adding and subtracting
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To add or subtract fractions with different denominators: 1) Find the least common denominator, which is the smallest number that is a multiple of both denominators. 2) Convert the fractions to equivalent fractions with the common denominator. 3) Either add or subtract the numerators, while keeping the common denominator.
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adding and subtracting fractions
To add or subtract fractions with different denominators:
1) Find the least common denominator, which is the smallest number that is a multiple of both denominators.
2) Convert the fractions to equivalent fractions with the common denominator.
3) Either add or subtract the numerators, while keeping the common denominator.
adding and subtracting fractions with different denominators
To add or subtract fractions with different denominators, one must find the least common denominator and convert the fractions so they have the same denominator. The document demonstrates converting 1/2 to 2/4 to add it to 3/4, finding the common denominator of 4. It also shows converting 3/5 to 6/10 to subtract it from 7/10, with the common denominator being 10.
Fractions with like Denominators
The document provides instructions on adding and subtracting fractions with like denominators. It explains that when adding or subtracting fractions, you copy the denominator and then perform the operation on the numerators. Several examples are worked through, demonstrating how to identify the denominator, copy it, and then add or subtract the numerators. The key steps are to check if the denominators are the same before working the problem, and to always copy the denominator when writing the answer.
Number Theory
The document discusses key concepts in number theory including natural numbers, divisibility, factors and multiples, prime and composite numbers, and divisibility tests. It defines natural numbers as the set of counting numbers {1,2,3,4...} and notes that number theory deals with studying the properties of these numbers, with a focus on divisibility. Divisibility is defined as one number being divisible by another if dividing the first by the second leaves no remainder. Factors are numbers that divide another number, while multiples are numbers that are divisible by another number. Prime numbers have only 1 and themselves as factors, while composite numbers have more than two factors. Divisibility tests provide ways to determine if one number is divisible by
Y4 Equivalent Fractions - Qwizdom ppt
The document discusses equivalent fractions and strategies for determining if fractions are equivalent. It explains that two fractions are equivalent if they represent the same amount or value. The key strategy taught is that for two fractions to be equivalent, whatever is done to the numerator must also be done to the denominator, such as dividing or multiplying both numbers by the same amount. Examples are provided to demonstrate this approach to deciding if fractions are equal or equivalent.
Even and odd numbers worksheet (grade 4 math)
The document defines even and odd numbers and provides examples. Even numbers have a last digit of 0, 2, 4, 6, or 8, while odd numbers end in 1, 3, 5, 7, or 9. Students are asked to identify whether example numbers like 35, 408, and 514 are even or odd and perform simple math problems like adding 13 to 24 and subtracting 15 from 28 to determine if the answers are even or odd.
Synthetic division
Synthetic division is a method of polynomial long division that is more efficient by omitting variables and exponents. It involves writing the coefficients in order, switching the sign of the divisor, and repeatedly multiplying and adding the coefficients. Any non-zero remainder at the end is added above the original divisor expression.
Adding Fractions: traditional approach
This slide show covers adding two fractions with the same denominator, adding two fractions with one denominator that is a factor of the other, and, finally adding fractions with different denominators. There are a small number of questions for a class to complete as a 'check on learning' during the presentation. I'm assuming the class have access to a textbook or other collection of problems for use after the presentation.
This slideshare version is pretty dry. I usually include a visual 'starter' image of some kind, often a funny sign or joke or screen grab of a news article.
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adding and subtracting fractions
To add or subtract fractions with different denominators:
1) Find the least common denominator, which is the smallest number that is a multiple of both denominators.
2) Convert the fractions to equivalent fractions with the common denominator.
3) Either add or subtract the numerators, while keeping the common denominator.
adding and subtracting fractions with different denominators
To add or subtract fractions with different denominators, one must find the least common denominator and convert the fractions so they have the same denominator. The document demonstrates converting 1/2 to 2/4 to add it to 3/4, finding the common denominator of 4. It also shows converting 3/5 to 6/10 to subtract it from 7/10, with the common denominator being 10.
