Transforming equations
•Download as PPT, PDF•
0 likes•866 views
This document provides background information on transforming equations and solving one-step equations using addition and subtraction. It explains that if the same number is added to or subtracted from both sides of an equation, the resulting equations will be equal. Examples are provided of solving equations by adding or subtracting the same number from both sides to isolate the variable.
Report
Share
Report
Share
![A little background information: ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]](data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7)
Recommended
Comparing and ordering integers
This document provides instruction on comparing and ordering integers. It defines integers as positive whole numbers, their opposites, and zero. It explains how to find the absolute value of integers and use comparison symbols like <, =, and > to compare integers. Examples are provided to demonstrate comparing integers, ordering integers from least to greatest on a number line, and using integer comparisons to rank scores like in golf from lowest to highest.
Understanding negative numbers
The document discusses negative numbers and how they relate to temperature scales. It provides examples of number lines that extend to the left of zero to demonstrate negative numbers. It then shows vertical and horizontal temperature scales and asks questions about finding missing numbers and comparing temperatures on the scales. Finally, it asks the reader to order a set of numbers from coldest to warmest based on their position on the temperature scale.
Integers numberline (1)
The document discusses the number line and integers. It defines a number line as having equal distances marked off from a starting point of usually 0, with arrowheads indicating the line continues infinitely in both directions. The set of numbers used on the number line is called the set of integers, which includes natural numbers, whole numbers, and negative numbers arranged in order from left to right.
Integers numberline
The document discusses the number line and integers. It defines a number line as having equal distances marked from a starting point, usually 0, and extending in both directions with arrowheads. The set of numbers used on the number line is called the integers, which includes natural numbers, whole numbers, and negative numbers arranged in order from left to right.
Integers numberline
The document discusses the number line and integers. It defines a number line as having equal distances marked off from a starting point, usually 0, and extending in both directions with arrowheads. The set of numbers used on the number line is called the integers, which includes natural numbers, whole numbers, and negative numbers arranged in order from left to right.
Adding and subtracting
The document describes several methods for adding and subtracting multi-digit numbers:
The partial-sums method involves adding numbers column-by-column from left to right, recording partial sums, and then adding the partial sums.
The column-addition method adds each column separately in any order, carrying numbers to the next column as needed.
The partial-difference method performs subtraction column-by-column from left to right, subtracting the smaller number from the larger number in each column and recording partial differences.
Introduction to Positive and Negative Numbers
The document provides an introduction to integers including:
- Definitions of positive and negative numbers and their representation on number lines
- Rules for comparing and ordering integers
- Real-world examples of how integers are used to represent things like temperature, sea level, and money
- Key concepts and rules for adding and subtracting integers including keeping the sign of the first integer the same and changing the operation and second integer's sign for subtraction
- Examples of using number lines to visually represent integer operations
- A method for proving that subtracting a negative number is the same as adding a positive number
Types of number
The document defines several types of numbers:
1) Natural numbers (counting numbers like 1, 2, 3)
2) Integers (natural numbers and their negatives)
3) Rational numbers (integers and fractions)
4) Real numbers (rational numbers and numbers that cannot be written as fractions like pi)
It also defines factors, prime numbers, and prime factors. Prime factors are factors of a number that are also prime numbers. The document provides examples of writing numbers as products of their prime factors and converting terminating decimals to fractions.
Recommended
Comparing and ordering integers
This document provides instruction on comparing and ordering integers. It defines integers as positive whole numbers, their opposites, and zero. It explains how to find the absolute value of integers and use comparison symbols like <, =, and > to compare integers. Examples are provided to demonstrate comparing integers, ordering integers from least to greatest on a number line, and using integer comparisons to rank scores like in golf from lowest to highest.
Understanding negative numbers
The document discusses negative numbers and how they relate to temperature scales. It provides examples of number lines that extend to the left of zero to demonstrate negative numbers. It then shows vertical and horizontal temperature scales and asks questions about finding missing numbers and comparing temperatures on the scales. Finally, it asks the reader to order a set of numbers from coldest to warmest based on their position on the temperature scale.
