Exponents

Multiplication and Division of Integers

Recognize the Operation

Because division is the inverse of multiplication, the rules for dividing integers are the same as the rules for multiplying integers. Dividing Integers.

Presentation transcript:

Integers Multiplying and Dividing

EXAMPLE 1 Multiplying Integers a. –5 ( –7 ) The product of two integers with the same sign is positive. b. –8 ( 2 ) The product of two integers with different signs is negative. c. –12 ( 0 ) The product of an integer and 0 is 0. = 35 = –16 = 0

EXAMPLE 2 Evaluating Variable Expressions a. Evaluate a 2 when a = –3. b. Evaluate xyz when x = 2, y = –4, and z = 6. SOLUTION Substitute – 3 for a. = –3 ( –3 ) Write – 3 as a factor two times. = 9 Multiply – 3 and – 3. Substitute 2 for x, – 4 for y, and 6 for z. = –8 ( 6 ) = –48 Multiply 2 and – 4. Multiply – 8 and 6. a. a 2 b. xyz = (–3) 2 = 2(–4)(6)

EXAMPLE 3 Using Integer Multiplication Greenland Most of Greenland is covered with ice that is almost two miles thick in some places. Scientists estimate that 3 feet of this ice melts each year. Find the change in the thickness of the ice after 10 years.

EXAMPLE 3 ANSWER The thickness of the ice will decrease 30 feet in 10 years. Change in ice thickness = –3 ( 10 ) = –30 SOLUTION You can find the total change in the ice thickness by multiplying the yearly change by the number of years. Use – 3 for the yearly change because the thickness of the ice decreases by 3 feet each year. Using Integer Multiplication

GUIDED PRACTICE Find the product. 1. –9(2) 2. –3(–4) ANSWER –18 ANSWER (–5) ANSWER – (–14) ANSWER 0

GUIDED PRACTICE 5. Evaluate the expressions x 2 y and –3xy 2 when x = –2 and y = 3. ANSWER 12, 54 ANSWER – 54 ft What If? What is the change in the thickness of the ice in Example 3 after 18 years? 6.

Dividing Integers EXAMPLE 1 The quotient of two integers with different signs is negative. The quotient of two integers with the same sign is positive. The quotient of 0 and any nonzero integer is 0. a. 28 (–4) = –7 –60 –12 b.b. = 5 = 0 c. 0 (–13)

GUIDED PRACTICE Find the quotient. ANSWER – ANSWER 4 – – – – 4.19 ( 1 ) – 3 ANSWER 19 – ANSWER

Rule for Multiply and Dividing Integers Multiplication: Same Signs: Multiply the absolute values, positive product Different Signs: Multiply the absolute values; negative product Division: Same Signs: Divide absolute values, positive quotient Different Signs: Divide absolute values, negative quotient.