Fractions with like Denominators
The document provides instructions on adding and subtracting fractions with like denominators. It explains that when adding or subtracting fractions, you copy the denominator and then perform the operation on the numerators. Several examples are worked through, demonstrating how to identify the denominator, copy it, and then add or subtract the numerators. The key steps are to check if the denominators are the same before working the problem, and to always copy the denominator when writing the answer.
Number Theory
The document discusses key concepts in number theory including natural numbers, divisibility, factors and multiples, prime and composite numbers, and divisibility tests. It defines natural numbers as the set of counting numbers {1,2,3,4...} and notes that number theory deals with studying the properties of these numbers, with a focus on divisibility. Divisibility is defined as one number being divisible by another if dividing the first by the second leaves no remainder. Factors are numbers that divide another number, while multiples are numbers that are divisible by another number. Prime numbers have only 1 and themselves as factors, while composite numbers have more than two factors. Divisibility tests provide ways to determine if one number is divisible by
Y4 Equivalent Fractions - Qwizdom ppt
The document discusses equivalent fractions and strategies for determining if fractions are equivalent. It explains that two fractions are equivalent if they represent the same amount or value. The key strategy taught is that for two fractions to be equivalent, whatever is done to the numerator must also be done to the denominator, such as dividing or multiplying both numbers by the same amount. Examples are provided to demonstrate this approach to deciding if fractions are equal or equivalent.
Even and odd numbers worksheet (grade 4 math)
The document defines even and odd numbers and provides examples. Even numbers have a last digit of 0, 2, 4, 6, or 8, while odd numbers end in 1, 3, 5, 7, or 9. Students are asked to identify whether example numbers like 35, 408, and 514 are even or odd and perform simple math problems like adding 13 to 24 and subtracting 15 from 28 to determine if the answers are even or odd.
Synthetic division
Synthetic division is a method of polynomial long division that is more efficient by omitting variables and exponents. It involves writing the coefficients in order, switching the sign of the divisor, and repeatedly multiplying and adding the coefficients. Any non-zero remainder at the end is added above the original divisor expression.
Adding Fractions: traditional approach
This slide show covers adding two fractions with the same denominator, adding two fractions with one denominator that is a factor of the other, and, finally adding fractions with different denominators. There are a small number of questions for a class to complete as a 'check on learning' during the presentation. I'm assuming the class have access to a textbook or other collection of problems for use after the presentation.
This slideshare version is pretty dry. I usually include a visual 'starter' image of some kind, often a funny sign or joke or screen grab of a news article.
Divisible rules
Divisibility rules provide ways to quickly determine if a number is divisible by another number without performing long division. The document outlines divisibility rules for several numbers:
- A number is divisible by 2 if the last digit is even. It is divisible by 5 if the last digit is 0 or 5. It is divisible by 10 if the last digit is 0.
- For divisibility by 3, add the digits and check if the sum is divisible by 3. For 6, check if it meets the rules for both 2 and 3. For 9, check the digit sum.
- To check divisibility by 4, see if the last two digits are divisible by 4 without a remainder. For 8,
Math 7 lesson 10 representing problems with negative numbers
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Tests of divisibility
This document provides simple tests and tricks for determining if a number is divisible by certain integers between 2 and 11. It explains that to check divisibility by:
- 2, look at the last digit
- 3, sum the digits and check if divisible by 3
- 4, check if the last two digits are divisible by 4
- 5, check if the last digit is 0 or 5
- 6, check if divisible by both 2 and 3
- 8, check if the last three digits are divisible by 8
- 9, sum the digits and check if divisible by 9
- 10, check if it ends in 0
- 11, take the difference of sums of odd and even place digits.
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Prime numbers are only divisible by 1 and themselves, while composite numbers are divisible by more than two numbers. The first six prime numbers are 2, 3, 5, 7, 11, 13. Prime factorization is writing a composite number as a product of prime factors, using tools like factor trees or ladders. Students will learn how to find factors and write numbers as products of prime factors through examples and reviewing rules for divisibility.