Integers numberline (1)
The document discusses the number line and integers. It defines a number line as having equal distances marked off from a starting point of usually 0, with arrowheads indicating the line continues infinitely in both directions. The set of numbers used on the number line is called the set of integers, which includes natural numbers, whole numbers, and negative numbers arranged in order from left to right.
Integers numberline
The document discusses the number line and integers. It defines a number line as having equal distances marked from a starting point, usually 0, and extending in both directions with arrowheads. The set of numbers used on the number line is called the integers, which includes natural numbers, whole numbers, and negative numbers arranged in order from left to right.
Integers numberline
The document discusses the number line and integers. It defines a number line as having equal distances marked off from a starting point, usually 0, and extending in both directions with arrowheads. The set of numbers used on the number line is called the integers, which includes natural numbers, whole numbers, and negative numbers arranged in order from left to right.
Adding and subtracting
The document describes several methods for adding and subtracting multi-digit numbers:
The partial-sums method involves adding numbers column-by-column from left to right, recording partial sums, and then adding the partial sums.
The column-addition method adds each column separately in any order, carrying numbers to the next column as needed.
The partial-difference method performs subtraction column-by-column from left to right, subtracting the smaller number from the larger number in each column and recording partial differences.
Introduction to Positive and Negative Numbers
The document provides an introduction to integers including:
- Definitions of positive and negative numbers and their representation on number lines
- Rules for comparing and ordering integers
- Real-world examples of how integers are used to represent things like temperature, sea level, and money
- Key concepts and rules for adding and subtracting integers including keeping the sign of the first integer the same and changing the operation and second integer's sign for subtraction
- Examples of using number lines to visually represent integer operations
- A method for proving that subtracting a negative number is the same as adding a positive number
Types of number
The document defines several types of numbers:
1) Natural numbers (counting numbers like 1, 2, 3)
2) Integers (natural numbers and their negatives)
3) Rational numbers (integers and fractions)
4) Real numbers (rational numbers and numbers that cannot be written as fractions like pi)
It also defines factors, prime numbers, and prime factors. Prime factors are factors of a number that are also prime numbers. The document provides examples of writing numbers as products of their prime factors and converting terminating decimals to fractions.
Number system
Introducing decimal octal hexadecimal and binary number system. Their Inter-conversion and basic arithmetic by sushil subedi
1.1 real number system dfs
This document provides an overview of different number systems:
1) It begins with an explanation of natural numbers, whole numbers, integers, rational numbers, and irrational numbers.
2) Rational numbers are defined as numbers that can be represented as fractions, while irrational numbers are non-repeating and non-terminating decimals.
3) The real number system is then introduced as the collection of all rational and irrational numbers.
Working with negative numbers The Minus times Minus thing that confuses so many
An attempt to remove the confusion so many people have when tying to do math(s) involving these little beasties.
Lesson 1.1 (8)
This document contains a mathematics lesson on writing numbers in different forms, including:
1. Converting fractions to decimals and decimals to fractions
2. Examples of solving proportions and writing decimals as fractions
3. The lesson discusses why it is helpful to write numbers in different ways, such as for measurements or when dealing with money.
C3 Ch02 01
The document provides examples and explanations for working with rational numbers, including:
- Simplifying fractions by dividing the numerator and denominator by common factors
- Writing decimals as fractions by identifying the place value of the last digit
- Writing fractions as decimals by dividing the numerator by the denominator
It includes practice problems for students to simplify fractions, write decimals as fractions, and write fractions as decimals. The quiz at the end tests these skills.
Integers
The document defines integers as numbers on the number line that include whole numbers and their opposites. Positive integers are whole numbers to the right of zero, while negative integers are whole numbers to the left of zero. Zero is neither positive nor negative. The sum of two positives or two negatives is either positive or negative, respectively. The document provides examples and links to interactive games and practice problems for adding, subtracting, and understanding integers on a number line.
