Subtraction

Subtraction is an arithmetic operation that represents the operation of removing objects from a collection. The result of a subtraction is called a difference. Subtraction is signified by the minus sign (−). For example, in the adjacent picture, there are 5 − 2 apples—meaning 5 apples with 2 taken away, which is a total of 3 apples. Therefore, the difference of 5 and 2 is 3, that is, 5 − 2 = 3. Subtraction represents removing or decreasing physical and abstract quantities using different kinds of objects including negative numbers, fractions, irrational numbers, vectors, decimals, functions, and matrices.1 + ... = 3The difference is written under the line.9 + ... = 5The required sum (5) is too small.So, we add 10 to it and put a 1 under the next higher place in the subtrahend.9 + ... = 15Now we can find the difference like before.(4 + 1) + ... = 7The difference is written under the line.The total difference.7 − 4 = 3This result is only penciled in.Because the next digit of the minuend is smaller than the subtrahend, we subtract one from our penciled-in-number and mentally add ten to the next.15 − 9 = 6Because the next digit in the minuend is not smaller than the subtrahend, We keep this number.3 − 1 = 23 − 1 = ...We write the difference under the line.5 − 9 = ... The minuend (5) is too small!So, we add 10 to it. The 10 is 'borrowed' from the digit on the left, which goes down by 1.15 − 9 = ... Now the subtraction works, and we write the difference under the line.6 − 4 = ...We write the difference under the line.The total difference.1 − 3 = not possible.We add a 10 to the 1. Because the 10 is 'borrowed' from the nearby 5, the 5 is lowered by 1.4 − 9 = not possible.So we proceed as in step 1.Working from right to left:11 − 3 = 814 − 9 = 56 − 4 = 2The smaller number is subtracted from the greater:700 − 400 = 300Because the minuend is greater than the subtrahend, this difference has a plus sign.The smaller number is subtracted from the greater:90 − 50 = 40Because the minuend is smaller than the subtrahend, this difference has a minus sign.The smaller number is subtracted from the greater:3 − 1 = 2Because the minuend is greater than the subtrahend, this difference has a plus sign.+300 − 40 + 2 = 262Addition (+)Subtraction (−)Multiplication (× or ·)Division (÷ or /) Subtraction is an arithmetic operation that represents the operation of removing objects from a collection. The result of a subtraction is called a difference. Subtraction is signified by the minus sign (−). For example, in the adjacent picture, there are 5 − 2 apples—meaning 5 apples with 2 taken away, which is a total of 3 apples. Therefore, the difference of 5 and 2 is 3, that is, 5 − 2 = 3. Subtraction represents removing or decreasing physical and abstract quantities using different kinds of objects including negative numbers, fractions, irrational numbers, vectors, decimals, functions, and matrices. Subtraction follows several important patterns. It is anticommutative, meaning that changing the order changes the sign of the answer. It is also not associative, meaning that when one subtracts more than two numbers, the order in which subtraction is performed matters. Because 0 is the additive identity, subtraction of it does not change a number. Subtraction also obeys predictable rules concerning related operations such as addition and multiplication. All of these rules can be proven, starting with the subtraction of integers and generalizing up through the real numbers and beyond. General binary operations that continue these patterns are studied in abstract algebra. Performing subtraction is one of the simplest numerical tasks. Subtraction of very small numbers is accessible to young children. In primary education, students are taught to subtract numbers in the decimal system, starting with single digits and progressively tackling more difficult problems. In advanced algebra and in computer algebra, an expression involving subtraction like A − B is generally treated as a shorthand notation for the addition A + (−B). Thus, A − B contains two terms, namely A and −B. This allows an easier use of associativity and commutativity. Subtraction is written using the minus sign '−' between the terms; that is, in infix notation. The result is expressed with an equals sign. For example,