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P.E.M.D.A.S is an acronym that represents the order of operations in mathematics: Parentheses, Exponents, Multiply, Divide, Add, Subtract. It provides a standard order to evaluate terms within an expression or equation. The document explains each step of P.E.M.D.A.S and provides examples to demonstrate how to use the order of operations to solve problems with multiple operations. It emphasizes that following P.E.M.D.A.S and checking your work is important to getting the right solution.

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Polygons

This document provides information about polygons, including definitions, terminology, properties of different types of polygons, and formulas relating the number of sides, angles, and diagonals. It defines a polygon as a closed, two-dimensional figure formed by three or more line segments. Regular polygons are introduced as those with all sides the same length and all interior angles the same measure. Formulas are given relating the number of sides of a regular polygon to the sum of its interior angles, the measure of each interior angle, and the number of diagonals and triangles it contains. Interior and exterior angles are defined and their relationships explored. Examples and problems are worked through, such as finding missing angle measures.

Positive and negative numbers

Positive numbers are greater than zero, negative numbers are less than zero. Opposite numbers are the same distance from zero but in opposite directions. Integers include all whole numbers and their opposites on a number line. When adding positive and negative numbers, if the signs are the same you add the numbers and keep the sign, if the signs are different you subtract the smaller number and use the sign of the larger number. Adding numbers on a number line involves counting right for positive numbers and left for negative numbers.

Algebraic expression

Algebra is a branch of mathematics that uses letters and symbols to represent numbers and quantities in expressions and equations. Key terms in algebra include variables, which can represent different numbers; replacement sets, which define the possible values a variable can take; and constants, which always represent the same number. Algebraic expressions combine variables, constants, and operation symbols using grouping symbols and relationship symbols to represent a mathematical relationship between quantities.

Converting units of time

This document provides conversions between units of time including minutes, hours, days, weeks, years, decades, centuries and millennia. Specifically, it notes that 1 minute equals 60 seconds, 1 hour equals 60 minutes, 1 day equals 24 hours, 1 week equals 7 days, and 1 year equals 365 days or 52 weeks.

4th grade geometry revised

This document provides an overview of the key topics and concepts covered in a 4th grade geometry unit, including learning to name, classify, and create different shapes (triangles, squares, circles etc.), polygons, and 3D objects; it also suggests various activities and online resources to reinforce these geometric concepts.

Fractions, Decimals, and Percents

This document defines decimals, fractions, and percents and provides steps for converting between them. Decimals are numbers with a decimal point, fractions show parts of a whole, and percents express amounts out of 100. To convert a fraction to a decimal, divide the numerator by the denominator. To convert a fraction to a percent, change it to a decimal then multiply by 100. Converting between other forms follows similar steps of changing the number to an equivalent decimal or percent value.

Perimeter and Area of irregular shapes

To find the perimeter and area of irregular shapes, the document explains breaking the shape into regular components and calculating their individual perimeters and areas. The perimeter is the distance around a shape found by adding all side lengths. Area is the space within a shape, found by breaking irregular shapes into rectangles, triangles, squares and calculating their individual areas. An example calculates the perimeter as 46 cm and area as 105 sq cm for a shape broken into a rectangle and square.

Area of-rectangles

The document discusses calculating the area and perimeter of rectangles and shapes made from rectangles. It defines area as a measure of surface covered and perimeter as the distance around a shape. It provides the formulas for calculating the perimeter and area of rectangles as well as squares, which are special rectangles where the length and width are equal. It also explains how to find the total area of shapes made up of multiple rectangles by calculating the individual areas and summing them.

Polygons

This document provides information about polygons, including definitions, terminology, properties of different types of polygons, and formulas relating the number of sides, angles, and diagonals. It defines a polygon as a closed, two-dimensional figure formed by three or more line segments. Regular polygons are introduced as those with all sides the same length and all interior angles the same measure. Formulas are given relating the number of sides of a regular polygon to the sum of its interior angles, the measure of each interior angle, and the number of diagonals and triangles it contains. Interior and exterior angles are defined and their relationships explored. Examples and problems are worked through, such as finding missing angle measures.

