This is Arithmetic two. It is about Prime factorisation. It contains the explanation of factors, prime factors, how prime factors are obtained, highest common factor (HCF), lowest common multiple (LCM), and rounding integers.
Mathematics for Grade 6: Prime Factorization - HCFBridgette Mackey
http://bit.ly/1LTzAo6
This video explains the term, highest common factor or HCF. It is a continuation of the video on factors. For the full FREE lesson on prime factorization and HCF, please visit http://bit.ly/1LTzAo6
This document discusses different methods for finding the least common multiple (LCM) of two or more numbers. It explains that the LCM is the smallest number that the given numbers will all divide into evenly. Then it describes four methods: multiplication, prime factorization, Venn diagrams, and using the greatest common factor (GCF). For each method it provides an example of finding the LCM of 24 and 18, and the answer is consistently 72.
Highest common factor and lowest common multipleXasan Khaliif
This document introduces the concepts of the highest common factor (HCF) and lowest common multiple (LCM) of two numbers. It explains that the HCF is the largest number that divides both numbers, while the LCM is the smallest number that is a multiple of both numbers. Examples are provided to illustrate finding the HCF and LCM through listing factors or prime factorizations. Finally, exercises are given for the reader to practice calculating the HCF and LCM of number pairs.
Lesson plan multiple and factors.ppt v 3Kavita Grover
This lesson plan outlines 10 lessons to teach students about multiples, factors, prime and composite numbers, divisibility rules, factorization, exponents, least common multiples (LCM), and highest common factors (HCF). Each lesson includes the topic, time, location, content overview, and learning objectives. Methods for finding LCM, HCF, prime factorization, and factorization are discussed. Practice problems are provided for students.
This document contains slides about multiples, factors, prime numbers, prime factor decomposition, highest common factor (HCF), and lowest common multiple (LCM). The slides define key terms, provide examples of finding factors and prime factors, discuss methods for determining if a number is prime, and explain how to use prime factor decomposition to calculate the HCF and LCM of two numbers. The final slide encourages supporting female education by clicking on advertisements.
What is HCF? What is LCM? How you calculate HCF & LCM
of numbers & fractions quickly?
Find out in this short presentation by https://allexammocktest.in
1) The document discusses factors, prime numbers, and composite numbers and how to use them to reduce fractions and find equivalent fractions.
2) It explains how to find all factors of a number using the rainbow method and defines prime and composite numbers.
3) It also covers prime factorization, using factor trees to break numbers down into their prime factors, and how to reduce fractions to lowest terms.
This document provides models and examples for calculating the highest common factor (HCF), lowest common multiple (LCM), and properties of exponents and factorials. It includes 3 models for finding the LCM and HCF of numbers. It also provides rules for determining the last digit of powers of a number, and finding the largest power of a prime number that divides a factorial.
Mathematics for Grade 6: Prime Factorization - HCFBridgette Mackey
http://bit.ly/1LTzAo6
This video explains the term, highest common factor or HCF. It is a continuation of the video on factors. For the full FREE lesson on prime factorization and HCF, please visit http://bit.ly/1LTzAo6
This document discusses different methods for finding the least common multiple (LCM) of two or more numbers. It explains that the LCM is the smallest number that the given numbers will all divide into evenly. Then it describes four methods: multiplication, prime factorization, Venn diagrams, and using the greatest common factor (GCF). For each method it provides an example of finding the LCM of 24 and 18, and the answer is consistently 72.
Highest common factor and lowest common multipleXasan Khaliif
This document introduces the concepts of the highest common factor (HCF) and lowest common multiple (LCM) of two numbers. It explains that the HCF is the largest number that divides both numbers, while the LCM is the smallest number that is a multiple of both numbers. Examples are provided to illustrate finding the HCF and LCM through listing factors or prime factorizations. Finally, exercises are given for the reader to practice calculating the HCF and LCM of number pairs.
Lesson plan multiple and factors.ppt v 3Kavita Grover
This lesson plan outlines 10 lessons to teach students about multiples, factors, prime and composite numbers, divisibility rules, factorization, exponents, least common multiples (LCM), and highest common factors (HCF). Each lesson includes the topic, time, location, content overview, and learning objectives. Methods for finding LCM, HCF, prime factorization, and factorization are discussed. Practice problems are provided for students.
This document contains slides about multiples, factors, prime numbers, prime factor decomposition, highest common factor (HCF), and lowest common multiple (LCM). The slides define key terms, provide examples of finding factors and prime factors, discuss methods for determining if a number is prime, and explain how to use prime factor decomposition to calculate the HCF and LCM of two numbers. The final slide encourages supporting female education by clicking on advertisements.