NEGATIVE NUMBERS
1. The document discusses addition and subtraction of positive and negative numbers through examples. It explains that subtracting a positive number means adding its negative, and vice versa.
2. An equation for the final position of an object is presented as the sum of its initial position and distance traveled. Examples are given of calculating the final position using different starting positions and distances.
3. It is concluded that the equation for calculating the final position based on the initial position and distance traveled holds true for any pair of numbers, positive or negative. Negative solutions were historically considered invalid but are actually correct.
Negative Numbers 1
Negative numbers can be added or subtracted in simple ways. When adding a positive and negative number, the result is negative. When adding two negative numbers, the result remains negative. When subtracting a positive from a negative, the result is negative. When subtracting a negative from a negative, the operation turns into addition where the negatives are made positive.
Integers
Integers are the collection of whole numbers and their negatives. There are two types of integers: positive integers like 1, 2, 3, etc. and negative integers like -1, -2, -3, etc. Integers are ordered on the number line, with positive integers to the right of zero and negative integers to the left. Addition and subtraction of integers follows sign rules - integers with the same sign are added/subtracted normally, and integers with different signs are subtracted but keep the sign of the larger integer. Integers are used in daily calculations like balances that can be positive or negative. Multiplication and division of integers also follows consistent sign rules.
Real numbers ppt
Rational numbers can be written as fractions with an integer as the numerator and a non-zero integer as the denominator that do not share any common factors. Rational numbers can be represented by either terminating or repeating decimals. Between any two rational numbers, there exist two additional rational numbers. Irrational numbers cannot be expressed as a fraction with an integer numerator and denominator. Prime numbers are only divisible by 1 and themselves, while composite numbers are numbers greater than 1 that are not prime numbers.
Rational numbers
This document contains a lesson on rational numbers that includes:
- Definitions of rational numbers as numbers that can be written as fractions with integer numerators and non-zero denominators.
- Methods for simplifying fractions by dividing the numerator and denominator by common factors.
- Techniques for writing decimals as fractions and fractions as decimals, including terminating, repeating, and mixed numbers.
- Examples and practice problems on rational number operations.
Adding and subtracting integers
This document provides steps for adding and subtracting integers:
1) Determine if addition or subtraction is being asked and follow appropriate step. For subtraction, use the KCO method - Keep the first integer the same, Change the subtraction sign to addition, Change the second integer's sign to its opposite.
2) Add the integers if they have the same sign, subtract if they have different signs.
3) The answer will take the sign of the larger whole number.
3 1 factors, multiples and divisibility
The document discusses factors, multiples, and divisibility of numbers. It defines a number as being divisible by another if the quotient is a whole number with no remainder. A multiple is the product of a number and any whole number greater than zero. A factor is a number that divides another number with no remainder. It provides examples showing 20 is divisible by 4 and 4 is a factor of 20. It also states 15 is a multiple of 3 and 5. Divisibility rules are outlined for numbers being divisible by 2, 3, 4, 5, 6, 9, and 10.
Real numbers system
Real numbers include decimals, fractions, integers, rational numbers like fractions and repeating decimals, and irrational numbers like pi. They can be positive or negative, and are organized on a number line that extends infinitely in both directions. Real numbers are grouped into categories including counting numbers, whole numbers, integers, rational numbers, and irrational numbers.
Cube Root by Prime Factorisation
This is my first PPT Upload on SlideShare.net
Please follow me and like this presentation.
This PPT is all about Prime Factorisation
Decimals Add Subtract
This document provides instructions for adding and subtracting decimals. It explains that decimals should be aligned by place value, with zeros added to make the columns even. It also notes that when whole numbers are used in calculations, an "understood" decimal point and zeros are present but not written. Examples are provided demonstrating how to correctly add, subtract, and align decimals by placing them in columns and only combining like place values.
Maths integers
In this I am going to you all about integers like operations which can be applied on them, absolute value , comparison , etc.
