Math Formulas
2026-02-28 09:10 Diff
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Arithmetic formulas form the base of all mathematical learning. They cover the four main operations: Addition, Subtraction, Multiplication, and Division, that help students calculate and understand numbers with ease, preparing them for problem-solving in advanced mathematics. Here are the following basic arithmetic operations:  

Addition (+): Addition is the process of combining two or more numbers to find their total or sum.

Formula: \(a + b = c\)
Here, a and b are the numbers being added, and c is the resulting sum.

Example: Jack has 4 Pokemon cards and John have 6 cards. If Jack decides to give his cards to John, how many cards will John have? 

Solution:
Number of cards Jack has = 4
Number of cards John has = 6 
After Jack gives John 4 cards, John will have \( = a + b = c\)
\(= 4 + 6\) 
\(= 10\)

                 So John will have a total of 10 Pokemon cards with him.

Explanation: We use addition because we are combining two amounts. Therefore, 6 cards become 10 cards.

Subtraction (-): Subtraction is used to find the difference between two numbers.

Formula: \(a − b = c\)
Here, a is the minuend, b is the subtrahend, and c is the difference.

Example : Jack takes 2 cards back from John's 10 cards. How many cards will John have left?

Solution:
Number of Cards John has = 10
Number of cards Jack takes away from John = 2
Number of cards remaining with John \(= a - b = c\) 
\(= 10 - 2\)
\(= 8\)

So now John will have a total of 8 cards with him.

Explanation: Jack took two of his cards back from your 10 cards. You will be left with only 8 cards.

Multiplication (×): Multiplication is the process of adding a number to itself a specific number of times.

Formula: \(a \times b = c\)
Here, a is the number being multiplied (the multiplicand), b shows how many times 'a' is multiplied by itself (the multiplier), and c is the final result (the product).

Example: Jack now surprised John with 3 unopened packs of pokemon cards each with 5 cards inside. How many cards in total will John get from these packs?

Solution:
Jack gives John 3 packs of Pokemon cards.
Each pack contains 5 cards.

To find the total number of cards John receives:
Total cards = \(a \times b = c\)
= Number of packs × Cards per pack
\(= 3 × 5\)
\(= 15\)

Therefore, John will get a total of 15 cards from the 3 unopened pokemon packs

Explanation: We use multiplication when we have groups of equal size. Adding would take more time, so we use multiplication instead. 

Division (÷): Division is the process of splitting a number into equal groups.

Example formula: \(a \over b\) \(= c\) or \(a ÷ b = c\).
Here, a (the dividend) is divided by b (the divisor) to get c (the quotient).


Example 4: If John have a total of 30 cards, and John decides to split the cards equally between him and Jack. How many cards would each of them get?
 

Solution:
Number of cards John has = 30
Number of people sharing the cards = 2
Number of cards each person gets = \({a \over b} = c\)
= Number of Cards John has \ Total  Number of People
= \({30} \over 2\)
\(= 15\)

Jack and John would get 15 cards each. 

Explanation: Division helps us split things into equal parts. It's especially useful when we want to share or distribute something in equal amounts.