Addition, Subtraction, Multiplication and Division
Addition, subtraction, multiplication, and division are the four basic arithmetic operations used to manipulate numbers. Addition combines two or more numbers to find their total, while subtraction finds the difference between two numbers. Multiplication is the process of repeated addition, and division is the process of splitting a number into equal parts. These operations are fundamental to solving mathematical problems.
8 Key excerpts on "Addition, Subtraction, Multiplication and Division"
eBook - ePubThe Problem with Math Is English
A Language-Focused Approach to Helping All Students Develop a Deeper Understanding of Mathematics
- Concepcion Molina(Author)
- 2012(Publication Date)
- Jossey-Bass(Publisher)
...Examine Box 6.1 to begin the investigation of this rich topic. Box 6.1 Answer the following: a. Define multiplication. b. How are division and multiplication similar? c. Define division. d. Define average (as a noun). Defining Multiplication As a fundamental operation in mathematics, multiplication appears in a variety of contexts. This makes the task of defining it more difficult because, for example, multiplication in a quadratic function does not yield the same type of result as multiplication in an area context. The focus is on fundamentals, so we will concentrate on the multiplication most applicable to real-life contexts. These would be scenarios where a total is sought based on knowing the number and size of groups or sets. Based on this application, many teachers define multiplication as “repeated addition.” Although true, this definition is woefully incomplete. Moreover, it substantially handicaps students' ability to connect to and understand critical related ideas, such as division and average. A better way to define multiplication is as “a faster process of finding a total by using equal-sized groups or sets.” The crucial idea to emphasize here is equal-sized groups. Instead of understanding 2 + 2 + 2 as the repeated addition of 2, students should view the expression as three equal-sized sets of two, which we express mathematically as 3 • 2. As noted in an earlier chapter, a national consensus does not exist as to which factor in multiplication represents the number of groups and which represents the size of each group. For the purpose of this text, the interpretation is that the first numeral represents the number of sets and the second represents the size of each set...
eBook - ePubRtI in Math
Evidence-Based Interventions
- Linda Forbringer, Wendy Weber(Authors)
- 2021(Publication Date)
- Routledge(Publisher)
...9 Operations with Whole Numbers: Multiplication and Division Number sense and operations with whole numbers form the foundation for all higher mathematics. The IES Practice Guide recommends that “instructional materials for students receiving interventions should focus intensely on in-depth treatment of whole numbers in kindergarten through grade 5” (Gersten et al., 2009, p. 6). In Chapter 7, we focused on developing number sense, and in Chapter 8, we addressed addition and subtraction of whole numbers. In this chapter, we focus on multiplication and division of whole numbers, The Common Core State Standards lay the foundation for multiplication in second grade, and it is a major focus of third grade mathematics. By the end of third grade, students should understand the concept of multiplication and division and have strategies for multiplying and dividing within 100. By the end of fourth grade, they should be fluent with multiplication and division facts and multi-digit multiplication, and begin developing an understanding of division using multi-digit dividends. Fluency with all whole number operations is expected by the end of sixth grade (National Governors Association, 2010). Developing Conceptual Understanding of Multiplication Multiplication is an extension of addition, and so students should master the concept of addition before multiplication is introduced. One of the simplest ways to show the relationship between addition and multiplication is with bar models or tape diagrams. In Chapter 8, we described how tape diagrams show the part/whole relationships in addition. The same diagrams also illustrate part/whole relationships in multiplication. See Figure 9.1 Figure 9.1 Tape Diagrams for Addition and Multiplication When the parts are of different sizes, as they are in the first drawing in Figure 9.1, we add to find the sum...