Integers, roots, powers, order of operations
The document provides information about integers and order of operations. It defines integers as positive and negative numbers including zero. It explains how to compare integers using less than, greater than, and equal signs. It also defines absolute value as the distance from zero on a number line and provides examples. Rules for multiplying, dividing, adding, and subtracting integers are outlined. Finally, it discusses order of operations and provides examples of solving expressions using PEMDAS.
Free video lectures for mba
This document provides an overview of B-trees and their properties and operations. It defines B-trees as balanced search trees where every node has between m/2 and m children, discusses their properties including storing data in leaves and keys in internal nodes, and provides examples of inserting and removing items from B-trees. It also briefly discusses related data structures like 2-3 trees.
Significant Digits
Significant digits are used to represent the level of uncertanty while reporting numbers collected through a measurement device
BIDMAS-4-Demonstration.pptx
This document provides an animated demonstration of the order of operations in mathematics (BIDMAS). It shows examples of calculations with different arrangements of addition, subtraction, multiplication and division and whether the results are correct according to the standard order of operations or not. The standard order is brackets, indices, division, multiplication, addition and subtraction from left to right. Several practice questions are provided for students to calculate following this order of operations.
BIDMAS-4-Demonstration.pptx
This document provides an animated demonstration of the order of operations in mathematics (BIDMAS). It shows examples of calculations with different arrangements of addition, subtraction, multiplication and division and whether the results are correct according to the standard order of operations or not. The standard order is brackets, indices, division, multiplication, addition and subtraction from left to right. Several practice questions are provided for students to calculate following this order of operations.
More Related Content
What's hot
Number system
Introducing decimal octal hexadecimal and binary number system. Their Inter-conversion and basic arithmetic by sushil subedi
1.1 real number system dfs
This document provides an overview of different number systems:
1) It begins with an explanation of natural numbers, whole numbers, integers, rational numbers, and irrational numbers.
2) Rational numbers are defined as numbers that can be represented as fractions, while irrational numbers are non-repeating and non-terminating decimals.
3) The real number system is then introduced as the collection of all rational and irrational numbers.
Working with negative numbers The Minus times Minus thing that confuses so many
An attempt to remove the confusion so many people have when tying to do math(s) involving these little beasties.
Lesson 1.1 (8)
This document contains a mathematics lesson on writing numbers in different forms, including:
1. Converting fractions to decimals and decimals to fractions
2. Examples of solving proportions and writing decimals as fractions
3. The lesson discusses why it is helpful to write numbers in different ways, such as for measurements or when dealing with money.
C3 Ch02 01
The document provides examples and explanations for working with rational numbers, including:
- Simplifying fractions by dividing the numerator and denominator by common factors
- Writing decimals as fractions by identifying the place value of the last digit
- Writing fractions as decimals by dividing the numerator by the denominator
It includes practice problems for students to simplify fractions, write decimals as fractions, and write fractions as decimals. The quiz at the end tests these skills.
Integers
The document defines integers as numbers on the number line that include whole numbers and their opposites. Positive integers are whole numbers to the right of zero, while negative integers are whole numbers to the left of zero. Zero is neither positive nor negative. The sum of two positives or two negatives is either positive or negative, respectively. The document provides examples and links to interactive games and practice problems for adding, subtracting, and understanding integers on a number line.
NEGATIVE NUMBERS
1. The document discusses addition and subtraction of positive and negative numbers through examples. It explains that subtracting a positive number means adding its negative, and vice versa.
2. An equation for the final position of an object is presented as the sum of its initial position and distance traveled. Examples are given of calculating the final position using different starting positions and distances.
3. It is concluded that the equation for calculating the final position based on the initial position and distance traveled holds true for any pair of numbers, positive or negative. Negative solutions were historically considered invalid but are actually correct.
Negative Numbers 1
Negative numbers can be added or subtracted in simple ways. When adding a positive and negative number, the result is negative. When adding two negative numbers, the result remains negative. When subtracting a positive from a negative, the result is negative. When subtracting a negative from a negative, the operation turns into addition where the negatives are made positive.
