In this lesson, we’ll look at the different types of numbers, and the 4 operations of numbers.
Different types of numbers
Whole numbers: Numbers that start from 0 and go up without fractions or decimals. Examples are 0, 1, 2, 3, 4, and so on.
Natural numbers: Counting numbers that start from 1 and go up. Examples are 1, 2, 3, 4, and so on.
Integers: All whole numbers and their negatives. Examples include -3, -2, -1, 0, 1, 2, 3.
Negative numbers: Numbers that are less than zero. They are written with a minus sign, such as -1, -5, and -100.
Rational numbers: Numbers that can be written as a fraction of two integers (a/b, where a and b are integers, and b is not zero). For example, 1/2, -3, and 0.75 are rational numbers.
Irrational numbers: Numbers that cannot be written as a simple fraction, a/b where a and b are integers, and b is not zero. For example, √2, π are irrational numbers.
Real numbers: All numbers that can be found on the number line, including both rational and irrational numbers. This means all integers, fractions, decimals, and roots are real numbers.
Order of Operation
PEMDAS is a helpful rule that tells us the order to solve math problems with more than one operation. It stands for Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right).
- We always start off with Parentheses (or brackets)
- Next, we’ll do exponents (or anything with the power)
- Followed by multiplication and division
- And finally addition and subtraction.
Example 1: Evaluate 8 + 2 × (5 − 3)² ÷ 2 without using a calculator.
8 + 2 × (5 − 3)² ÷ 2 ==> we’ll start off with the parentheses or brackets:
8 + 2 × (2)² ÷ 2
Next, we’ll do the exponent here, which is (2)² or 4:
8 + 2 × 4 ÷ 2
Next we’ll do the multiplication and division from left to right. Since the multiplication sign is on the left, we will do it first before we do the division:
8 + 8÷ 2 = 8+4
Finally, as we are only left with the addition, we’ll do it:
8+ 4 = 12
Hence, 8 + 2 × (5 − 3)² ÷ 2 = 12