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The document discusses multiplying and dividing integers. It states that the product of two integers with different signs is negative, while the product of two integers with the same sign is positive. It also notes that the quotient of two integers with the same sign is positive, but the quotient of two integers with different signs is negative. The class is assigned to work examples on specific pages and problems from their workbook for homework.
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Section 14.ppt
1. The document discusses properties and rules for multiplying and dividing real numbers, including integers and rational numbers.
2. When multiplying integers, the product is negative if the factors have different signs and positive if they have the same sign. When dividing integers, the quotient is negative if the divisor and dividend have different signs and positive if they have the same sign.
3. Multiplying and dividing rational numbers follows similar sign rules, and involves reducing common factors and multiplying/dividing the numerators and denominators.
Integers
The document discusses integers and the number line. It introduces addition and multiplication rules for integers.
- Integers include whole numbers and their opposites, and are represented on the number line.
- For addition, the sign of the sum is the same as the signs of the addends if they are the same, and follows the sign of the larger addend if the signs are different.
- For multiplication, the product is positive if the factors have the same sign and negative if the signs are different.
TechMathII - 2.1 - Variables and Expressions
The document provides examples and practice problems for evaluating algebraic expressions using the order of operations (PEMDAS). It includes solving expressions for given values of variables, writing expressions from phrases, defining variables in phrases, and writing equations from word problems. Students are asked to evaluate, write expressions, define variables, and write equations based on the examples and rules provided.
4 ma0 3h_msc_20150305
This document provides the marking scheme for the Pearson Edexcel International GCSE Mathematics A (4MA0) Paper 3H exam from January 2015. It begins with some general marking guidance on how to apply the mark scheme positively and award marks for what students show they can do. It provides details on the types of marks that can be awarded and abbreviations used in the mark scheme. It also provides guidance on aspects like showing working, ignoring subsequent work, and awarding marks for parts of questions. The document then provides the mark scheme for specific questions on the exam.
2.7 distributive property day 2
This document discusses combining like terms in algebraic expressions through examples and guided practice problems. It introduces the distributive property and explains that like terms are terms with the same variable raised to the same power. Examples show distributing a number over a sum and combining like terms. Guided practice problems have students simplify expressions using these steps. Key terms introduced are distributive property and like terms.
Msm1 fl ch11_06
This document contains a math lesson on multiplying integers. It includes examples of multiplying different combinations of positive and negative integers. It provides practice problems and checks for understanding. It then gives a lesson quiz to assess understanding with multiple choice questions involving multiplying integers in various contexts.
1.6 notes 7th
The document discusses multiplying and dividing integers. It states that if the signs of two integers being multiplied are the same, the product is positive, and if the signs are different, the product is negative. It also notes that if a quotient is negative, there must be an even number of positive factors in the numerator and denominator combined. Several examples are provided of multiplying, dividing, simplifying expressions, and evaluating expressions involving integers.
Multiplication and Division of Integers
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Reference:
Nivera, G. C. (2013), Grade 7 Mathematics: Pattern and Practicalities. Don Bosco Press Inc. Makati City, Philippines.
1.3 variables and expressions 1
The document provides lesson material on evaluating variable expressions from algebra. It includes examples of writing variable expressions from word phrases, evaluating expressions by substituting values for variables, and solving multi-step expressions. Students are provided vocabulary for mathematical operations and guided practice problems to work through. There is a reminder for students to bring their math book and calculator to class and that an NWEA test will be taken in the computer lab the next day.
2.7 distributive property day 1
This document provides lesson materials for algebra topics including the distributive property. It includes examples of using the distributive property to evaluate expressions like 12(-10 + -2) and 8(-3 - 6). The homework assigned for the week is also listed, covering topics like the distributive property, solving equations, and vocabulary terms.
Teacher Lecture
The document discusses exponents and order of operations. It defines exponents as indicating how many times the base is used as a factor. It provides examples of evaluating exponential expressions by writing repeated factors with exponents. Rules for exponents include: any number to the power of 0 equals 1; any number to the power of 1 equals the number; and multiplying exponents when the bases are the same. The order of operations is explained as: exponents, multiplication/division from left to right, and addition/subtraction from left to right. Grouping symbols like parentheses and fraction bars dictate that operations within are completed first. Several examples demonstrate applying these rules to simplify expressions.
October. 27, 2014
The document provides information about an upcoming math exam and homework assignments. It includes a schedule for the week which focuses on absolute value, inequalities, and beginning a review for the final exam. Topics to study this week include absolute value equations, linear equation word problems, and solving rational equations. The document also provides practice problems and examples for the final exam review involving order of operations, simplifying expressions, integers, and solving absolute value equations.
1150 day 6
Integers include positive and negative whole numbers. Absolute value is the distance from zero. Addition and subtraction on a number line involve moving left or right. Multiplication follows patterns based on sign. Division is the inverse of multiplication regarding sign. A number is divisible by another if it can be written as a product of an integer multiple. Divisibility tests identify patterns in a number's digits.
Orderof operations
The document discusses evaluating expressions using the proper order of operations. It provides the mnemonic device PEMDAS (Parentheses, Exponents, Multiply, Divide, Add, Subtract) to remember the correct sequence. Several examples are worked through step-by-step to demonstrate applying the order of operations. The objective is for students to be able to evaluate expressions like 7 + 4 * 3 as 19, not 33, by following PEMDAS.
Chapter 1.5 1.6
This document discusses multiplying and dividing integers. It states that if the signs are the same when multiplying integers, the answer is positive, and if the signs are different, the answer is negative. It also notes that if a product is negative, there must be an odd number of negative factors, and if a quotient is negative, there must be an even number of positive factors in the numerator and denominator combined. Several examples are provided of multiplying, dividing, simplifying, and evaluating expressions with integers.
Orderofoperations 201217015300
The document discusses using the order of operations to evaluate expressions. It provides the mnemonic "Please Excuse My Dear Aunt Sally" (PEMDAS) to remember the order: Parentheses, Exponents, Multiply/Divide (left to right), Add/Subtract (left to right). Several examples are worked through step-by-step to demonstrate evaluating expressions according to this order. The document also covers evaluating expressions when variables are substituted with values.
(8) Lesson 2.2 - Solve Two-Step Equations
Here is a two-step equation example with steps to solve it:
2x + 3 = 11
Subtract 3 from both sides using the subtraction property of equality:
2x + 3 - 3 = 11 - 3
2x = 8
Divide both sides by 2 using the division property of equality:
2x/2 = 8/2
x = 4
To solve a two-step equation:
1) Use addition or subtraction to isolate the variable term on one side of the equation.
2) Use multiplication or division to solve for the variable.
By applying the properties of equality, this allows you to transform the original equation into an equivalent equation where the variable term is alone
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