Positive and negative numbers

Positive numbers are greater than zero, negative numbers are less than zero. Opposite numbers are the same distance from zero but in opposite directions. Integers include all whole numbers and their opposites on a number line. When adding positive and negative numbers, if the signs are the same you add the numbers and keep the sign, if the signs are different you subtract the smaller number and use the sign of the larger number. Adding numbers on a number line involves counting right for positive numbers and left for negative numbers.

Algebraic expression

Algebra is a branch of mathematics that uses letters and symbols to represent numbers and quantities in expressions and equations. Key terms in algebra include variables, which can represent different numbers; replacement sets, which define the possible values a variable can take; and constants, which always represent the same number. Algebraic expressions combine variables, constants, and operation symbols using grouping symbols and relationship symbols to represent a mathematical relationship between quantities.

Converting units of time

This document provides conversions between units of time including minutes, hours, days, weeks, years, decades, centuries and millennia. Specifically, it notes that 1 minute equals 60 seconds, 1 hour equals 60 minutes, 1 day equals 24 hours, 1 week equals 7 days, and 1 year equals 365 days or 52 weeks.

4th grade geometry revised

This document provides an overview of the key topics and concepts covered in a 4th grade geometry unit, including learning to name, classify, and create different shapes (triangles, squares, circles etc.), polygons, and 3D objects; it also suggests various activities and online resources to reinforce these geometric concepts.

Fractions, Decimals, and Percents

This document defines decimals, fractions, and percents and provides steps for converting between them. Decimals are numbers with a decimal point, fractions show parts of a whole, and percents express amounts out of 100. To convert a fraction to a decimal, divide the numerator by the denominator. To convert a fraction to a percent, change it to a decimal then multiply by 100. Converting between other forms follows similar steps of changing the number to an equivalent decimal or percent value.

Perimeter and Area of irregular shapes

To find the perimeter and area of irregular shapes, the document explains breaking the shape into regular components and calculating their individual perimeters and areas. The perimeter is the distance around a shape found by adding all side lengths. Area is the space within a shape, found by breaking irregular shapes into rectangles, triangles, squares and calculating their individual areas. An example calculates the perimeter as 46 cm and area as 105 sq cm for a shape broken into a rectangle and square.

Area of-rectangles

The document discusses calculating the area and perimeter of rectangles and shapes made from rectangles. It defines area as a measure of surface covered and perimeter as the distance around a shape. It provides the formulas for calculating the perimeter and area of rectangles as well as squares, which are special rectangles where the length and width are equal. It also explains how to find the total area of shapes made up of multiple rectangles by calculating the individual areas and summing them.

Factors and Multiples

Factors are numbers that when multiplied together equal another number. The document provides examples of finding the factors of numbers like 8, 12, 17, and 30. It also has students find the factors of 16 and 24. Multiples are numbers obtained by multiplying a number by 1, 2, 3, and so on. Examples of multiples of 2, 3, and 10 are given. Students are assigned to write the factors of 28, 50, and 21 and the multiples of 5 and 9 on a quarter sheet of paper.

Decimal

The document provides an overview of decimals, including what they are, their history, place value, comparing, rounding, adding, subtracting, multiplying, and dividing decimals. Key points covered include how decimals are used to represent fractional values, the importance of place value when working with decimals, and techniques for rounding, adding, subtracting, multiplying and dividing decimals accurately.

Ratio & proportion

The document discusses ratios, proportions, and scale drawings. It begins by defining a ratio as a comparison of two or more quantities without units. Ratios can be written in different forms such as a:b or a to b. A proportion is an equation stating that one ratio is equal to another. Direct proportion means that as one quantity increases, the other also increases by the same factor. Inverse proportion means that as one quantity increases, the other decreases. Scale drawings use a scale ratio to show the relationship between an object's depicted size and its actual size. Examples are provided to demonstrate calculating ratios, proportions, direct and inverse proportions, and using scale ratios.

