Guide in Mastering the Rules of Integers

One of the first few topics during my first year in high school was Integers, and I was like "Oh, it's interesting!" And it really is. Aside from the fact that I love Math, this topic is not that complex. It's like the fundamental operations only with just a little bit of difficulty.

However, the way I view it may not be the same for others. As such, here's my discussion on how you can learn to love this topic as well. 

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What are Integers?

They are numbers that include positive and negative numbers and zero. We use integers for counting and working with whole quantities. Remember, integers do not have any fractions or decimals. They are just whole numbers.

In a number line, positive numbers are on the right side of zero, negative numbers are on the left side, and zero is right in the middle.

Positive + Positive = Positive

Example:

10 + 10 = 20

35 + 46 = 81

16 + 23 = 39

48 + 55 = 103

67 +11 = 78

Remember: When you add two positive numbers together, the result is also positive.

Negative + Negative = Negative

Example:

-12 + -16 = -28

-35 + -56 = -91

-23 + -34 = -57

-67 + -12 = -79

-57 + -45 = -102

Remember: When you add two negative numbers together, the result is negative.

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Negative + Positive = subtract, then you need to copy the sign of the larger number.

Example:

-25 + 26 = 1

-34 + 12 =-22

-67 + 89 =22

-53 + 46 = -7

-1 + 100 = 99

Remember: When you add a negative number and a positive number together, you subtract the smaller number from the bigger number, and then you keep the sign of the bigger number.

Negative - Positive = change the sign of the subtrahend then proceeds in addition.

Example:

-12 - 16 =

-12 + -16 = -28

-35 - 56 = 

-35 + -56 = -91

-23 - 34 = 

-23 + -34 = -57

-67 - 12 = 

-67 + -12 = -79

-57 - 45 = 

-57 + -45 = -102

Remember: When you subtract a positive number from a negative number, you change the sign of the number you are subtracting (the subtrahend) and then proceed with addition.

Positive × Positive = Positive

Example:

12 x 3 = 36

25 x 7 = 175

37 x 10 = 370

49 x 13 = 637

61 x 16 = 976

Remember: When you multiply two positive numbers together, the result is positive.

Negative × Positive = Negative

Example:

-4 x 5 = -20

-10 x 11 = -110

-14 x 16 = -224

-18 x 21 = -378

-22 x 26 = -572

Remember: When you multiply a negative number by a positive number, the result is ALWAYS negative.

Negative × Negative = Positive

Example:

-12 x -3 = 36

-25 x -7 = 175

-37 x -10 = 370

-49 x -13 = 637

-61 x -16 = 976

Remember: When you multiply two negative numbers together, the result is positive.

Positive ÷ Positive = Positive

Example:

100 ÷ 5 = 20

88 ÷ 4 = 22

64 ÷ 8 = 8

42 ÷ 7 = 6

36 ÷ 3 = 12

Remember: When you divide a positive number by a positive number, the result is positive.

Positive ÷ Negative = Negative

Example:

100 ÷ -5 = -20

88 ÷ -4 = -22

64 ÷ -8 = -8

42 ÷ -7 = -6

36 ÷ -3 = -12

Remember: When you divide a positive number by a negative number, the result is ALWAYS negative.

Negative ÷ Negative = Positive

Example:

-40 ÷ -5 = 8

-38 ÷ -2 = 19

-27 ÷ -9 =3

-18 ÷ -3 = 6

-12 ÷ -4 = 3

Remember: When you divide a negative number by a negative number, the result is ALWAYS positive.

The Bottom Line

That's how integers work! There are certain rules to follow, but with the right mindset and attitude for practice solving, you will master it soon.

Please leave a comment if you appreciate it, and do not forget to share to help others understand its fundamentals too!

Junior High School Notes