Integers
Integers are the collection of whole numbers and their negatives. There are two types of integers: positive integers like 1, 2, 3, etc. and negative integers like -1, -2, -3, etc. Integers are ordered on the number line, with positive integers to the right of zero and negative integers to the left. Addition and subtraction of integers follows sign rules - integers with the same sign are added/subtracted normally, and integers with different signs are subtracted but keep the sign of the larger integer. Integers are used in daily calculations like balances that can be positive or negative. Multiplication and division of integers also follows consistent sign rules.
Real numbers ppt
Rational numbers can be written as fractions with an integer as the numerator and a non-zero integer as the denominator that do not share any common factors. Rational numbers can be represented by either terminating or repeating decimals. Between any two rational numbers, there exist two additional rational numbers. Irrational numbers cannot be expressed as a fraction with an integer numerator and denominator. Prime numbers are only divisible by 1 and themselves, while composite numbers are numbers greater than 1 that are not prime numbers.
Rational numbers
This document contains a lesson on rational numbers that includes:
- Definitions of rational numbers as numbers that can be written as fractions with integer numerators and non-zero denominators.
- Methods for simplifying fractions by dividing the numerator and denominator by common factors.
- Techniques for writing decimals as fractions and fractions as decimals, including terminating, repeating, and mixed numbers.
- Examples and practice problems on rational number operations.
Adding and subtracting integers
This document provides steps for adding and subtracting integers:
1) Determine if addition or subtraction is being asked and follow appropriate step. For subtraction, use the KCO method - Keep the first integer the same, Change the subtraction sign to addition, Change the second integer's sign to its opposite.
2) Add the integers if they have the same sign, subtract if they have different signs.
3) The answer will take the sign of the larger whole number.
3 1 factors, multiples and divisibility
The document discusses factors, multiples, and divisibility of numbers. It defines a number as being divisible by another if the quotient is a whole number with no remainder. A multiple is the product of a number and any whole number greater than zero. A factor is a number that divides another number with no remainder. It provides examples showing 20 is divisible by 4 and 4 is a factor of 20. It also states 15 is a multiple of 3 and 5. Divisibility rules are outlined for numbers being divisible by 2, 3, 4, 5, 6, 9, and 10.
Real numbers system
Real numbers include decimals, fractions, integers, rational numbers like fractions and repeating decimals, and irrational numbers like pi. They can be positive or negative, and are organized on a number line that extends infinitely in both directions. Real numbers are grouped into categories including counting numbers, whole numbers, integers, rational numbers, and irrational numbers.
Cube Root by Prime Factorisation
This is my first PPT Upload on SlideShare.net
Please follow me and like this presentation.
This PPT is all about Prime Factorisation
Decimals Add Subtract
This document provides instructions for adding and subtracting decimals. It explains that decimals should be aligned by place value, with zeros added to make the columns even. It also notes that when whole numbers are used in calculations, an "understood" decimal point and zeros are present but not written. Examples are provided demonstrating how to correctly add, subtract, and align decimals by placing them in columns and only combining like place values.
Maths integers
In this I am going to you all about integers like operations which can be applied on them, absolute value , comparison , etc.
Integers, roots, powers, order of operations
The document provides information about integers and order of operations. It defines integers as positive and negative numbers including zero. It explains how to compare integers using less than, greater than, and equal signs. It also defines absolute value as the distance from zero on a number line and provides examples. Rules for multiplying, dividing, adding, and subtracting integers are outlined. Finally, it discusses order of operations and provides examples of solving expressions using PEMDAS.
Free video lectures for mba
This document provides an overview of B-trees and their properties and operations. It defines B-trees as balanced search trees where every node has between m/2 and m children, discusses their properties including storing data in leaves and keys in internal nodes, and provides examples of inserting and removing items from B-trees. It also briefly discusses related data structures like 2-3 trees.
Significant Digits
Significant digits are used to represent the level of uncertanty while reporting numbers collected through a measurement device
What's hot (20)
Working with negative numbers The Minus times Minus thing that confuses so many
Working with negative numbers The Minus times Minus thing that confuses so many
Similar to Transforming equations
BIDMAS-4-Demonstration.pptx
This document provides an animated demonstration of the order of operations in mathematics (BIDMAS). It shows examples of calculations with different arrangements of addition, subtraction, multiplication and division and whether the results are correct according to the standard order of operations or not. The standard order is brackets, indices, division, multiplication, addition and subtraction from left to right. Several practice questions are provided for students to calculate following this order of operations.