Comparing And Ordering Decimals

1) The document discusses ordering decimals from least to greatest using place value and number lines. It provides examples of ordering prices from a McDonald's menu and test scores.
2) Equivalent decimals have the same value even if they have a different number of decimal places. Annexing zeros by adding trailing zeros does not change a decimal's value.
3) To order decimals from least to greatest, decimals are first lined up and zeros are annexed to give each number the same number of decimal places. Then the decimals are compared using place value starting from the left.

Commutative And Associative Properties

The document discusses the commutative and associative properties of real numbers. The commutative property states that the order of numbers does not matter in addition and multiplication, but it does matter in subtraction and division. The associative property states that the grouping of numbers does not matter in addition and multiplication, but it does matter in subtraction and division. Both properties only apply to addition and multiplication, not subtraction and division.

PERIMETER AND AREA

This document provides examples and explanations of how to calculate the area and perimeter of various shapes, including squares, rectangles, and irregular figures. It gives step-by-step instructions on using the formulas for area (A=s x s for squares, A=l x w for rectangles) and counting sides to find perimeter. Students are then given practice problems to measure perimeters of shapes from a previous activity using rulers.

Properties of 3 d shapes

The document defines and provides information about various 3D shapes. It discusses cubes, cuboids, triangular prisms, regular tetrahedrons, spheres, cylinders, cones, square-based pyramids and their key features such as the number of faces, vertices and edges. It also provides information about prisms and nets of 3D shapes.

Place value 4 digit numbers

- Welcome to the Virtual Math Lesson on Place Value in Numbers up to 10 000
- The class will learn about place value through understanding digits and their place values in numbers up to 10 000.
- Activities will include making numbers from number cards, identifying place values on an abacus and place value chart, writing numbers, and testing learning.

Proportion

This document discusses ratios, rates, proportions, and how to use them to solve real-life problems. It provides examples of how to:
- Write ratios comparing two numbers or quantities
- Calculate rates when the numerator and denominator are in different units
- Use unit analysis to determine the correct units for rates and proportions
- Set up and solve proportions using the reciprocal and cross product properties

Bar graphs intro lesson

This document explains how to create a bar graph to represent data. It uses a set of data counting the number of skittles of different colors as an example. The document outlines the steps to make a bar graph, including determining the axes, labeling them, and then graphing the data points. It then discusses what can be observed from the completed bar graph, such as which color has the most or least skittles and determining the total number counted.

Fraction | Grade 5 | PowerPoint Slides

These slides are related to the topic fraction. It includes definitions of fractions, equivalent fractions, types of fractions, and much more...

Intro to ratios, rates, and unit rates

This document introduces ratios, rates, and unit rates. It defines ratios as comparisons using quantities, rates as comparisons of quantities with different units, and unit rates as comparisons where one quantity is 1 unit. Examples are given such as the ratio of green to purple aliens. Rates are defined using examples like miles per hour. Unit rates are introduced as comparisons where one quantity is 1 unit, like eyes per alien. The document includes activities to identify and represent different ratios, rates, and unit rates.

Factors and multiples

The document provides an overview of factors and multiples in mathematics. It defines factors as numbers that divide evenly into another number, and multiples as numbers that another number divides evenly into. It discusses finding common factors and common multiples between two numbers, as well as decomposing numbers into their prime factors. The document also covers calculating the highest common factor and lowest common multiple of two numbers using prime factor decomposition. Finally, it provides some practice problems for readers to work through.

Decimals

This document provides an introduction to decimals for students. It begins with an overview of decimals and then discusses how to write, read, and compare decimal values. Examples are provided such as writing amounts of money in decimal form. The document explains place value of decimals and how to use symbols like tenths, hundredths and thousandths. Students are given opportunities to practice writing, reading and comparing decimal values through interactive exercises.

Translations, rotations, reflections, and dilations

This document discusses different types of geometric transformations including translations, rotations, reflections, and dilations. Translations move a figure across a plane without changing its size. Rotations turn a figure around a point or line. Reflections flip a figure across a line to create a mirror image. Dilation changes the size of a figure by enlarging or reducing it using a scale factor, while keeping the shape intact. The document provides examples and definitions of each transformation type.

