Basic (4 Function) Calculator
Basic Calculator - In most countries, students use calculators for schoolwork. There was some initial resistance to the idea out of fear that basic arithmetic skills would suffer. There remains disagreement about the importance of the ability to perform calculations "in the head", with some curricula restricting calculator use until a certain level of proficiency has been obtained, while others concentrate more on teaching estimation techniques and problem-solving. Research suggests that inadequate guidance in the use of calculating tools can restrict the kind of mathematical thinking that students engage in. Others have argued that calculator use can even cause core mathematical skills to atrophy, or that such use can prevent understanding of advanced algebraic concepts.
There are other concerns - for example, that a pupil could use the calculator in the wrong fashion but believe the answer because that was the result given. Teachers try to combat this by encouraging the student to make an estimate of the result manually and ensuring it roughly agrees with the calculated result. Also, it is possible for a child to type in -1 x -1 and obtain the correct answer '1' without realizing the principle involved. In this sense, the calculator becomes a crutch rather than a learning tool, and it can slow down students in exam conditions as they check even the most trivial result on a calculator.
Addition - Addition is the mathematical process of putting things together. The plus sign "+" means that numbers are added together. For example, in the picture on the right, there are 3 + 2 apples - meaning three apples and two other apples—which is the same as five apples, since 3 + 2 = 5. Besides counts of fruit, addition can also represent combining other physical and abstract quantities using different kinds of numbers: negative numbers, fractions, irrational numbers, vectors, and more.
As a mathematical operation, addition follows several important patterns. It is commutative, meaning that order does not matter, and it is associative, meaning that when one adds more than two numbers, order in which addition is performed does not matter (see Summation). Repeated addition of 1 is the same as counting; addition of 0 does not change a number. Addition also obeys predictable rules concerning related operations such as subtraction and multiplication. All of these rules can be proven, starting with the addition of natural numbers and generalizing up through the real numbers and beyond. General binary operations that continue these patterns are studied in abstract algebra.
Performing addition is one of the simplest numerical tasks. Addition of very small numbers is accessible to toddlers; the most basic task, 1 + 1, can be performed by infants as young as five months and even some animals. In primary education, children learn to add numbers in the decimal system, starting with single digits and progressively tackling more difficult problems. Mechanical aids range from the ancient abacus to the modern computer, where research on the most efficient implementations of addition continues to this day.
Subtraction - Subtraction is one of the four basic arithmetic operations; it is the inverse of addition, meaning that if we start with any number and add any number and then subtract the same number we added, we return to the number we started with. Subtraction is denoted by a minus sign in infix notation. The traditional names for the parts of the formula c - b = a are minuend (c) - subtrahend (b) = difference (a). The words "minuend" and "subtrahend" are uncommon in modern usage. Instead we say that c and −b are terms, and treat subtraction as addition of the opposite. The answer is still called the difference.
Subtraction is used to model four related processes: From a given collection, take away (subtract) a given number of objects. For example, 5 apples minus 2 apples leaves 3 apples. From a given measurement, take away a quantity measured in the same units. If I weigh 200 pounds, and lose 10 pounds, then I weigh 200 - 10 = 190 pounds. Compare two like quantities to find the difference between them. For example, the difference between $800 and $600 is $800 - $600 = $200. Also known as comparative subtraction. To find the distance between two locations at a fixed distance from starting point. For example if, on a given highway, you see a mileage marker that says 150 miles and later see a mileage marker that says 160 miles, you have traveled 160 - 150 = 10 miles.
In mathematics, it is often useful to view or even define subtraction as a kind of addition, the addition of the opposite. We can view 7 - 3 = 4 as the sum of two terms: seven and negative three. This perspective allows us to apply to subtraction all of the familiar rules and nomenclature of addition. Subtraction is not associative or commutative- in fact, it is anticommutative- but addition of signed numbers is both.
Multiplication - Multiplication is the mathematical operation of scaling one number by another. It is one of the four basic operations in elementary arithmetic (the others being addition, subtraction and division). Multiplication is defined for whole numbers in terms of repeated addition; for example, 3 multiplied by 4 (often said as "3 times 4") can be calculated by adding 3 copies of 4 together. Multiplication of rational numbers (fractions) and real numbers is defined by systematic generalization of this basic idea.
Multiplication can also be visualized as counting objects arranged in a rectangle (for whole numbers) or as finding the area of a rectangle whose sides have given lengths (for numbers generally). The inverse of multiplication is division: as 3 times 4 is equal to 12, so 12 divided by 3 is equal to 4. Multiplication is generalized further to other types of numbers (such as complex numbers) and to more abstract constructs such as matrices.
Division - In mathematics, especially in elementary arithmetic, division (÷) is the arithmetic operation that is the inverse of multiplication. Division can be described as repeated subtraction whereas multiplication is repeated addition.
Conceptually, division describes two distinct but related settings. Partitioning involves taking a set of size a and forming b groups that are equal in size. The size of each group formed, c, is the quotient of a and b. Quotative division involves taking a set of size a and forming groups of size b. The number of groups of this size that can be formed, c, is the quotient of a and b.
Teaching division usually leads to the concept of fractions being introduced to students. Unlike addition, subtraction, and multiplication, the set of all integers is not closed under division. Dividing two integers may result in a remainder. To complete the division of the remainder, the number system is extended to include fractions or rational numbers as they are more generally called.