eBook - ePubUnderstanding Mathematics for Young Children
A Guide for Teachers of Children 3-7
- Derek Haylock, Anne D Cockburn(Authors)
- 2017(Publication Date)
- SAGE Publications Ltd(Publisher)
...This means that the order of two numbers in a product (or a sum) makes no difference to the result. For example, 3 × 5 = 5 × 3 (just as 3 + 5 = 5 + 3). The commutative property of multiplication is most clearly seen in a rectangular array. This image, together with the associated language, is an important component in the network of connections for understanding multiplication and division. Strictly speaking, in the repeated addition structure 9 × 3 means ‘three sets of nine’. But once commutativity is established both 9 × 3 and 3 × 9 can be connected with either ‘three sets of nine’ or ‘nine sets of three’. Another category of situations to which the language and symbols of multiplication can be connected is scaling (Multiplication Structure 2). The first experience of scaling is doubling. This leads on to relationships such as ‘twice as many’, ‘three times as much’ and ‘ten times as heavy’. Four categories of situations to which the language and symbols of division can be connected are: equal sharing between (Division Structure 1); inverse of multiplication, also called grouping (Division Structure 2); repeated subtraction (Division Structure 3); and ratio (Division Structure 4). Teachers tend to over-emphasize sharing in division. In the long run the most important structures of division are the inverse of multiplication and ratio. Ratio and difference are two ways of comparing quantities, using division and subtraction respectively. Children have many other experiences of sharing that do not correspond to the equal sharing structure of division. Multiplication and division often arise in situations involving two different contexts, such as money and weight, or distance and time. Unit fractions are those with 1 as the top number (numerator), such as a half (1 / 2), a third (1 / 3) and a quarter (1 / 4). These represent the parts that you get when one whole thing or unit is divided equally into parts...
eBook - ePubMath Intervention 3-5
Building Number Power with Formative Assessments, Differentiation, and Games, Grades 3-5
- Jennifer Taylor-Cox(Author)
- 2016(Publication Date)
- Routledge(Publisher)
...Chapter Multiplication and Division Concepts Repeated Addition Multiplication Repeated Subtraction Division Fair Shares Division Rectangular Arrays for Multiplication and Division Multiplying and Dividing by Ten Perfect Squares and Near Squares Near Tens for Multiplication Fact Families—Multiplication and Division Partial Products Partial Quotients Equal Products Repeated Addition Multiplication What is the Repeated Addition Multiplication Concept? When we multiply, the result is the total number, referred to as the product. In multiplication, we combine a certain number of groups, which is the multiplier. Each group has the same quantity, which is the multiplicand. Because addition and multiplication are interrelated operations, we obtain the same results by repeated addition. For example, 3 x 5 = 5 + 5 + 5. There are 3 groups of 5. Some students are encouraged to memorize multiplication facts before they understand the concept of multiplication. The result is inconsistent surface knowledge. Working with repeated addition builds the necessary foundations for permanent ownership of multiplication facts. CCSS Operations and Algebraic Thinking Formative Assessment To find out if a student understands repeated addition multiplication, give the student the following repeated addition equations and ask the student to give the related multiplication equation. 3 + 3 + 3 + 3 = 8 + 8 + 8 = If the student is successful, provide the following multiplication equations and ask the student to give the related repeated addition equations. 7 x 4 = 6 x 9 = If the student is not successful with either set of problems, try groups of two, five, or ten. If the student is successful with both sets of problems, try more complex problems. Successful Strategies When working with the repeated addition multiplication concept, it is often beneficial to model the groups with manipulatives or show the groups with pictures. It is also helpful to put the mathematical situations in context...
eBook - ePubHow to Teach Maths
Understanding Learners' Needs
- Steve Chinn(Author)
- 2020(Publication Date)
- Routledge(Publisher)
...There are patterns in the sequences for these sub-tasks. Counting on sets the foundation for addition, and counting back the foundation for subtraction. A difficulty with being able to count backwards is often an indicator of potential problems in maths. It can overload working memory. Materials and visuals can help learners to see the patterns and develop confidence rather than confusion. Being able to reverse sequences and procedures is a key skill for being good at maths. There is, of course, a strong link in this topic to place value. We need to keep in mind that very few skills exist in isolation. Number: Addition and subtraction Year 4. Add and subtract numbers with up to four digits using the formal written methods of columnar addition and subtraction. Where appropriate, estimate and use inverse operations to check answers to a calculation. Solve addition and subtraction two-step problems in contexts, deciding which operations and methods to use and why. Year 3. Add and subtract numbers mentally, including a three-digit number and ones, a three-digit number and tens, and a three-digit number and hundreds. Add and subtract numbers with up to three digits, using formal written methods of columnar addition and subtraction. Estimate the answer to a calculation and use inverse operations to check answers. Solve problems, including missing number problems, using number facts, place value, and more complex addition and subtraction. Year 2. Solve problems with addition and subtraction, using concrete objects and pictorial representations. Apply their increasing knowledge of mental and written methods. Recall and use addition and subtraction facts to 20 fluently. Derive and use related facts up to 100. Add and subtract numbers using concrete objects, pictorial representations and mentally. This includes a two-digit number and ones, a two-digit number and tens, and two two-digit numbers. Add three one-digit numbers...