Basic algebra

Algebra is used in many field in many different ways to solve equation problems, and in business algebra is also used or in our day to day life it is also used. ... Algebra is a way of keeping track of unknown values, which can be used in equations.

Quadrilaterals

The document defines and compares different types of quadrilaterals (shapes with four sides):
- Squares and rhombi both have four sides of equal length but squares have four right angles while rhombi have two acute and two obtuse angles.
- Rectangles and parallelograms both have two sets of parallel sides but rectangles have four right angles while parallelograms have two acute and two obtuse angles.
- Trapezoids have two sides that are parallel and two sides that are not parallel.

Oprations Of Decimal Numbers

This document provides instructions for performing basic operations with decimals such as addition, subtraction, multiplication, and division. It explains how to align the decimals and describes the steps for each operation. Examples are provided for adding, subtracting, multiplying, and dividing decimals. The document also covers comparing and converting fractions and decimals, with examples of how to convert a fraction to a decimal and vice versa. It concludes with contact information.

Multiply by 10, 100, 1000, etc...

The document explains how to multiply numbers by 10, 100, and 1,000. It notes that in the decimal system, each place value represents a number 10 times greater than the place to its right. To multiply a number like 6 by 10, we write the 6 in the ones place of the next column with a 0 placeholder. The same process is followed for multiplying by 100 and 1,000, moving the number over two and three columns respectively and adding zero placeholders. Examples are provided to demonstrate multiplying single-digit numbers by 10, 100 and 1,000.

Least common multiple

The document discusses the concept of the least common multiple (LCM). It defines the LCM as the lowest number that is a multiple of two or more numbers. It provides examples of finding the LCM of different pairs of numbers by listing their multiples and circling the first number that is common to both lists. The document also discusses how the LCM can be used to find patterns involving multiples and to add or subtract fractions by finding a common denominator.

PEDMAS ppt. For Mrs. Ewart

This document explains the order of operations using the acronym PEMDAS:
1. PEMDAS stands for Parentheses, Exponents, Multiplication, Division, Addition, Subtraction. This determines the order you solve terms in a mathematical expression.
2. First you solve anything inside parentheses. Then exponents, then multiplication and division from left to right. Finally, addition and subtraction are solved from left to right.
3. Some example problems are worked out step-by-step to demonstrate using PEMDAS, with the answers provided to check your work. Key vocabulary terms are also defined.

Business Mathematics

The document provides an overview of a business mathematics course presented by a group of students from Aklan State University. It covers several topics in business mathematics including rounding numbers, fundamental arithmetic operations with decimals and fractions, algebraic symbols and expressions, writing equations, income statements, and bank reconciliation. The document contains examples and explanations for each topic.

Factors and Multiples

Factors are numbers that when multiplied together equal another number. The document provides examples of finding the factors of numbers like 8, 12, 17, and 30. It also has students find the factors of 16 and 24. Multiples are numbers obtained by multiplying a number by 1, 2, 3, and so on. Examples of multiples of 2, 3, and 10 are given. Students are assigned to write the factors of 28, 50, and 21 and the multiples of 5 and 9 on a quarter sheet of paper.

Decimal

The document provides an overview of decimals, including what they are, their history, place value, comparing, rounding, adding, subtracting, multiplying, and dividing decimals. Key points covered include how decimals are used to represent fractional values, the importance of place value when working with decimals, and techniques for rounding, adding, subtracting, multiplying and dividing decimals accurately.

Ratio & proportion

The document discusses ratios, proportions, and scale drawings. It begins by defining a ratio as a comparison of two or more quantities without units. Ratios can be written in different forms such as a:b or a to b. A proportion is an equation stating that one ratio is equal to another. Direct proportion means that as one quantity increases, the other also increases by the same factor. Inverse proportion means that as one quantity increases, the other decreases. Scale drawings use a scale ratio to show the relationship between an object's depicted size and its actual size. Examples are provided to demonstrate calculating ratios, proportions, direct and inverse proportions, and using scale ratios.

