Loading…
Free Content10 MCQs
Imagine you have a big box of colourful building blocks. Each block is a number! The Number System is like the instruction manual for playing with these blocks. It tells us what kind of blocks there are (like big ones, small ones, or special ones) and how we can put them together or take them apart. Understanding this helps us count our pocket money, share chocolates equally with friends, or even understand big scores in a cricket match!
Want to know if a big number can be divided by 9 without a remainder? Just add up all its digits! If that total can be divided by 9, then the big number can also be. This trick works because 9 is special in how numbers are built.
When you multiply many big numbers, you might only need the last digit of the answer. Don't multiply everything! Just multiply the last digits of each number. The last digit of that small product will be the last digit of your big answer.
Finding HCF or LCM of fractions (like 1/2, 3/4) looks tough, but it's not! To find the HCF of fractions, find the HCF of the top numbers (numerators) and LCM of the bottom numbers (denominators). For LCM of fractions, do the opposite: LCM of numerators / HCF of denominators.
Do you need to square a number that ends with 5, like 25 or 65? It's super fast! Take the digit before the 5 (e.g., for 25, it's 2). Multiply this digit by the next counting number (2 × 3 = 6). Then, just put 25 at the end. That's your answer!
If you want to quickly add up the first few odd numbers (like 1+3+5), there's a neat trick! Just count how many odd numbers you are adding (let's say 'n' numbers). The sum will always be n multiplied by itself (n²). It's like building a perfect square with numbers!
The Number System is simply a way to write down and work with numbers. Think of it as a language for numbers! We use numbers every day for counting, measuring, and comparing things. Knowing about the different types of numbers and how they behave is super important for solving maths problems quickly in exams.
In a number like 345:
These are quick tricks to check if a number can be divided by another number without actually doing the long division!
Understanding these basic number concepts is very useful for cracking competitive exams quickly and correctly!
Divisibility Rule of 2
A number is divisible by 2 if its last digit is 0, 2, 4, 6, or 8.Divisibility Rule of 3
A number is divisible by 3 if the sum of its digits is divisible by 3.Prime Numbers Definition
Numbers greater than 1 that have only two factors: 1 and themselves.Sum of First N Natural Numbers
Sum = n(n+1)/2HCF and LCM Product Rule
HCF(a,b) × LCM(a,b) = a × b| Type of Number | Definition | Examples |
|---|---|---|
| Natural Numbers | Counting numbers (starts from 1) | 1, 2, 3, 100 |
| Whole Numbers | Natural numbers + zero (starts from 0) | 0, 1, 5, 200 |
| Integers | Whole numbers and their negatives | -3, 0, 1, 15 |
| Rational Numbers | Can be written as p/q (fraction) | 1/2, 0.75 (3/4), -4 ( -4/1) |
| Irrational Numbers | Cannot be written as p/q (non-repeating, non-terminating decimals) | √2, π (Pi), √7 |
Q: Identify if 29 is a Prime or Composite number.
Q: What is the smallest 3-digit number that is exactly divisible by 6?
Q: Find the HCF (Highest Common Factor) of 24 and 36.
Q: The sum of three consecutive odd numbers is 69. Find the numbers.
Your mom gave you ₹500. You spent ₹250 on mobile recharge. If you want to buy a game for ₹300, how much more money do you need? This involves understanding positive and negative numbers.
In a T20 match, Team A scored 180 runs. Team B has to chase this target. If the current score of Team B is 123 runs, how many more runs do they need to win? Here you are dealing with whole numbers and simple subtraction.
You ordered a large pizza with 8 slices. If you want to share it equally among 4 friends (including yourself), how many slices does each person get? This is a division problem with natural numbers.
Your water tank has 1000 litres capacity. It is currently half full. If you use 200 litres for bathing, how many litres are left? This is about calculating with fractions and whole numbers.
What is the sum of the place value and face value of the digit '7' in the number 9735?
If a number is divisible by both 4 and 9, by which other number will it always be divisible?
Which of the following statements is true?
What is the remainder when (17 × 23 × 56) is divided by 5?
1Which of the following is an irrational number?
2The smallest prime number is:
3What is the place value of 6 in the number 45678?
4Which of the following numbers is divisible by 3?
5The product of two consecutive odd numbers is 143. What are the numbers?
6What is the HCF of 12, 18, and 30?
7Which of these numbers is divisible by 5 but not by 10?
8The sum of the first 10 natural numbers is:
9How many prime numbers are there between 1 and 20?
10If a number is multiplied by itself, the result is 169. What is the number?
Want to know if a big number can be divided by 9 without a remainder? Just add up all its digits! If that total can be divided by 9, then the big number can also be. This trick works because 9 is special in how numbers are built.
When you multiply many big numbers, you might only need the last digit of the answer. