The Four Fundamental Operations On Numbers

1. The Four Fundamental Operations On Numbers THE 4 FUNDAMENTAL OPERATIONS ARE 1.)addition 2.)subtraction 3.)multiplication 4.)division

2. Example: 1) Change the lower exponent to match (by dividing its number by 10 successively).2) Add the numbers.3) Keep the bigger exponent (then adjust if necessary).Example 1:4×10^6 + 9×10^41) 9×10^4 = 0.9×10^5 = 0.09×10^62) 4 + 0.09 = 4.093) 4.09×10^6Example 2:6×10^7 + 5.5×10^71) No change needed (same exponent)2) 6 + 5.5 = 113) 11×10^7 = 1.1×10^8Notice in example 1 we didn't change the exponent in step 3, but in example 2 we did.

3. Subtraction:1) Change the lower exponent to match (by dividing its number by 10 successively).2) Add the numbers.3) Keep the bigger exponent (adjust if necessary).Example 1:4×10^6 - 9×10^41) 9×10^4 = 0.9×10^5 = 0.09×10^62) 4 - 0.09 = 3.913) 3.91×10^6Example 2:6×10^7 + 5.5×10^71) No change needed (same exponent)2) 6 - 5.5 = 0.53) 0.5×10^7 = 5×10^6Notice in example 1 we didn't change the exponent in step 3, but in example 2 we did.

4. Multiplication:1) Multiply the numbers.2) Add the exponents.3) If necessary, adjust the exponent.Example:3×10^8 × 5×10^41) 3×5 = 152) 8+4 = 123) 15×10^12 = 1.5×10^13Division:1) Divide the numbers.2) Subtract the exponents.3) If necessary, adjust the exponent.Example:2×10^9 / 5×10^4 1) 3×5 = 152) 8+4 = 123) 15×10^12 = 1.5×10^13

5. Axioms Numbers Axioms of numbers are mathematical statements that are the starting points for other statements. The axioms cannot be proved mathematically, because they are the foundation from which we get mathematical theorems. These axioms are considered self-evident. Even though we don't have mathematical proof, we take it for granted that they are true. The following is axioms of the fundamental operations for the real number system. (Real numbers are every number except imaginary numbers.) These axioms lay the ground work for the properties of addition and multiplication. There is some mathematical proof for these laws, but the validity of it is controversial enough to still call them axioms. The vast majority of mathematicians however, stick with these laws whole heartedly as theorems. We have the commutative laws, the closure laws, the associative laws, the distributive laws, the identity laws, and the inverse laws. Commutative Laws: The commutative laws state that the order in addition and multiplication does not matter. Thus x+y=y+x and xy = yx. We can try out the commutative laws using two real numbers. 4+5 = 5+4 = 9, and 4*5 = 5*4 = 45.

6. Closure Laws: From the Closure Laws we get that the sum of x+y, and the product x*y are unique numbers. Associative Laws: The associative laws states that in repeated multiplication or addition, grouping does not matter. We can look at an example of the associative laws: x+(y+z) = (x+y) +z = x+y+z 3+(4+5) = (3+4)+5 = 3+4+5 = 12 x(yz) = (xy)z = xyz 3(4*5) = (3*4)5 = 60 Distributive Laws: The distributive laws states that multiplication is, as the axiom implies, distributed over addition. An example of the Distribute Laws is: x(y+z) = xy+yz 3(4+5) = 3*4+3*5 = 12+15 = 27 Identity Laws From the identity laws we get two things. First, there is a unique number 0 with the property that 0 plus any given number equals the number itself. 0+x = x 0+4 = 4

7. Fundamental Operations Operations are the arithmetic skills introduced and practiced in elementary school. The fundamental operations are addition, subtraction, multiplication, and division. Exponentiation is also an operation. In algebra, the fundamental operations are as important as they are in arithmetic. In fact, if you ever want to check your algebraic work by substituting a number for the variable, you’ll be reminded of the arithmetic exercises that look more familiar. PART1

8. Introduction to Algebraic Thinking Algebraic thinking is the bridge between arithmetic and algebra. Representing, analyzing, and generalizing a variety of patterns with tables, graphs, words, and, when possible, symbolic rules are all part of thinking algebraically.

9. Variables A variable is a symbol like x or a that stands for an unknown quantity in a mathematical expression or equation. If you remember that the word variable means changeable, then it is a little easier to remember that the value of the x or a changes depending on the situation. For example, what if you are thinking about the number of tires you need for a certain number of cars? You know that 4 tires are needed for each car. You can write 4c = t, where c is the number of cars, t is the number of tires, and 4c means 4 times c. If there are 25 cars, you can figure out that 4(25) = 100, so you will need 100 tires. If there are 117 cars, you know that 4(117) = 468 and you will need 468 tires. Because the number of cars can change but the relationship between the cars and tires stays the same, the formula 4c = t is a useful way to explain the general situation.

10. Exponents Exponents Until about four hundred years ago, nobody used exponents, but they were perfectly able to do mathematics. For example, they would write 5 · 5 · 5 · 5 · 5 · 5. But between the fourteenth and seventeenth centuries, mathematicians in Europe developed the concept of raised exponential notation. They decided to use exponents to mean how many times they wrote down the number. So, 5 · 5 · 5 · 5 · 5 · 5 was written quickly as 56.

11. Michael Dass a/l devadason 2011-01-0001 COMPUTER APPLICATIONS 2011-01-0066 Kaarthik a/l subramaniam

12. THANK YOU