Arithmetic 2

Secondary One Mathematics

-Lesson


Basically, there are four types of arithmetic operation. They are addition, substruction, multiplication and division.


Addition


Addition is the basic operation of arithmetic. In its simplest form, addition combines two numbers, the addends or terms, into a single number, the sum of the numbers. Adding more than two numbers can be viewed as repeated addition; this procedure is known as summation and includes ways to add infinitely many numbers in an infinite series; repeated addition of the number one is the most basic form of counting. Addition is commutative and associative so the order in which the terms are added does not matter. The identity element of addition (the additive identity) is 0, that is, adding zero to any number will yield that same number. Also, the inverse element of addition (the additive inverse) is the opposite of any number, that is, adding the opposite of any number to the number itself will yield the additive identity, 0. For example, the opposite of 7 is (-7), so 7 + (-7) = 0. Addition can be given geometrically as follows. If a and b are the lengths of two sticks, then if we place the sticks one after the other, the length of the stick thus formed will be a+b


Subtraction



Subtraction is essentially the opposite of addition. Subtraction finds the difference between two numbers, the minuend minus the subtrahend. If the minuend is larger than the subtrahend, the
difference will be positive; if the minuend is smaller than the subtrahend, the difference will be negative; and if they are equal, the difference will be zero. Subtraction is neither commutative nor associative. For that reason, it is often helpful to look at subtraction as addition of the minuend and the opposite of the subtrahend, that is a − b = a + (−b). When written as a sum, all the properties of addition hold.


Multiplication



Multiplication is the second basic operation of arithmetic. Multiplication also combines two numbers into a single number, the product. The two original numbers are called the multiplier and the multiplicand, sometimes both simply called factors. Multiplication is best viewed as a scaling operation. If the real numbers are imagined as lying in a line, multiplication by a number, say "x", greater than 1 is the same as stretching everything away from zero uniformly, in such a way that the number 1 itself is stretched to where x was. Similarly, multiplying by a number less than 1 can be imagined as squeezing towards zero. (Again, in such a way that 1 goes to the multiplicand.) Multiplication is commutative and associative; further it is distributive over addition and subtraction. The multiplicative identity is 1, that is, multiplying any number by 1 will yield that same number. Also, the multiplicative inverse is the reciprocal of any number, that is, multiplying the reciprocal of any number by the number itself will yield the multiplicative identity.


Division

Division is essentially the opposite of multiplication. Division finds the quotient of two numbers, the dividend divided by the divisor. Any dividend divided by zero is undefined. For positive numbers, if the dividend is larger than the divisor, the quotient will be greater than one, otherwise it will be less than one (a similar rule applies for negative numbers). The quotient multiplied by the divisor always yields the dividend. Division is neither commutative nor associative. As it is helpful to look at subtraction as addition, it is helpful to look at division as multiplication of the dividend times the reciprocal of the divisor, that is a ÷ b = a × 1/b. When written as a product, it will obey all the properties of multiplication.

-Rules/ formulae



BODMAS- Bracket of Division, Multiplication, Addition and Subtraction



Basically it means that when facing an equation, you should simplify everything in the brackets first, followed by division, multiplication, addition and last but not least, subtraction.



Here's and example: (2+4)x14/7-12=?



Well, if you followed the BODMAS rule, you should get a staggering 0. Wow. Amazing.


-National Education

When was Singapore grouped together with Penang and Malacca to form the Straits Settlements?

Clue: (500x6)/(1+2-1x2/2)+500-174

Answer: Please highlight the blank--> In the year 1826

Well, that's the end for today's lesson. Come back tomorrow for the next lesson. P.S. I wonder why no one has entered the "daily" contest? Hmm.. I wonder why?

-END-

Sources: Wikipedia, Google and images.google