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This document defines key math terms related to integers, the coordinate system, and rules for integer operations. It explains integers, absolute value, the x-axis, y-axis, quadrants, ordered pairs, and rules for addition, subtraction, multiplication, and division of integers. It also defines mean, commutative, associative, identity, multiplicative inverse, and distributive properties and includes example problems.
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Prime numbers are only divisible by 1 and themselves, while composite numbers are divisible by more than two numbers. The first six prime numbers are 2, 3, 5, 7, 11, 13. Prime factorization is writing a composite number as a product of prime factors, using tools like factor trees or ladders. Students will learn how to find factors and write numbers as products of prime factors.
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Prime numbers are only divisible by 1 and themselves, while composite numbers are divisible by more than two numbers. The first six prime numbers are 2, 3, 5, 7, 11, 13. Prime factorization is writing a composite number as a product of prime factors, using tools like factor trees or ladders. Students will learn how to find factors and write numbers as products of prime factors.
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This document defines integers and the rules for adding and subtracting them. It explains that integers include all whole numbers and their opposites on the number line, including zero. It provides two main rules for adding integers: 1) if the signs are the same, add the numbers and use that sign, and 2) if the signs are different, subtract the smaller number from the larger and use the sign of the number with the larger absolute value. It also notes that subtracting a negative number is the same as adding a positive number.
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The document discusses adding and subtracting simple fractions and harder fractions. It explains that when adding or subtracting fractions, they must have the same denominator. It provides examples such as 3/5 + 1/5 = 4/5 and 7/8 - 3/8 = 4/8. For harder fractions with different denominators, the document explains that we can find equivalent fractions with a common denominator to add them.
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Divisibility refers to whether a number can be divided by another number without a remainder. A number is divisible by another number if when you divide them, the result is a whole number. The document then provides rules for determining if a number is divisible by 2, 3, 5, 6, 8, 9, 10, and 4. It explains that you cannot divide by 0 because there is no number that when multiplied by 0 equals the original number.
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This document provides an overview of fractions including: examples of proper and improper fractions and mixed fractions; equivalent fractions; adding, subtracting, multiplying, and dividing fractions; comparing fractions; and how the numerator and denominator affect the size of a fraction. It explains key fraction concepts and mathematical operations involving fractions through examples.
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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.
Integers
Integers include whole numbers and their negatives, and can be located on the number line. Positive integers are to the right of zero, negatives are to the left, and zero is neutral. Integers can be compared by their positions, with larger numbers further right. Operations with integers follow rules where like signs yield a positive result, unlike signs a negative result, and zero as a product or dividend yields zero.
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This document discusses divisibility rules for numbers 0-12. It provides shortcuts to determine if a number is divisible by certain divisors without performing long division. For each rule, it explains the pattern to look for in the digits of the number. For example, a number is divisible by 2 if its last digit is even, by 5 if its last digit is 0 or 5, and by 11 if adding all even and odd digits separately and subtracting the results equals 0. The document aims to teach efficient ways to test divisibility through brief explanations and examples.
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This document provides an overview of divisibility tests for numbers 2 through 11. It explains the tests to check divisibility by each number without performing long division. For each number, it gives the rule to use (e.g. for 2 check the last digit is even), provides an example, then has practice problems checking divisibility for 5 numbers. The tests allow determining divisibility in a faster way than long division.
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Divisibility rules provide ways to quickly determine if a number is divisible by another number without performing long division. The document outlines divisibility rules for several numbers:
- A number is divisible by 2 if the last digit is even. It is divisible by 5 if the last digit is 0 or 5. It is divisible by 10 if the last digit is 0.
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This document provides simple tests and tricks for determining if a number is divisible by certain integers between 2 and 11. It explains that to check divisibility by:
- 2, look at the last digit
- 3, sum the digits and check if divisible by 3
- 4, check if the last two digits are divisible by 4
- 5, check if the last digit is 0 or 5
- 6, check if divisible by both 2 and 3
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Prime numbers are only divisible by 1 and themselves, while composite numbers are divisible by more than two numbers. The first six prime numbers are 2, 3, 5, 7, 11, 13. Prime factorization is writing a composite number as a product of prime factors, using tools like factor trees or ladders. Students will learn how to find factors and write numbers as products of prime factors through examples and reviewing rules for divisibility.