What is HCF? What is LCM? How you calculate HCF & LCM
of numbers & fractions quickly?
Find out in this short presentation by https://allexammocktest.in
1) The document discusses factors, prime numbers, and composite numbers and how to use them to reduce fractions and find equivalent fractions.
2) It explains how to find all factors of a number using the rainbow method and defines prime and composite numbers.
3) It also covers prime factorization, using factor trees to break numbers down into their prime factors, and how to reduce fractions to lowest terms.
This document provides models and examples for calculating the highest common factor (HCF), lowest common multiple (LCM), and properties of exponents and factorials. It includes 3 models for finding the LCM and HCF of numbers. It also provides rules for determining the last digit of powers of a number, and finding the largest power of a prime number that divides a factorial.
This document discusses factors and the greatest common factor (GCF). It provides examples of finding the factors of different numbers and identifying the common factors and GCF of sets of numbers. It includes practice problems for students to list the factors of numbers, find the common factors and GCF, and answer questions about factors and the GCF.
This document discusses factors, multiples, primes, lowest common multiples (LCM), and highest common factors (HCF). It provides examples and exercises on determining if a number is a multiple, factor, or prime. It also demonstrates how to find the LCM and HCF of two or more numbers, including using Venn diagrams to show the overlapping prime factors. Readers learn to write numbers as a product of prime factors using factor trees.
Common Factors And Greatest Common FactorBrooke Young
This document discusses finding the common factors and greatest common factor (GCF) of two numbers. It provides examples of finding the common factors and GCF of 40 and 45 (which is 5), 13 and 15 (which is 1), and 18 and 24 (which is 6). To find the GCF, you list all the factors of each number, identify the common factors, and from those choose the greatest value as the GCF. While there may be multiple common factors, there is only one GCF.
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.
Quantitative aptitude h.c.f & l.c.mDipto Shaha
The document discusses concepts related to factors, multiples, highest common factors (HCF), and least common multiples (LCM) of numbers. It provides definitions and examples of factors, multiples, HCF, and LCM. Several examples of finding the HCF and LCM of numbers using factorization and other methods are shown. The document also presents solutions to example problems involving HCF, LCM, ratios, remainders, and word problems related to these concepts.
The document provides instructions for factorizing numbers into their prime factors. It explains that students will learn to express whole numbers as the sum and product of their prime factors by drawing factor trees. It provides an example of factorizing the number 36 into 22 x 32 to show the prime factors of 2 and 3 and their exponents.
Mathematics for Grade 6: Prime Factorization - LCMBridgette Mackey
http://bit.ly/1LTzAo6
This slide explains what is the Lowest Common Multiple (LCM) of a pair of numbers. For a full free video on factors, multiples, HCF and LCM please visit http://bit.ly/1LTzAo6
The document discusses finding the least common multiple (LCM) of numbers. It provides examples of finding the LCM of pairs of numbers by listing their multiples and finding the smallest number that is a multiple of both. It also introduces finding the LCM using prime factorizations and Venn diagrams, showing how to find the greatest power of each prime factor and multiply them to get the LCM. Students are given practice problems to find the LCM of various number pairs using these methods.
This document discusses highest common factors (HCF) and least common multiples (LCM). It defines prime numbers, co-prime numbers, and twin prime numbers. It explains that Euclid discovered any composite number can be written as the product of prime factors, in a process called factorisation. Examples of factorising numbers and using the prime factor method to find the HCF of two numbers are provided. The document recaps the key topics and asks review questions.
The document discusses finding the greatest common factor (GCF) of two numbers:
1) The GCF is the largest factor that is common to both numbers.
2) To find the GCF, list all the factors of each number and identify the common factors.
3) The greatest of the common factors is the GCF.
Prime factorization can be found using a factor tree method. The steps are to start with a composite number, write it as a multiplication problem of factors, and continue breaking numbers down until only prime numbers remain. The prime factorization is the product of the prime factors, and different factor trees for the same number will result in the same prime factorization that can be checked by multiplying the factors.
The document is a summary of a Khan Academy math lesson on ordering fractions, prime factorization, and working with fractions. It includes warm-up problems on ordering fractions, adding and subtracting fractions with different denominators, and multiplying and dividing mixed numbers. It defines key vocabulary terms like fundamental theorem of arithmetic, prime number, prime factorization, and greatest common factor. It provides examples of using prime factorization to simplify fractions by finding their greatest common factor. It also includes practice problems identifying numbers as prime or composite, writing their prime factorizations, and finding the prime factorizations of given numbers.