BIDMAS-4-Demonstration.pptx
This document provides an animated demonstration of the order of operations in mathematics (BIDMAS). It shows examples of calculations with different arrangements of addition, subtraction, multiplication and division and whether the results are correct according to the standard order of operations or not. The standard order is brackets, indices, division, multiplication, addition and subtraction from left to right. Several practice questions are provided for students to calculate following this order of operations.
Solving equations
This document provides an introduction to solving equations. It explains the key properties of equality that must be followed when solving equations, such as performing the same operation to both sides of the equal sign. Examples are provided to demonstrate applying these properties to solve one-step, two-step, and multi-step equations. Students are instructed to show their work and given practice problems applying the steps to solve different types of equations.
1-5.ppt
This document discusses adding integers. It defines additive inverses as two numbers with a sum of zero, such as 23 and -23. When adding opposites, their sum is zero. To add integers that are not opposites, number lines can be used. An example word problem involves subtracting 8 yards and adding 3 yards for a football team, resulting in a loss of 5 yards. The rules for adding integers are provided: numbers with the same sign are added, numbers with different signs are solved by subtracting the digits and keeping the sign of the larger number.
adding integers.ppt
The document discusses adding integers. It defines additive inverses as two numbers with a sum of zero, such as 23 and -23. When adding opposites, their sum is zero. A number line is an excellent way to add positive and negative numbers that are not opposites. An example problem asks for the yardage of a football team's first two plays, where the first play lost 8 yards and the second gained 3 yards. By representing this on a number line, the total yardage is calculated to be -5 yards. General rules are provided for adding numbers with the same or different signs.
Long division and synthetic division
In algebra, polynomial long division is an algorithm for dividing a polynomial by another polynomial of the same or lower degree, a generalized version of the familiar arithmetic technique called long division. It can be done easily by hand, because it separates an otherwise complex division problem into smaller ones.
In algebra, the synthetic division is a method for manually performing Euclidean division of polynomials, with less writing and fewer calculations than the long division. It is mostly taught for division by linear monic polynomials, but the method can be generalized to division by any polynomial.
References:
https://en.wikipedia.org/wiki/Polynomial_long_division
https://en.wikipedia.org/wiki/Synthetic_division
Chapter 2 Review
This document discusses equivalence and solving equations. It begins with defining equivalence as the product of a number and its multiplicative inverse being 1. It then provides examples of solving various equations using properties of equality like addition, subtraction, multiplication and division. These include one-step, two-step and multi-step equations with or without variables on both sides. It also discusses equations having no solutions, one solution, or infinitely many solutions.
Chapter 3
1. The document discusses solving and checking equations, solving and graphing inequalities, finding area and perimeter of shapes, and writing word problems as equations.
2. Key concepts covered include using inverse operations to solve one-step and two-step equations, checking equations by rewriting and substituting values, and solving and graphing inequalities.
3. Examples are provided for solving equations, finding missing dimensions of shapes, writing and solving inequalities to model word problems, and translating verbal expressions into mathematical equations.
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.
AFS7 Math 1
The document provides explanations and examples for adding, subtracting, multiplying, and dividing integers:
1) When adding integers with the same sign, add their absolute values and use the common sign. When adding integers with opposite signs, take the absolute difference and use the sign of the larger number.
2) To subtract an integer, add its opposite and then follow the addition rules.
3) When multiplying an even number of negatives, the result is positive. With an odd number of negatives, the result is negative.
AFS Math 3
The document provides explanations and examples for adding, subtracting, multiplying, and dividing integers.
It begins by explaining the rules for adding integers with the same sign and integers with different signs, providing examples such as -6 + -2 = -8. It then explains that subtracting integers uses the rule of "adding the opposite" and provides examples like 7 - (-6) = 13.
