Rules for integers for class 6
Answers
The product of a positive integer and a negative integer is negative. RULE 2: The product of two positive integers is positive. ... RULE 1: The quotient of a positive integer and a negative integer is negative. RULE 2: The quotient of two positive integers is positive.
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Answer:
Step-by-step explanation:
Rules to Add and Subtract
Integers are a special group of numbers that are positive, negative and zero, which are not fractions. Rules for addition and subtraction are the same for all.
Negative Sign and Positive Sign
The integers which we add or subtract could be positive or negative. Hence, it is necessary to know the rules for positive and negative symbols.
Positive sign/symbol: (+)
Negative sign/symbol: (-)
Addition of Integers
The three main possibilities in the addition of integers are:
Addition between two positive numbers
Addition between two negative numbers
Addition between a positive number and a negative number
Type of Numbers Operation Result Example
Positive + Positive Add Positive (+) 10 + 15 = 25
Negative + Negative Add Negative (-) (-10) + (-15) = -25
Positive + Negative* Subtract Positive (+) (-10) + 15 =5
Negative + Positive* Subtract Negative (-) 10 + (-15)= -5
Whenever a positive number and a negative number are added, the sign of the greater number will decide the operation and sign of the result. In the above example 10 + (-15) = -5 and (-10) + 15 =5; here, without sign 15 is greater than 10 hence, numbers will be subtracted and the answer will give the sign of the greater number.
We know that the multiplication of negative sign and a positive sign will result in negative sign, therefore if we write 10 + (-5), it means the ‘+’ sign here is multiplied by ‘-’ inside the bracket. Therefore, the result becomes 10 – 5 = 5.
Alternatively, to find the sum of a positive and a negative integer, take the absolute value (“absolute value” means to remove any negative sign of a number, and make the number positive) of each integer and then subtract these values. Take the above example, 10 + (-15); absolute value of 10 is 10 and -15 is 15.
⇒ 10 – 15 = -5
Thus, we can conclude the above table as follow:
Adding two positive integers results in positive integer
Adding two negative integers results in a sum of integers with a negative sign.
Addition of a positive and a negative integer gives either a positive or negative-sum depending on the value of the given numbers.
Note: The sum of an integer and its opposite is always zero. (For example, -5 + 5= 0)
Subtraction of Integers
Like in addition, the subtraction of integers also has three possibilities. They are:
Subtraction between two positive numbers
Subtraction between two negative numbers
Subtraction between a positive number and a negative number
For ease of calculation, we need to renovate subtraction problems the addition problems. There are two steps to perform this and are given below.
Convert the subtraction sign into an addition sign.
After converting the sign, take the inverse of the number which comes after the sign.
Once the transformation is done, follow the rules of addition given above.
For example, find the value of: (-5) – (7)
Step 1: Change the subtraction sign into an addition sign
⇒ (-5) + (7)
Step 2: Take the inverse of the number which comes after the sign
⇒ –5 + (-7) (opposite of 7 is -7)
⇒ –5 + (-7) = -12 [Add and put the sign of greater number]
Multiplication of Integers
In addition and subtraction, the sign of the resulting integer depends on the sign of the largest value. For example, -7+4 = -3 but in the case of multiplication of integers, two signs are multiplied together.
(+) × (+) = + Plus x Plus = Plus
(+) x (-) = – Plus x Minus = Minus
(-) × (+) = – Minus x Plus = Minus
(-) × (-) = + Minus x Minus = Plus
Rules:
When two positive integers are multiplied then the result is positive.
When two negative integers are multiplied then also the result is positive.
But when one positive and one negative integer is multiplied, then the result is negative.
When there is no symbol, then the integer is positive.
Solved Examples
Example 1: Evaluate the following:
(-5 )+ 9
(-1) – ( -2)
Solution:
(-5 )+ 9 = 4 [Subtract and put the sign of greater number]
(-1) – ( -2)
⇒ (-1) + (-2) [Transform subtraction problems into addition problems]
⇒ (-1) + (2) [Subtract and put the sign of greater number]
Hence,
(-1) – ( -2) = 1