This document is a summary of a math class that includes warm-up problems, lessons on fractions, decimals, factoring, and vocabulary. It contains practice problems on these topics. The warm-up includes problems on averages, converting fractions to decimals, adding and subtracting mixed fractions. The lessons define fractions and their relationship to decimals, and how to simplify fractions using the greatest common factor. Practice problems apply these skills to factoring and solving inequalities.
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.
This document provides an overview of multiples, factors, least common multiples (LCM), highest common factors (HCF), prime numbers, and divisibility rules for numbers 2, 3, and 5 in a 7th grade mathematics chapter. It defines key terms, provides examples of finding multiples, factors, LCM, HCF, and discusses prime vs. composite numbers. Evaluation questions and group work assessing these concepts are assigned, along with homework reviewing common multiples, LCM, common factors, HCF, and listing prime numbers.
The document provides examples and explanations for dividing real numbers, including finding multiplicative inverses, determining the sign of quotients based on the signs of the numbers, and calculating the mean of a data set. It demonstrates how to simplify expressions by dividing both the numerator and denominator by the same value. The examples guide the reader through dividing positive and negative numbers, as well as calculating the mean minimum daily temperature over a five day period.
The document discusses prime factorization, HCF (highest common factor), and LCM (lowest common multiple). It explains that prime factorization is expressing a number as the product of prime numbers. There are factor tree and division methods for finding prime factors. HCF is the greatest number that divides two or more numbers. LCM is the lowest number that is a multiple of two or more numbers. Methods for finding HCF and LCM include prime factorization, common division, and long division. HCF and LCM are related in that the product of two numbers equals HCF times LCM.
The document provides steps to find the greatest common factor (GCF) of multiple numbers. It shows finding the GCF of 18 and 27, then of 15 and 20. Finally, it shows finding the GCF of 27, 36, and 45 by listing the factors of each number, identifying the common factors, and determining that the greatest common factor is 9.
Based on Maths chapter 1 of class 8 it consists of every topic and a good explanation. Please read the full ppt. It will also teach you how to design a ppt also. so reading these is a good way of gaining knowledge. It consists of every topic in the book and can be used a a teaching purpose also.
Three students were asked to draw rectangles with an area of 24 square inches. The first student drew a rectangle with dimensions of 2 inches by 12 inches. The second drew a rectangle of 3 inches by 8 inches. The third drew a rectangle of 1 inch by 24 inches. Since all three rectangles have an area of 24 square inches, this shows that multiplying different factors can result in the same product.
This document provides an overview of rational exponents through a series of examples and explanations. It begins by introducing integer exponents and the rules for adding and subtracting them. It then extends these rules to rational exponents by defining rational powers in terms of nth roots. Examples are provided to illustrate how to simplify expressions using properties of exponents and the exponent-to-root rule for rational exponents. The key ideas are that rational exponents can be used when the nth root makes sense as a real number and that operations with rational exponents follow the same rules as integer exponents.
This document discusses factors and the greatest common factor (GCF). It provides examples of finding the factors of different numbers and identifying the common factors and GCF of sets of numbers. It includes practice problems for students to list the factors of numbers, find the common factors and GCF, and answer questions about factors and the GCF.
This document discusses factors, multiples, primes, lowest common multiples (LCM), and highest common factors (HCF). It provides examples and exercises on determining if a number is a multiple, factor, or prime. It also demonstrates how to find the LCM and HCF of two or more numbers, including using Venn diagrams to show the overlapping prime factors. Readers learn to write numbers as a product of prime factors using factor trees.
Common Factors And Greatest Common FactorBrooke Young
This document discusses finding the common factors and greatest common factor (GCF) of two numbers. It provides examples of finding the common factors and GCF of 40 and 45 (which is 5), 13 and 15 (which is 1), and 18 and 24 (which is 6). To find the GCF, you list all the factors of each number, identify the common factors, and from those choose the greatest value as the GCF. While there may be multiple common factors, there is only one GCF.
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.
Quantitative aptitude h.c.f & l.c.mDipto Shaha
The document discusses concepts related to factors, multiples, highest common factors (HCF), and least common multiples (LCM) of numbers. It provides definitions and examples of factors, multiples, HCF, and LCM. Several examples of finding the HCF and LCM of numbers using factorization and other methods are shown. The document also presents solutions to example problems involving HCF, LCM, ratios, remainders, and word problems related to these concepts.
The document provides instructions for factorizing numbers into their prime factors. It explains that students will learn to express whole numbers as the sum and product of their prime factors by drawing factor trees. It provides an example of factorizing the number 36 into 22 x 32 to show the prime factors of 2 and 3 and their exponents.