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This document defines key math terms related to integers, the coordinate system, and rules for integer operations. It explains integers, absolute value, the x-axis, y-axis, quadrants, ordered pairs, and rules for addition, subtraction, multiplication, and division of integers. It also defines mean, commutative, associative, identity, multiplicative inverse, and distributive properties and includes example problems.
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Prime numbers are only divisible by 1 and themselves, while composite numbers are divisible by more than two numbers. The first six prime numbers are 2, 3, 5, 7, 11, 13. Prime factorization is writing a composite number as a product of prime factors, using tools like factor trees or ladders. Students will learn how to find factors and write numbers as products of prime factors.
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This document is a PowerPoint presentation about fractions for 8th grade students. It contains definitions of key fraction terms like numerator, denominator, improper fractions, and mixed numbers. It explains how to add, subtract, multiply, and divide fractions, including using common denominators for addition and subtraction of unlike fractions. It also discusses equivalent fractions and how to determine if two fractions are equivalent using scale factors or cross-multiplication. The learning objectives are for students to understand fraction operations and how to find equivalent fractions.
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The real number system consists of two kinds of numbers: rational numbers and irrational numbers. Rational numbers include integers like counting numbers, whole numbers, and their opposites, as well as fractions that can be written as a ratio of two integers. Irrational numbers are any real numbers that cannot be expressed as a ratio of integers, and are therefore non-repeating and non-terminating decimals like pi.
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This document defines integers and the rules for adding and subtracting them. It explains that integers include all whole numbers and their opposites on the number line, including zero. It provides two main rules for adding integers: 1) if the signs are the same, add the numbers and use that sign, and 2) if the signs are different, subtract the smaller number from the larger and use the sign of the number with the larger absolute value. It also notes that subtracting a negative number is the same as adding a positive number.
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The document discusses adding and subtracting simple fractions and harder fractions. It explains that when adding or subtracting fractions, they must have the same denominator. It provides examples such as 3/5 + 1/5 = 4/5 and 7/8 - 3/8 = 4/8. For harder fractions with different denominators, the document explains that we can find equivalent fractions with a common denominator to add them.
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Divisibility refers to whether a number can be divided by another number without a remainder. A number is divisible by another number if when you divide them, the result is a whole number. The document then provides rules for determining if a number is divisible by 2, 3, 5, 6, 8, 9, 10, and 4. It explains that you cannot divide by 0 because there is no number that when multiplied by 0 equals the original number.
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This document provides an overview of fractions including: examples of proper and improper fractions and mixed fractions; equivalent fractions; adding, subtracting, multiplying, and dividing fractions; comparing fractions; and how the numerator and denominator affect the size of a fraction. It explains key fraction concepts and mathematical operations involving fractions through examples.
8 1 Exponents
The document discusses exponents and multiplying monomials. It provides examples of exponents like 32 meaning 3 x 3 and explains that 32 does not mean 3 x 2. It also shows how to evaluate exponents, like 63 = (6 x 6) x 6 = 216. The document then explains that when multiplying terms with the same base, you add the exponents, like 32 x 33 = 35. Finally, it defines monomials as expressions involving constants and variables and shows how to multiply them by separating coefficients and variables, like (5t)(20t3) = 100t4.
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.
Integers
Integers include whole numbers and their negatives, and can be located on the number line. Positive integers are to the right of zero, negatives are to the left, and zero is neutral. Integers can be compared by their positions, with larger numbers further right. Operations with integers follow rules where like signs yield a positive result, unlike signs a negative result, and zero as a product or dividend yields zero.
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This document discusses divisibility rules for numbers 0-12. It provides shortcuts to determine if a number is divisible by certain divisors without performing long division. For each rule, it explains the pattern to look for in the digits of the number. For example, a number is divisible by 2 if its last digit is even, by 5 if its last digit is 0 or 5, and by 11 if adding all even and odd digits separately and subtracting the results equals 0. The document aims to teach efficient ways to test divisibility through brief explanations and examples.