The document also covers multiplying and dividing integers, noting that an even number of negatives yields a positive result and an odd number yields a negative result. It provides examples such as -2(-2)(-2)= 16 and 2 (-5)= -10.
Similar to Transforming equations (12)
More from joannahstevens
Linear combination
This document provides instructions on how to solve systems of linear equations using the linear combination method, also known as the elimination method or add/subtract method. It gives examples of using this method to solve systems by eliminating a variable through adding or subtracting the equations. Practice problems are provided for the reader to solve systems of equations using the linear combination method.
Solving systems by substitution
Here are the steps to solve this problem:
Let x = one number
Let y = the other number
x + y = 84
x = 3y
x + 3y = 84
4y = 84
y = 21
x = 3(21) = 63
The numbers are 21 and 63.
Jeopardy review
1. This document contains math word problems and questions about graphing lines, writing equations of lines, finding slopes, and solving inequalities.
2. It asks the learner to summarize slope, graph lines, find slopes of lines, write equations in slope-intercept form, and solve various math problems.
3. The questions cover topics like finding slopes, writing equations, graphing lines and inequalities, finding intercepts, parallel and perpendicular lines, and solving systems of equations.
Introduction to coordinate geometry
Any point on a plane can be named with two numbers called coordinates - an x-coordinate for the distance from the origin along the x-axis and a y-coordinate for the distance along the y-axis. The coordinate grid is divided into four quadrants by the x and y axes, and points can be plotted in the grid and identified by their coordinates and quadrant. Linear equations can be graphed by making a table of solutions and plotting the points, then drawing a straight line through them.
F(x) terminology
This document contains terminology and examples related to functions. It defines f(x) as "the value of y in function f, where the independent variable is x". It provides examples of evaluating functions like f(x) = -7x + 100 for different x values. It also gives examples of composite functions like f(f(x)) and using different functions like f(x) and g(x) together. The examples relate to word problems about distances over time on a boat trip.
Translating words into symbols
This document provides examples of translating word problems into mathematical equations and then solving those equations. It contains sample word problems that translate to equations involving addition, subtraction, multiplication and division. It also includes guidance on common phrases like "less than" and their symbolic representations. Finally, it provides two word problems as examples for students to practice translating words into mathematical symbols.
Inequalities
This document provides information and examples about solving inequalities:
1) It gives examples of solving linear equations with one variable and two variables.
2) It explains the symbols used for different inequality types and how to graph them, including shading the correct side of the inequality.
3) It provides rules for solving inequalities, such as reversing the inequality sign when multiplying or dividing both sides by a negative number.
4) Multiple examples are worked through step-by-step of solving and graphing various inequalities with one variable and multiple variables.
Solving equations with variables on both sides & translating words into symbols
This document contains sample math problems and notes about solving equations with variables on both sides. It includes examples of solving equations like 5y - 3y + 13 = 26, 3s + 2 = 8, 2d + 3d = 15, and 2(w -1) + 8 = 16. The notes provide instructions for solving equations where variables are on both sides, such as 6x = 4x + 18, 3y = 15 - 2y, and 7(a - 2) - 6 = 2a + 8 + a. The document also references a Solving Equations BINGO activity and exit slip homework.
4.3 cramer’s rule
The document provides information about solving systems of linear equations using Cramer's rule, including:
- Cramer's rule uses determinants of the coefficient matrix to solve systems of linear equations.
- For a 2x2 system, if the determinant of the coefficient matrix is not equal to 0, there is exactly one solution.
- The solutions are found by taking the determinants of the numerator matrices (with one column replaced by the constants) divided by the determinant of the coefficient matrix.
- Several examples demonstrate solving 2x2 systems using Cramer's rule.
Solving percent equations
The document discusses percentages and solving percentage equations. It provides examples of how to write percentage equations for word problems, such as finding what percentage one number is of another or finding the total given a percentage. It demonstrates solving equations to find percentages and totals in various contexts like test scores, class sizes, sales, and more. Percentages allow for easier comparison of quantities and are used in many everyday situations like grades, weather, nutrition labels, and shopping.