Mathematics for Grade 6: Prime Factorization - LCMBridgette Mackey
http://bit.ly/1LTzAo6
This slide explains what is the Lowest Common Multiple (LCM) of a pair of numbers. For a full free video on factors, multiples, HCF and LCM please visit http://bit.ly/1LTzAo6
The document discusses finding the least common multiple (LCM) of numbers. It provides examples of finding the LCM of pairs of numbers by listing their multiples and finding the smallest number that is a multiple of both. It also introduces finding the LCM using prime factorizations and Venn diagrams, showing how to find the greatest power of each prime factor and multiply them to get the LCM. Students are given practice problems to find the LCM of various number pairs using these methods.
This document discusses highest common factors (HCF) and least common multiples (LCM). It defines prime numbers, co-prime numbers, and twin prime numbers. It explains that Euclid discovered any composite number can be written as the product of prime factors, in a process called factorisation. Examples of factorising numbers and using the prime factor method to find the HCF of two numbers are provided. The document recaps the key topics and asks review questions.
The document discusses finding the greatest common factor (GCF) of two numbers:
1) The GCF is the largest factor that is common to both numbers.
2) To find the GCF, list all the factors of each number and identify the common factors.
3) The greatest of the common factors is the GCF.
Prime factorization can be found using a factor tree method. The steps are to start with a composite number, write it as a multiplication problem of factors, and continue breaking numbers down until only prime numbers remain. The prime factorization is the product of the prime factors, and different factor trees for the same number will result in the same prime factorization that can be checked by multiplying the factors.
The document is a summary of a Khan Academy math lesson on ordering fractions, prime factorization, and working with fractions. It includes warm-up problems on ordering fractions, adding and subtracting fractions with different denominators, and multiplying and dividing mixed numbers. It defines key vocabulary terms like fundamental theorem of arithmetic, prime number, prime factorization, and greatest common factor. It provides examples of using prime factorization to simplify fractions by finding their greatest common factor. It also includes practice problems identifying numbers as prime or composite, writing their prime factorizations, and finding the prime factorizations of given numbers.
This document is a summary of a math class that includes warm-up problems, lessons on fractions, decimals, factoring, and vocabulary. It contains practice problems on these topics. The warm-up includes problems on averages, converting fractions to decimals, adding and subtracting mixed fractions. The lessons define fractions and their relationship to decimals, and how to simplify fractions using the greatest common factor. Practice problems apply these skills to factoring and solving inequalities.
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.
This document provides an overview of multiples, factors, least common multiples (LCM), highest common factors (HCF), prime numbers, and divisibility rules for numbers 2, 3, and 5 in a 7th grade mathematics chapter. It defines key terms, provides examples of finding multiples, factors, LCM, HCF, and discusses prime vs. composite numbers. Evaluation questions and group work assessing these concepts are assigned, along with homework reviewing common multiples, LCM, common factors, HCF, and listing prime numbers.
The document provides examples and explanations for dividing real numbers, including finding multiplicative inverses, determining the sign of quotients based on the signs of the numbers, and calculating the mean of a data set. It demonstrates how to simplify expressions by dividing both the numerator and denominator by the same value. The examples guide the reader through dividing positive and negative numbers, as well as calculating the mean minimum daily temperature over a five day period.
The document discusses prime factorization, HCF (highest common factor), and LCM (lowest common multiple). It explains that prime factorization is expressing a number as the product of prime numbers. There are factor tree and division methods for finding prime factors. HCF is the greatest number that divides two or more numbers. LCM is the lowest number that is a multiple of two or more numbers. Methods for finding HCF and LCM include prime factorization, common division, and long division. HCF and LCM are related in that the product of two numbers equals HCF times LCM.
The document provides steps to find the greatest common factor (GCF) of multiple numbers. It shows finding the GCF of 18 and 27, then of 15 and 20. Finally, it shows finding the GCF of 27, 36, and 45 by listing the factors of each number, identifying the common factors, and determining that the greatest common factor is 9.
Based on Maths chapter 1 of class 8 it consists of every topic and a good explanation. Please read the full ppt. It will also teach you how to design a ppt also. so reading these is a good way of gaining knowledge. It consists of every topic in the book and can be used a a teaching purpose also.
Three students were asked to draw rectangles with an area of 24 square inches. The first student drew a rectangle with dimensions of 2 inches by 12 inches. The second drew a rectangle of 3 inches by 8 inches. The third drew a rectangle of 1 inch by 24 inches. Since all three rectangles have an area of 24 square inches, this shows that multiplying different factors can result in the same product.