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Knowing the rules of divisibility will help you do mental math more efficiently. This presentation has tricks for 2-13.
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The document discusses divisibility rules and concepts related to prime and composite numbers. It provides definitions and examples of divisors, divisibility rules, prime numbers, composite numbers, prime factorization, greatest common divisor (GCD), and lowest common multiple (LCM). Divisibility rules allow testing if one number can be evenly divided by another without calculation. Prime numbers have only two factors, one and itself, while composite numbers have more than two factors. Prime factorization involves writing a composite number as a product of prime factors. The GCD is the largest number that divides into a group of numbers, and the LCM is the lowest number that all numbers in a group divide into evenly.
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This document provides an overview of divisibility tests for numbers 2 through 11. It explains the tests to check divisibility by each number without performing long division. For each number, it gives the rule to use (e.g. for 2 check the last digit is even), provides an example, then has practice problems checking divisibility for 5 numbers. The tests allow determining divisibility in a faster way than long division.
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Adding and Subtracting fractions
To add or subtract fractions with different denominators, one must first find a common denominator that both denominators evenly divide into. Then, each fraction's numerator and denominator are multiplied by the same number to convert it to equivalent fractions with the common denominator, allowing the fractions to be added or subtracted. For subtraction, the process is the same as addition except the second fraction's numerator is subtracted rather than added.
Unit 5
The document provides information about fractions, percents, and circle graphs. It includes steps for adding fractions, comparing fractions, converting between fractions and percents, drawing and interpreting circle graphs, and finding equivalent fractions. Interactive games and worksheets are referenced throughout to provide additional practice opportunities.
Marh algebra lesson
1. Natural numbers include counting numbers like 1, 2, 3, and continue indefinitely. Whole numbers include natural numbers plus zero. Integers include whole numbers and their opposites.
2. Rational numbers can be written as a fraction, like 1.5 = 3/2. Irrational numbers cannot be written as a fraction, like π.
3. The four basic operations are addition, subtraction, multiplication, and division. Addition and subtraction follow rules about sign and order. Multiplication and division rules depend on the signs of the factors or dividend and divisor.
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Adding fractions involves finding a common denominator so the fractions have the same bottom number. To do this, you multiply the denominator of one fraction by the numerator of the other fraction. Then you add the numerators and keep the common denominator. For example, to add 1/4 + 2/5, you multiply 4 by 5 to get 1/20 and multiply 5 by 4 to get 2/20. Then you add the numerators to get 3/20.
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Even and odd numbers
Even numbers are numbers that can be divided evenly by 2 and end in 0, 2, 4, 6, or 8, while odd numbers cannot be divided evenly by 2 and end in 1, 3, 5, 7, or 9. The rules for adding, subtracting and multiplying even and odd numbers always result in a whole number that is either even or odd, but dividing numbers can result in a fraction which is neither even nor odd.
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adding and subtracting
- 1. Adding & Subtracting fractions with Different Denominators By SG
- 2. 3/4 + 4/5 To find the answer to this questions you‘ll have to find the common denominator To find the common denominator (4 and 5) , you can multiply the two numbers or you could list both of the denominators and find the same number from the list. 4,8,12,16,20,24,28,32,36,40 5,10,15,20,25,30,35,40,45,50
- 3. 15/20+16/20 Now, you’ve got a common denominator. let’s find the numerator. In order to find the numerator you have to multiply what you have multiplied with the common denominator in both sides. Add the numbers you have found but you don’t add the common denominator .
- 4. The answer Now you add the numerator and leave the denominator as a same number If you add the numerator and leave the denominator the answer will come out like this (31/20) You can change it to a mixed number.
- 5. 3/6 – 3/8 For subtraction, you have to find the common denominator. To find the common denominator, the denominator have to be same so you could multiply the number or you could find it like this 6,12,18.24,30,36,42,48,54,60 8,16,24,32,40,48,56,64,72 Subtract the fraction
- 6. Subtract the numerator and leave the denominators behind 12/24 – 9/24 After you subtract the numerator you will get an answer like this (3/24)