Decimals, fractions, and percents
This document discusses how to convert between decimals, fractions, and percents. It provides examples for converting non-repeating and repeating decimals to fractions by dropping the decimal point and putting the number over the place value. It also demonstrates how to convert fractions to decimals by dividing the numerator by the denominator and moving the decimal point. Additionally, it shows how to convert decimals to percents by moving the decimal point two places to the right and adding the percent sign, and how to convert percents to decimals by moving the decimal point two places to the left and dropping the percent sign.
Notes on 3.2 properties of linear frunction graphs
The document discusses key properties of linear function graphs, including that the y-intercept is the y-value when x=0 and the x-intercept is the x-value when y=0. It defines slope as m in the slope-intercept equation y=mx+b and describes horizontal and vertical lines having slopes of 0 and undefined respectively. It lists three common forms for linear functions: slope-intercept, point-slope, and Ax+By=C and provides examples of transforming between the forms.
Proportions & school pictures
The document discusses proper proportions for various items like wallets, photos, and the American flag. It poses a math problem asking what the width of a 57cm long American flag would need to be in order to have the official proportion of 19 units in length for every 10 units in width.
Inequalities
This document discusses inequalities and provides examples of solving various inequality expressions. It begins by giving an example of a negative number that is not closed under multiplication. It then defines common inequality symbols like less than, greater than, less than or equal to, and greater than or equal to. The document proceeds to give examples of solving linear inequalities assuming the domain is all real numbers, including compound inequalities involving absolute value expressions. It concludes with examples for an exit slip problem set involving solving several inequalities.
The matrix
The document contains information about the reciprocal of 1/9, the value of |-8+-2|, the difference between a January wind chill of -8 degrees and an August heat index of 108 degrees. It also contains a summary of the 1999 film The Matrix and definitions of a matrix and rules for adding, subtracting and multiplying matrices by scalars.
Simplifying expressions, solving, domain and range
This document appears to be notes from a math class covering simplifying expressions, solving equations, and domain and range. It includes examples of irrational and imaginary numbers, naming polynomials by degree and terms, multiplying binomials, homework assignments on the topics, and notes on using the vertical line test to determine if a relation is a function by checking if each x-value has exactly one y-value. Sketching graphs of functions given domains and ranges is also mentioned.
04.07.10 more volume exercises
The document provides instructions to sketch and calculate the volumes of different shapes, including a rectangular prism with dimensions of 3 mm by 5 mm by 15 mm, a cylinder with a diameter of 2.6 m and height of 3.5 m, a rectangular prism with dimensions of 6 inches by 6 inches by 9 inches, and a cylinder with a radius of 3 yards and height of 10 yards. It also gives problems to find the height of a rectangular prism with given length, width, and volume, and to find the radius and height of cylinders with given dimensions and volumes.
04.08.10 applications of volume and surface area
The document contains 4 applications that use surface area and volume concepts:
1) Finding the height of an aquarium tank given its dimensions and volume.
2) Comparing the surface area and volume of a can and box to determine which holds more juice.
3) Calculating the surface area of a gift to see if a sheet of wrapping paper is large enough.
4) Determining which pizza sauce jar is a better buy based on price and volume.
04.07.10 more volume
The document provides instructions for calculating the volumes of different shapes, including a rectangular prism and cylinder. It asks the reader to first predict which solids have the greatest and least volumes without calculations. It then has the reader measure dimensions of different solids to calculate their actual volumes and rank them. Finally, it gives two word problems to find heights using given lengths, widths, radii and volumes.
More from joannahstevens (20)
Solving equations with variables on both sides & translating words into symbols
Solving equations with variables on both sides & translating words into symbols
Notes on 3.2 properties of linear frunction graphs
Notes on 3.2 properties of linear frunction graphs
Simplifying expressions, solving, domain and range
Simplifying expressions, solving, domain and range
Transforming equations
- 1. Section 3.1 Transforming Equations