This document provides an overview of rational exponents through a series of examples and explanations. It begins by introducing integer exponents and the rules for adding and subtracting them. It then extends these rules to rational exponents by defining rational powers in terms of nth roots. Examples are provided to illustrate how to simplify expressions using properties of exponents and the exponent-to-root rule for rational exponents. The key ideas are that rational exponents can be used when the nth root makes sense as a real number and that operations with rational exponents follow the same rules as integer exponents.
The document discusses factors, prime numbers, composite numbers, and methods for finding highest common factors (HCF) and lowest common multiples (LCM) of numbers. It defines factors as numbers that divide evenly into a given number. Prime numbers have exactly two factors, 1 and the number itself. Composite numbers have more than two factors. The HCF is the largest number that divides two numbers, found by listing all common factors. The LCM is the smallest number that is a multiple of two numbers, found using the prime factors of each number.
1. This document discusses divisibility, prime numbers, and finding the highest common factor and least common multiple of numbers. It defines divisibility as being able to divide one number by another with no remainder. Prime numbers only have two factors, themselves and 1, while composite numbers have more than two factors. The highest common factor is the largest factor that is common to two or more numbers, while the least common multiple is the smallest number that is a multiple of the given numbers.
Gcse maths resources higher 01.1 primes number and prime indexLiveOnlineClassesInd
The document discusses prime numbers, including:
- Prime numbers only have two factors - 1 and themselves.
- Prime numbers up to 20 are listed as: 2, 3, 5, 7, 11, 13, 17, 19.
- Examples are provided of finding the prime factors of various numbers and expressing them as products of primes.
The document provides an overview of various algebra topics including:
- Multiplying and dividing monomials by adding/subtracting exponents and multiplying/dividing coefficients
- Adding and subtracting polynomials by combining like terms
- Multiplying polynomials using the distributive property
- Factoring trinomials of the forms x2 + bx + c and ax2 + bx + c by finding two integers with a certain product and sum
- Factoring the difference of squares by taking the square root of each term
- Dividing a polynomial by a binomial by using reverse of multiplication
1) Fractions represent parts of a whole. They are written as a/b where a is the numerator and b is the denominator. Fractions can be reduced by dividing the numerator and denominator by common factors.
2) To multiply fractions, multiply the numerators and multiply the denominators. To divide fractions, multiply the first fraction by the reciprocal of the second fraction.
3) Mixed numbers represent an integer plus a fraction, such as 5 3/4. Improper fractions have a numerator larger than or equal to the denominator, such as 7/2, and can be converted to mixed numbers.
This document provides a tutorial on factors and multiples in GCSE Maths. It defines factors as numbers that divide evenly into a given number, and multiples as numbers that the given number divides into evenly. The document explains how to find common factors and common multiples between two numbers. It also introduces prime factorization, using factor trees to break numbers down into their prime factors. Several practice problems are provided to reinforce these concepts.
Arithmetic is the oldest branch of mathematics dealing with basic operations like addition, subtraction, multiplication and division. It includes counting, as well as more advanced calculations used in science and business. The fundamental arithmetic operations are performed on different types of numbers, and concepts like order of operations, fractions, decimals, ratios, exponents, and roots are part of this subject. Key ideas in arithmetic also include factors and multiples, prime and composite numbers, the greatest common factor, lowest common multiple, and operations on fractions like finding a common denominator.
The document discusses divisibility patterns and prime factorization. It provides examples of writing the prime factorization of numbers by decomposing them into prime factors using factor trees. It also discusses factoring monomials by writing them as a product of numbers and variables with exponents. Examples are provided of determining if a number is prime or composite, writing the prime factorization of various numbers, and factoring monomials like 12x2y and 18t2. Homework problems involve writing factors and prime factorizations.
The document discusses divisibility patterns and prime factorization. It provides examples of writing the prime factorization of numbers by decomposing them into prime factors using factor trees. It also discusses factoring monomials by writing them as a product of numbers and variables with exponents. Examples are provided of determining if a number is prime or composite, writing the prime factorization of various numbers, and factoring monomials like 12x2y and 18t2 into prime factors with exponents. Homework problems involve writing factors and prime factorizations.
CLASS VII -operations on rational numbers(1).pptxRajkumarknms
This document discusses properties of operations on rational numbers. It covers:
1) Addition of rational numbers, including having the same or different denominators. Properties include closure, commutativity, and additive identity.
2) Subtraction of rational numbers and its properties, noting the difference property and lack of an identity element.
