Imagine a world where everything—patterns, nature, technology—can be explained through numbers. To navigate this world, we must first understand its language. We start at the very beginning: whole numbers, the first building blocks of mathematics, before venturing into the intricate web of real numbers, fractions, and beyond.
Natural numbers are numbers we use for counting. It doesn’t include zero and negatives
1,2,3,4,5 ....
The place value of a number depends on its location.
5738 - 8 is in ones place so the value is 8. 3 is in tens place so the value is 30. 7 is in hundreds place so the value is 700. 5 is in thousands place so the value is 5000.
Whole numbers AKA Integers include numbers from negative, zero to positive. But it doesn’t include fractions or decimals.
Even Numbers are numbers divisible by 2.
Odd Numbers are numbers that are not divisible by 2
Arithmetic Operations
Lets look at the basic arithmetic operations. Addition, Subtraction, Multiplication, Division
4+2
6
4-2
4*2
4/2
The order of operations goes as (BODMAS) or (PEDMAS) That means
Brackets/ Parenthesis
Orders/ Exponents
Division
Multiplication
Addition
Subtraction
(8*5) - (12/4)
Out[3]:
37.0
Negative Numbers
When multiplying/ Dividing negative numbers (-) (-) always becomes +
(-) (+) always becomes (-)
Adding a negative number is like moving right along the number line.
8 + -5
Out[4]:
3
Subtracting negative numbers is something I struggled to grasp initially.
how does 3 - -5 becomes +8
8 - -5
Out[5]:
13
Subtracting a negative number is the same as adding its positive counterpart. Mathematically, this is based on the rule:
a−(−b)=a+b
A negative sign in front of a negative number cancels out.
Whenever I have trouble with this, I think of this example, If you owe someone 5(−5) and then that debt is removed(−−5),you actually gain 5 back!
Now we know what the number line is. An Absolute Value is the distance from zero on the number line. This value is always positive.
The notation is as follows, |-8| = 8 |5| = 5
Fractions
Fractions are a part of a whole.
Rational Numbers include integers and fractions.
1/2
1 is the numerator 2 is the denominator
Fraction to decimal - divide the numerator from the denominator Decimal to percentage - multiply by 100 Percentage to Fraction - divide by 100
1/2
Out[6]:
0.5
0.5*100
Out[7]:
50.0
50/100 = 1/2
Fractions Operations
Adding/ Subtracting - the denominator needs to be the same to add fractions.
1/4 + 1/2
\= 1+2/4
\= 3/4
Multiplication - Multiply numerator*numerator / denominator*denominator
2/3 * 3/4 = 6/12 = 1/2
Division - Multiply by the reciprocal of the second fraction (2/3) ÷ (3/4) = (2/3) × (4/3) = 8/9
Rations and Proportions
Rations compare 2 quantities. If there are 3 girls and 2 boys then the girls to boys ration is 3:2
Proportion is the equation that shows two rations are equal.
Prime Numbers are only divisible by 1 and itself 2,3,5,7,9,11,13,17,19,23,29
Factorization means breaking down a number to its prime factors
This is all for basic arithmetic. I understand that this is very basic level of math but this is the absolute beginning of a successful journey to conquer math. If you don’t understand the basics like the order of operations or the multiplication of fractions, then complex math will be harder to grasp. I believe starting from the beginning will help your mind to gradually grasp math from simple to complex.