Integers

Integers

An integer is a number that can be written without a fractional component. For example, 21, 4, 0, and −2048 are integers, while 9.75,
5 1⁄2, and √2 are not

Source

Source

0 is an integer, but it is neither positive nor negative.

Positive and negative integers are called directed numbers.  It is because an integer shows its direction from 0 as well as its distance from 0.

Number line

If we look at the number line from left to right, the numbers get BIGGER.  They increase in size.  This is called ascending order.  

If we look at the number line from right to left, the numbers get SMALLER.  They decrease in size.   This is called descending order.

Every integer has an opposite.  The opposite of +6 is -6.  These numbers are called additive inverse.  If we add a number to its additive inverse, the answer will always be 0 (zero).

For example: 6 and -6 are additive inverses as -6 + 6 = 0

Addition and subtraction of integers:

For learners in Gr 7, a number line will be helpful until learners understand that whole concept.

Lets take an example:

7 - 9 =a

Learners can circle positive 7

They have to take 9 away. Taking 9 away will send us in a negative direction which is to the left.

Learners will end up by -2 (negative two)

We can say that 7 - 9 = -2

An easier way learners can do this after learning the basics:

7 - 9 = []

• Take the biggest number (without the sign)
• The biggest number is 9. Now we can say that the biggest number has a negative in front of it.  This means that the answer will also be negative (-)
• Take both numbers now, 7 is positive and 9 is negative.  We already know the answer will be negative. 
• Subtract the bigger number with the smaller number.  (9-7 = 2)
• The answer will be 2.
• Now we add the negative sign.  
• The final answer will be -2

If both numbers are negative:

-5 - 5 =[]

• Both of these numbers are negative. On a number line the learners will circle -5 and subtract another 5, going in the left direction.

Doing this sum without a number line we can say that both numbers are negative.  So the answer will still be negative.  Take the two numbers and add them together..  

• 5 + 5 = 10
• The final answer will be - 10

Conclusion:

When adding or subtracting integers we can do the following without a number line:

• If both number has a + sign we just add the numbers together. (7 + 5 = 12)
• If one number is positive and the other negative, we subtract the numbers and use the sign of the biggest number to use at the answer.  ( -8 + 5 = - 3) 
• If both numbers are negative, the answer stays negative and we add the digits together.  (- 19 - 5 = -24)

Make sure learners understand the concept of adding and subtracting integers before we can move on to multiplying integers.