Comparing And Ordering Decimals

1) The document discusses ordering decimals from least to greatest using place value and number lines. It provides examples of ordering prices from a McDonald's menu and test scores.
2) Equivalent decimals have the same value even if they have a different number of decimal places. Annexing zeros by adding trailing zeros does not change a decimal's value.
3) To order decimals from least to greatest, decimals are first lined up and zeros are annexed to give each number the same number of decimal places. Then the decimals are compared using place value starting from the left.

Commutative And Associative Properties

The document discusses the commutative and associative properties of real numbers. The commutative property states that the order of numbers does not matter in addition and multiplication, but it does matter in subtraction and division. The associative property states that the grouping of numbers does not matter in addition and multiplication, but it does matter in subtraction and division. Both properties only apply to addition and multiplication, not subtraction and division.

PERIMETER AND AREA

This document provides examples and explanations of how to calculate the area and perimeter of various shapes, including squares, rectangles, and irregular figures. It gives step-by-step instructions on using the formulas for area (A=s x s for squares, A=l x w for rectangles) and counting sides to find perimeter. Students are then given practice problems to measure perimeters of shapes from a previous activity using rulers.

Properties of 3 d shapes

The document defines and provides information about various 3D shapes. It discusses cubes, cuboids, triangular prisms, regular tetrahedrons, spheres, cylinders, cones, square-based pyramids and their key features such as the number of faces, vertices and edges. It also provides information about prisms and nets of 3D shapes.

Place value 4 digit numbers

- Welcome to the Virtual Math Lesson on Place Value in Numbers up to 10 000
- The class will learn about place value through understanding digits and their place values in numbers up to 10 000.
- Activities will include making numbers from number cards, identifying place values on an abacus and place value chart, writing numbers, and testing learning.

Proportion

This document discusses ratios, rates, proportions, and how to use them to solve real-life problems. It provides examples of how to:
- Write ratios comparing two numbers or quantities
- Calculate rates when the numerator and denominator are in different units
- Use unit analysis to determine the correct units for rates and proportions
- Set up and solve proportions using the reciprocal and cross product properties

Bar graphs intro lesson

This document explains how to create a bar graph to represent data. It uses a set of data counting the number of skittles of different colors as an example. The document outlines the steps to make a bar graph, including determining the axes, labeling them, and then graphing the data points. It then discusses what can be observed from the completed bar graph, such as which color has the most or least skittles and determining the total number counted.

Fraction | Grade 5 | PowerPoint Slides

These slides are related to the topic fraction. It includes definitions of fractions, equivalent fractions, types of fractions, and much more...

Intro to ratios, rates, and unit rates

This document introduces ratios, rates, and unit rates. It defines ratios as comparisons using quantities, rates as comparisons of quantities with different units, and unit rates as comparisons where one quantity is 1 unit. Examples are given such as the ratio of green to purple aliens. Rates are defined using examples like miles per hour. Unit rates are introduced as comparisons where one quantity is 1 unit, like eyes per alien. The document includes activities to identify and represent different ratios, rates, and unit rates.

Factors and multiples

The document provides an overview of factors and multiples in mathematics. It defines factors as numbers that divide evenly into another number, and multiples as numbers that another number divides evenly into. It discusses finding common factors and common multiples between two numbers, as well as decomposing numbers into their prime factors. The document also covers calculating the highest common factor and lowest common multiple of two numbers using prime factor decomposition. Finally, it provides some practice problems for readers to work through.

Decimals

This document provides an introduction to decimals for students. It begins with an overview of decimals and then discusses how to write, read, and compare decimal values. Examples are provided such as writing amounts of money in decimal form. The document explains place value of decimals and how to use symbols like tenths, hundredths and thousandths. Students are given opportunities to practice writing, reading and comparing decimal values through interactive exercises.

Translations, rotations, reflections, and dilations

This document discusses different types of geometric transformations including translations, rotations, reflections, and dilations. Translations move a figure across a plane without changing its size. Rotations turn a figure around a point or line. Reflections flip a figure across a line to create a mirror image. Dilation changes the size of a figure by enlarging or reducing it using a scale factor, while keeping the shape intact. The document provides examples and definitions of each transformation type.