3) Multiplication of rational numbers by multiplying numerators and denominators. Properties are closure, commutativity, associativity, identity of 1, and annihilation by 0.
4) Distributive property relating multiplication and addition/subtraction of rational numbers.
The document discusses prime factorization and factoring monomials. It provides examples and guided practice for writing the prime factorization of numbers by decomposing them into prime factors using exponents. It also demonstrates factoring monomials by writing variables with exponents as products of the same variable.
The document provides information on rational numbers and operations involving fractions and integers:
1. It defines rational numbers as numbers that can be represented as fractions a/b where a and b are integers and b is not equal to 0.
2. Rules for addition, subtraction, multiplication, and division of integers and fractions are presented, such as signs of terms determine sign of sum/product.
3. Examples demonstrate applying the rules to evaluate expressions involving integers and fractions.
The document summarizes Chapter 13 on factoring polynomials. It covers the greatest common factor, factoring trinomials of the forms x^2 + bx + c, ax^2 + bx + c, and x^2 + bx + c by grouping. It also discusses factoring perfect square trinomials, difference of two squares, and solving quadratic equations by factoring. Examples are provided to demonstrate each technique.
This document outlines key concepts and examples for factoring polynomials. It covers factoring trinomials of the forms x^2 + bx + c, ax^2 + bx + c, and x^2 + bx + c by grouping. Examples are provided to demonstrate finding the greatest common factor of terms, factoring trinomials by finding two numbers whose product and sum meet the given criteria, and checking factoring results using FOIL multiplication. Sections include the greatest common factor, factoring trinomials of the forms x^2 + bx + c and ax^2 + bx + c.
This document outlines key concepts and examples for factoring polynomials. It discusses factoring trinomials of the forms x^2 + bx + c, ax^2 + bx + c, and x^2 + bx + c by grouping. Examples are provided to demonstrate finding the greatest common factor of terms, factoring trinomials by finding two numbers whose product and sum meet the given criteria, and checking factoring results using FOIL. Sections cover the greatest common factor, factoring trinomials of different forms, and solving quadratic equations by factoring.
This presentation is Arithmetic one. It contains the following content: whole numbers, integers, terms used in solving, sum, difference, product, quotient, things to note, commutativity, associativity, tips used in solving and BODMAS ( Bracket Of Division Multiplication Addition and Subtraction).
This presentation discusses factoring polynomials by finding the greatest common factor. It defines key terms like factors, common factors, and greatest common factor. It explains how to find all the factors of a number and determine common factors between two numbers. Examples are provided of factoring polynomials by identifying the greatest common monomial factor and factoring it out of each term. Steps for factoring a monomial out of a polynomial are outlined.
Travis Hills' Endeavors in Minnesota: Fostering Environmental and Economic Pr...Travis Hills MN
Travis Hills of Minnesota developed a method to convert waste into high-value dry fertilizer, significantly enriching soil quality. By providing farmers with a valuable resource derived from waste, Travis Hills helps enhance farm profitability while promoting environmental stewardship. Travis Hills' sustainable practices lead to cost savings and increased revenue for farmers by improving resource efficiency and reducing waste.
Remote Sensing and Computational, Evolutionary, Supercomputing, and Intellige...University of Maribor
Slides from talk:
Aleš Zamuda: Remote Sensing and Computational, Evolutionary, Supercomputing, and Intelligent Systems.
11th International Conference on Electrical, Electronics and Computer Engineering (IcETRAN), Niš, 3-6 June 2024
Inter-Society Networking Panel GRSS/MTT-S/CIS Panel Session: Promoting Connection and Cooperation
https://www.etran.rs/2024/en/home-english/
ANAMOLOUS SECONDARY GROWTH IN DICOT ROOTS.pptxRASHMI M G
Abnormal or anomalous secondary growth in plants. It defines secondary growth as an increase in plant girth due to vascular cambium or cork cambium. Anomalous secondary growth does not follow the normal pattern of a single vascular cambium producing xylem internally and phloem externally.
ESR spectroscopy in liquid food and beverages.pptxPRIYANKA PATEL
With increasing population, people need to rely on packaged food stuffs. Packaging of food materials requires the preservation of food. There are various methods for the treatment of food to preserve them and irradiation treatment of food is one of them. It is the most common and the most harmless method for the food preservation as it does not alter the necessary micronutrients of food materials. Although irradiated food doesn’t cause any harm to the human health but still the quality assessment of food is required to provide consumers with necessary information about the food. ESR spectroscopy is the most sophisticated way to investigate the quality of the food and the free radicals induced during the processing of the food. ESR spin trapping technique is useful for the detection of highly unstable radicals in the food. The antioxidant capability of liquid food and beverages in mainly performed by spin trapping technique.
