INTEGERS Q1. What are integers ? A1. The First numbers to be discovered were natural numbers i.e.1, 2,3,4,… After including Zero to them we get whole numbers. But there are negative numbers too. If we put whole numbers and negative together, the new collection is called Integers.
INTEGERS TYPES OF INTEGERS 1. Positive Integers- The positive numbers are called positive Integers e.g. 1,2,3,4,… 2. Negative Integers-The negative numbers are called Negative Integers e.g. -1,-2,-3,-4,….
INTEGERS ORDERING OF INTEGERS The numbers on the right side of zero on number line will be the bigger one, i.e. 0<1<2<3<4,…. The numbers on the left side of Zero on Number line will be smaller one, i.e. 0>-1>-2>-3>-4,…..
INTEGERS ADDITION AND SUBTRACTION WITH THE SAME SIGN We add the two positive Integers like(+3)+(+2) = +5 [=3+2] We also add when we have two negative Integers but the answer will take a minus (-) sign like (-2) +(-1)= -(2+1)= -3
INTEGERS ADDITION OF INTEGERS OF DIFFERENT SIGN When we have one positive and one negative integer, we must subtract , but the answer will take the sign of the bigger integer. ( Ignoring the sign of the numbers decide which is bigger) Example:- (+5) + (-8) = (5-8) = -3 (+6) + (- 4) = ( 6 – 4) = +2
INTEGERS USES OF INTEGERS IN DAILY LIFE Every day in our daily life we use the integers for calculations . The figures are taken in positive and negative terms and it becomes possible to do the calculations. This can be understood by the following examples.
INTEGERS RULES FOR MULTIPLICATION (-) x (+) = (-) (-) x ( -) = ( +) (+ ) x ( +) = ( +) (+ ) x ( - ) = ( - ) FROM THE ABOVE RULES IT IS CLEAR THAT REMEMBERING THE SIGN RULES IS VERY IMPORTANT IN SOLVING INTEGERS PROBLEMS OF MULTILICATION.
INTEGERS RULES FOR DIVISION ( -) / ( + ) = ( - ) ( -) / ( - ) = ( + ) ( + ) / ( + ) = ( + ) (+ ) / ( - ) = ( -) AS MULTIPLICATION IN CASE OF DIVISION ALSO THE SIGN RULES ARE VERY IMPORTANT. THE NEGATIVE AND POSITIVE NUMBERS WILL BE VALUED AS PER THE ABOVE RULES.