Basic algebra

Algebra is used in many field in many different ways to solve equation problems, and in business algebra is also used or in our day to day life it is also used. ... Algebra is a way of keeping track of unknown values, which can be used in equations.

Quadrilaterals

The document defines and compares different types of quadrilaterals (shapes with four sides):
- Squares and rhombi both have four sides of equal length but squares have four right angles while rhombi have two acute and two obtuse angles.
- Rectangles and parallelograms both have two sets of parallel sides but rectangles have four right angles while parallelograms have two acute and two obtuse angles.
- Trapezoids have two sides that are parallel and two sides that are not parallel.

Oprations Of Decimal Numbers

This document provides instructions for performing basic operations with decimals such as addition, subtraction, multiplication, and division. It explains how to align the decimals and describes the steps for each operation. Examples are provided for adding, subtracting, multiplying, and dividing decimals. The document also covers comparing and converting fractions and decimals, with examples of how to convert a fraction to a decimal and vice versa. It concludes with contact information.

Multiply by 10, 100, 1000, etc...

The document explains how to multiply numbers by 10, 100, and 1,000. It notes that in the decimal system, each place value represents a number 10 times greater than the place to its right. To multiply a number like 6 by 10, we write the 6 in the ones place of the next column with a 0 placeholder. The same process is followed for multiplying by 100 and 1,000, moving the number over two and three columns respectively and adding zero placeholders. Examples are provided to demonstrate multiplying single-digit numbers by 10, 100 and 1,000.

Least common multiple

The document discusses the concept of the least common multiple (LCM). It defines the LCM as the lowest number that is a multiple of two or more numbers. It provides examples of finding the LCM of different pairs of numbers by listing their multiples and circling the first number that is common to both lists. The document also discusses how the LCM can be used to find patterns involving multiples and to add or subtract fractions by finding a common denominator.

Factors and Multiples

Factors and Multiples

Decimal

Decimal

Ratio & proportion

Ratio & proportion

Comparing And Ordering Decimals

Comparing And Ordering Decimals

Commutative And Associative Properties

Commutative And Associative Properties

PERIMETER AND AREA

PERIMETER AND AREA

Properties of 3 d shapes

Properties of 3 d shapes

Place value 4 digit numbers

Place value 4 digit numbers

Proportion

Proportion

Bar graphs intro lesson

Bar graphs intro lesson

Fraction | Grade 5 | PowerPoint Slides

Fraction | Grade 5 | PowerPoint Slides

Intro to ratios, rates, and unit rates

Intro to ratios, rates, and unit rates

Factors and multiples

Factors and multiples

Decimals

Decimals

Translations, rotations, reflections, and dilations

Translations, rotations, reflections, and dilations

Basic algebra

Basic algebra

Quadrilaterals

Quadrilaterals

Oprations Of Decimal Numbers

Oprations Of Decimal Numbers

Multiply by 10, 100, 1000, etc...

Multiply by 10, 100, 1000, etc...

Least common multiple

Least common multiple

PEDMAS ppt. For Mrs. Ewart

This document explains the order of operations using the acronym PEMDAS:
1. PEMDAS stands for Parentheses, Exponents, Multiplication, Division, Addition, Subtraction. This determines the order you solve terms in a mathematical expression.
2. First you solve anything inside parentheses. Then exponents, then multiplication and division from left to right. Finally, addition and subtraction are solved from left to right.
3. Some example problems are worked out step-by-step to demonstrate using PEMDAS, with the answers provided to check your work. Key vocabulary terms are also defined.

Business Mathematics

The document provides an overview of a business mathematics course presented by a group of students from Aklan State University. It covers several topics in business mathematics including rounding numbers, fundamental arithmetic operations with decimals and fractions, algebraic symbols and expressions, writing equations, income statements, and bank reconciliation. The document contains examples and explanations for each topic.