Current Ms word generated power point presentation covers major details about the micronuclei test. It's significance and assays to conduct it. It is used to detect the micronuclei formation inside the cells of nearly every multicellular organism. It's formation takes place during chromosomal sepration at metaphase.
Comparing Evolved Extractive Text Summary Scores of Bidirectional Encoder Rep...University of Maribor
Slides from:
11th International Conference on Electrical, Electronics and Computer Engineering (IcETRAN), Niš, 3-6 June 2024
Track: Artificial Intelligence
https://www.etran.rs/2024/en/home-english/
Or: Beyond linear.
Abstract: Equivariant neural networks are neural networks that incorporate symmetries. The nonlinear activation functions in these networks result in interesting nonlinear equivariant maps between simple representations, and motivate the key player of this talk: piecewise linear representation theory.
Disclaimer: No one is perfect, so please mind that there might be mistakes and typos.
dtubbenhauer@gmail.com
Corrected slides: dtubbenhauer.com/talks.html
The use of Nauplii and metanauplii artemia in aquaculture (brine shrimp).pptxMAGOTI ERNEST
Although Artemia has been known to man for centuries, its use as a food for the culture of larval organisms apparently began only in the 1930s, when several investigators found that it made an excellent food for newly hatched fish larvae (Litvinenko et al., 2023). As aquaculture developed in the 1960s and ‘70s, the use of Artemia also became more widespread, due both to its convenience and to its nutritional value for larval organisms (Arenas-Pardo et al., 2024). The fact that Artemia dormant cysts can be stored for long periods in cans, and then used as an off-the-shelf food requiring only 24 h of incubation makes them the most convenient, least labor-intensive, live food available for aquaculture (Sorgeloos & Roubach, 2021). The nutritional value of Artemia, especially for marine organisms, is not constant, but varies both geographically and temporally. During the last decade, however, both the causes of Artemia nutritional variability and methods to improve poorquality Artemia have been identified (Loufi et al., 2024).
Brine shrimp (Artemia spp.) are used in marine aquaculture worldwide. Annually, more than 2,000 metric tons of dry cysts are used for cultivation of fish, crustacean, and shellfish larva. Brine shrimp are important to aquaculture because newly hatched brine shrimp nauplii (larvae) provide a food source for many fish fry (Mozanzadeh et al., 2021). Culture and harvesting of brine shrimp eggs represents another aspect of the aquaculture industry. Nauplii and metanauplii of Artemia, commonly known as brine shrimp, play a crucial role in aquaculture due to their nutritional value and suitability as live feed for many aquatic species, particularly in larval stages (Sorgeloos & Roubach, 2021).
When I was asked to give a companion lecture in support of ‘The Philosophy of Science’ (https://shorturl.at/4pUXz) I decided not to walk through the detail of the many methodologies in order of use. Instead, I chose to employ a long standing, and ongoing, scientific development as an exemplar. And so, I chose the ever evolving story of Thermodynamics as a scientific investigation at its best.
Conducted over a period of >200 years, Thermodynamics R&D, and application, benefitted from the highest levels of professionalism, collaboration, and technical thoroughness. New layers of application, methodology, and practice were made possible by the progressive advance of technology. In turn, this has seen measurement and modelling accuracy continually improved at a micro and macro level.
Perhaps most importantly, Thermodynamics rapidly became a primary tool in the advance of applied science/engineering/technology, spanning micro-tech, to aerospace and cosmology. I can think of no better a story to illustrate the breadth of scientific methodologies and applications at their best.
Phenomics assisted breeding in crop improvementIshaGoswami9
As the population is increasing and will reach about 9 billion upto 2050. Also due to climate change, it is difficult to meet the food requirement of such a large population. Facing the challenges presented by resource shortages, climate
change, and increasing global population, crop yield and quality need to be improved in a sustainable way over the coming decades. Genetic improvement by breeding is the best way to increase crop productivity. With the rapid progression of functional
genomics, an increasing number of crop genomes have been sequenced and dozens of genes influencing key agronomic traits have been identified. However, current genome sequence information has not been adequately exploited for understanding
the complex characteristics of multiple gene, owing to a lack of crop phenotypic data. Efficient, automatic, and accurate technologies and platforms that can capture phenotypic data that can
be linked to genomics information for crop improvement at all growth stages have become as important as genotyping. Thus,
high-throughput phenotyping has become the major bottleneck restricting crop breeding. Plant phenomics has been defined as the high-throughput, accurate acquisition and analysis of multi-dimensional phenotypes
during crop growing stages at the organism level, including the cell, tissue, organ, individual plant, plot, and field levels. With the rapid development of novel sensors, imaging technology,
and analysis methods, numerous infrastructure platforms have been developed for phenotyping.