eBook - ePubNumeracy in Nursing and Healthcare
Calculations and Practice
- Pearl Shihab(Author)
- 2014(Publication Date)
- Routledge(Publisher)
...Chapter 1 Basic arithmetic skills The things you don't want to ask about but need to know DOI: 10.4324/9781315735092-1 You need to be able to add and subtract to complete patient records accurately. You must be confident with basic arithmetic skills so that you are able to work out correct drug doses to ensure patient safety. When you have completed this chapter, you should be able to Identify your strengths and areas needing further practice or help. Understand the different ways in which the four basic operations of arithmetic can be written. Add and subtract single and multiple columns of figures without a calculator. Multiply and divide simple numbers without a calculator. Understand how exponents are used to simplify large whole numbers. Use ‘BODMAS’ to work out calculations that involve different types of operation. Use a calculator with care. Meet some of the numeracy outcomes in the Essential Skills Clusters (NMC 2010): Is competent in basic medicine calculations. Is competent in the process of medication-related calculations in the nursing field. The language Table 1.1 shows the symbols that will be used in this chapter – more later! You are probably familiar with them, which is good, but just refresh your memory of these and the rules that apply to them. Table 1.1 Symbol Meaning and uses + Plus, the sum, altogether, total or increase all indicate that one number is added to the. other, e.g. six plus three: 6 + 3. The numbers can be added in any order, the answer is the same. + can also be used as shorthand for ‘positive’; ‘ve’ is sometimes added and is written as + ve with the + sign near the top of the ve. − Decrease, difference between, reduce by, minus or ‘take away’ all indicate that the second number is subtracted from the first, e.g. six minus three: 6 − 3...
eBook - ePubMore Trouble with Maths
A Complete Manual to Identifying and Diagnosing Mathematical Difficulties
- Steve Chinn(Author)
- 2020(Publication Date)
- Routledge(Publisher)
...6 Tests of basic facts – Addition, Subtraction, Multiplication and Division Their role in mathematical learning difficulties and dyscalculia Four tests are included, one for each of the four operations. The age range covered is from 7 years to 15 years (though for 7 years only addition and subtraction are included). For test subjects above the age of 15 years, informal questions are suggested. The tests are norm-referenced from a sample of 2058 children, from over 40 independent and state schools across the UK. The tests for addition and subtraction facts have a time limit of 60 seconds. The tests for multiplication and division facts have a time limit of 120 seconds. The interpretation and implications of the answers and scores are discussed. What is a ‘basic fact’? These are the 121 addition and subtraction facts from 0 to 20 (0 + 0 to 10 + 10) and the 121 multiplication facts from 0 to 100 (0 × 0 to 10 × 10) and 100 division facts. Despite decimalisation across most measures, currently (2019) the Department of Education in England is trialling tests for ten-year-old pupils of multiplication facts up to 12 × 12. Presumably the principle behind the drive to memorise and quickly retrieve these facts from memory is that they are the basic essential facts and that they can then be used in all future calculations and computations. In Chapter 5 of ‘The Trouble with Maths’, I explain how a smaller collection of basic facts can be used, in a mathematical way, to achieve the same objectives...
eBook - ePub- Julie Henry, Henry(Authors)
- 2018(Publication Date)
- QuickStudy Reference Guides(Publisher)
...MATH Order of Operations Calculations inside parentheses should be performed first. Next, do multiplication and division, moving from left to right. Then, do addition and subtraction, moving from left to right. 5 + (6 × 4 – 3) – 13 = 5 + (24 – 3) – 13 = 5 + 21 – 13 = 13 Addition The sum of two positive numbers is a positive number. 3 + 4 = 7 The sum of two negative numbers is a negative number. –3 + (–4) = –7 The sum of one positive number and one negative number can be either a positive or a negative number, depending on which number is greater. –3 + 4 = 1 –4 + 3 = –1 When adding large numbers, line them up so the right sides are aligned vertically. 344 +299 643 Subtraction Subtraction is taking away one number from another. 8 – 4 = 4 3–8 = 3 + (–8) = –3 When subtracting large numbers, line them up so the right sides are aligned vertically. 344 –299 45 Multiplication The product of two positive numbers is a positive number. 3 × 8 = 24 The product of two negative numbers is a positive number. (–3) × (–8) = 24 The product of a positive number and a negative number is a negative number. 8 × (–3) = –24 When multiplying large numbers, line them up so...