Order of Operations

This document provides an explanation of the order of operations, known by the acronym PEMDAS. It explains each component of PEMDAS in order: parenthesis, exponents, multiplication, division, addition, subtraction. For each operation, it provides examples of how to evaluate them based on their place in the order of operations. It also recommends writing out PEMDAS next to problems and crossing out operations as they are used to help solve problems correctly according to the proper order. The document ends by posing a sample problem using PEMDAS for the reader to solve.

My Order of Operations Slide show

The document explains the order of operations (PEMDAS) for evaluating mathematical expressions. PEMDAS stands for Parentheses, Exponents, Multiplication, Division, Addition, Subtraction. It should be followed from left to right. Parentheses contain expressions that are evaluated first. Exponents represent multiplication and are done before multiplication and division from left to right. The same order applies to multiplication/division and addition/subtraction from left to right. An example equation is worked through step-by-step to demonstrate PEMDAS.

Order Of Operations

The document discusses the order of operations for evaluating mathematical expressions. It explains that the order is: 1) Parentheses, 2) Exponents, 3) Multiplication and Division from left to right, and 4) Addition and Subtraction from left to right. Examples are provided to illustrate how to evaluate expressions step-by-step using this order. Mnemonic phrases like "Please Excuse My Dear Aunt Sally" are also mentioned to help remember the order of operations.

Orders of Operations

The document discusses the order of operations, known by the acronym PEMDAS. PEMDAS stands for Parentheses, Exponents, Multiplication, Division, Addition, Subtraction. It explains each step in order: evaluate expressions within parentheses first, then exponents, then multiply/divide from left to right, and finally add/subtract from left to right. The document provides examples for exponents and the basic operations and advises writing out PEMDAS and crossing out steps as they are completed to solve problems correctly according to the order of operations. It concludes by posing the example problem (2x4)+6/7.

Expressions, equations, and functions variable expressions

This video discusses key concepts in algebra including expressions, equations, functions, variables, and operations. It explains that an algebraic expression contains numbers, operators, and at least one variable. Variables act as nouns that represent unknown or changing quantities, while operations like addition or multiplication are verbs that describe actions. The document provides examples of how to write expressions and equations using variables to represent real-world situations involving money earned at a job, numbers of cars on a road, or distance from an object.

Journal math

This document summarizes key concepts from a 7th grade math chapter, including:
1) How to translate word problems into mathematical equations, with examples of translating sentences about Johnny and Mary's work and eating apples into equations.
2) The order of operations (PEMDAS) and why it is important for getting the right results when calculating expressions.
3) What perfect square numbers are with examples of perfect square numbers up to 25.

Maths glossary

The document provides definitions for mathematical terms that students in 5th/6th class primary school and junior cycle secondary school may encounter. It includes over 50 terms defined with diagrams and examples. The glossary is designed to inform students, parents, and teachers about the vocabulary and meanings of key mathematical terms as students transition between primary and post-primary education in Ireland.

Edu 635 curriculum map grade 3 m alvarez

This curriculum map outlines the essential concepts, skills, activities, and assessments for 3rd grade mathematics over the school year. From September to October, students will learn addition and subtraction of 3-digit numbers through strategies like rounding, estimating, and regrouping. From October to December, the focus is on multiplication and division, including interpreting situations, properties, and solving word problems. Students will also learn to measure area from December to January by finding the area of rectangles and composing figures. Fractions will be covered from January to March, where students will describe, compare, and represent fractions. Finally, measurement and data will be addressed in two parts, with graphing and data displayed covered from March to April, and geometry and

1-Introduction-to-Maths.pdf

This math module covers basic arithmetic concepts such as rounding, order of operations, and mental computation strategies. It includes 1) an introduction to arithmetic focusing on integers, operations, and place value; 2) refreshing skills like addition, subtraction, multiplication, and division of whole numbers; and 3) working with decimals, rounding, and estimating. The document provides examples and practice problems to help explain and apply these fundamental math topics.

variables_expressions

This document defines key terms related to variables and expressions:
- A variable represents an unknown number using a symbol like x or n.
- A variable expression contains variables and numbers with arithmetic operations but no equal sign, like n - 5.
- To evaluate an expression means to substitute numbers for the variables and simplify the result.