The ability to recreate computational results with minimal effort and actionable metrics provides a solid foundation for scientific research and software development. When people can replicate an analysis at the touch of a button using open-source software, open data, and methods to assess and compare proposals, it significantly eases verification of results, engagement with a diverse range of contributors, and progress. However, we have yet to fully achieve this; there are still many sociotechnical frictions.
Inspired by David Donoho's vision, this talk aims to revisit the three crucial pillars of frictionless reproducibility (data sharing, code sharing, and competitive challenges) with the perspective of deep software variability.
Our observation is that multiple layers — hardware, operating systems, third-party libraries, software versions, input data, compile-time options, and parameters — are subject to variability that exacerbates frictions but is also essential for achieving robust, generalizable results and fostering innovation. I will first review the literature, providing evidence of how the complex variability interactions across these layers affect qualitative and quantitative software properties, thereby complicating the reproduction and replication of scientific studies in various fields.
I will then present some software engineering and AI techniques that can support the strategic exploration of variability spaces. These include the use of abstractions and models (e.g., feature models), sampling strategies (e.g., uniform, random), cost-effective measurements (e.g., incremental build of software configurations), and dimensionality reduction methods (e.g., transfer learning, feature selection, software debloating).
I will finally argue that deep variability is both the problem and solution of frictionless reproducibility, calling the software science community to develop new methods and tools to manage variability and foster reproducibility in software systems.
Exposé invité Journées Nationales du GDR GPL 2024
The binding of cosmological structures by massless topological defectsSérgio Sacani
Assuming spherical symmetry and weak field, it is shown that if one solves the Poisson equation or the Einstein field
equations sourced by a topological defect, i.e. a singularity of a very specific form, the result is a localized gravitational
field capable of driving flat rotation (i.e. Keplerian circular orbits at a constant speed for all radii) of test masses on a thin
spherical shell without any underlying mass. Moreover, a large-scale structure which exploits this solution by assembling
concentrically a number of such topological defects can establish a flat stellar or galactic rotation curve, and can also deflect
light in the same manner as an equipotential (isothermal) sphere. Thus, the need for dark matter or modified gravity theory is
mitigated, at least in part.
What is greenhouse gasses and how many gasses are there to affect the Earth.moosaasad1975
What are greenhouse gasses how they affect the earth and its environment what is the future of the environment and earth how the weather and the climate effects.
3. INTRODUCTION
Any pair of natural number are called factors of their
product.
E.g. what are factors of 18?
1 × 18 = 18
2 × 9 = 18
3 × 6 = 18
Therefore, the factors of 18 are: 1, 2, 3. 6, 9 and 18.
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4. Introduction
A prime number is any natural number that is only
divisible by itself and one (1).
E.g. 2 ÷ 2 = 1 and 2 ÷ 1 = 2
A Prime number only has two factors; itself and one
7 ÷ 7 = 1 and 7 ÷ 1 = 7.
9 is not a Prime number.
9 ÷ 3 = 3.
Note that 1 is not a prime number because it is only
divisible by itself (1). Thus, it has only one factor.
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5. PRIME FACTORIZATION
This is obtained by dividing a number by successively
increasing prime numbers.
E.g. 2, 3, 5, 7 …
Find the prime factors of 24
Therefore, the prime factors of 24 are 2 × 2 × 2 × 3
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6. HCF & LCM
HIGHEST COMMON FACTOR (HCF)
The HCF of two natural numbers is the largest factor
that they have in common.
LOWEST COMMON MULTIPLE (LCM)
The LCM is the Lowest natural number two natural
numbers will divide into whole numbers of times.
Find the HCF and LCM of 24 and 32
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9. ROUNDING INTEGERS
Integers are rounded to their nearest multiples of 10.
If the number is less than half way to the nearest multiples of
10, it is rounded down to the previous multiples of 10.
But if the number is more than half way to the nearest
multiples of 10, it is rounded up to the nearest multiples of 10.
And if the number is half way, it is either rounded down or up
to the nearest multiples of 10.
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10. Rounding Integers
Round the following to the multiples of 10.
34 ≅ 30
36 ≅ 40
35 ≅ 30 / 40
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11. CONTACT DETAILS
Follow this YouTube link to watch the video on
Arithmetic 2
https://youtu.be/woSnNTlHBxc
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E-mail: adjexacademy@gmail.com
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