1-1-Slide-Show-Writing-and-Interpreting-Numerical-Expressions.pptx

1) The document discusses writing and interpreting numerical expressions. It defines numerical expressions and their key components like numbers and operations.
2) It provides examples of writing numerical expressions from verbal phrases by recognizing clue words for operations. Proper grouping using parentheses is important to show the correct order of operations.
3) The document also discusses interpreting numerical expressions without evaluating them using visual models like tape diagrams to compare expressions.

Generalizing Addition and Multiplication to an Operator Parametrized by a Rea...

Exploration of an mathematical idea that leads to a investigation of fractionally iterated exponential functions. Addition, multiplication... what's next? Powers lacks pleasant group properties. We invent a way around that. We find a general operator that reduces to addition, or multiplication, or that next operation, for special cases. There's even an operation "before" addition. Furthermore, there are operations between addition and multiplication.
Includes an original invention of a form of fractionally iterated exponential functions based on symmetry. It leads to some interesting strange functions.
The presentation ends with a few questions suitable for your own research.
Overall level is typical undergrad with some basic knowledge of real analysis and group theory, but a bright high school student will probably follow most of this.
This presentation is expository, not rigorous. The author hopes interested readers will enjoy digging in for their own exploration.

Translating Mathematical Phrases to Rational Algebraic Expressions

This document provides instruction on translating mathematical phrases to rational algebraic expressions. It begins by stating the objectives of determining symbols, variables, and operations, and translating phrases to expressions. It then reviews polynomials and introduces translating phrases using numbers, symbols, variables, grouping symbols, and constants. Various representations for multiplication and division are described. Additional terms corresponding to operations are mentioned. An activity and biblical proverbs are included to reinforce learning.

1.1 Real Number Properties

This document provides an overview of real number properties and operations. It defines natural numbers, integers, rational numbers, and irrational numbers. It discusses order of operations and using properties like commutative, associative, distributive, identity, and inverse. Examples are provided of simplifying algebraic expressions and evaluating expressions using order of operations. Formulas are defined as relationships between quantities that can be used to find variable values. The document concludes with examples of simplifying algebraic expressions using properties of real numbers.

Order of operations

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- 2. What is P.E.M.D.A.S? P.E.M.D.A.S is the acronym we use to explain the order of ooperations. The order of operations are Parentheses, Exponents, Multiply, Divide, Add or Subtract. We must use this order to solve problems with multiple sign being used.
- 3. Parentheses You may see Parentheses like ( or ) to show that this is part of the problem that must be computed first. Parentheses may go around multiple numbers and signs. Example: (9+67)x36 76x36=2736
- 4. Exponents Exponents are basically the fancy name for powers on numbers. They mean that there is a number raised to a base number. To show an exponent you may use a sign like ^ before the power. Example: 7^2x4 49x4=196
- 5. Multiply The next stetp to P.E.M.D.A.S is to multiply, then divide to make the equasion easier, but you may also multiply or divide left to right. Multiplication is done normally in order of operations. Example: 9x5-3 40-3=37
- 6. Divide After multipling, its time to divide. Dividing is also done regularlly in order of operations. We should divide left to right, but it is not necessary. Example: 6/3-1 2-1=1
- 7. Add Now it is tiime to add. We can add or subtract left to right, but is usually easier to add first. We add normally. Example: 7+4-3 11-3=8
- 8. Subtract The last step before computing your answer is to subtract. As I said, we do not need to subtract for multiplying going left to right, but you may. Subtract normally, then its time to compute your answer. Example: 7-5+4 2+4=6
- 9. Check One important thing to do once you have computed your answer is to check it. First, check your math with a calculator, then make sure that you have answered the question entirely. Example: First Answer Once Checked 3x4/6-1 3x4/6-1 12/6-1 12/6-1 6-1=5 2-1=1
- 10. My Question What is (5+21)x(6/2)-4 ? Remember to check!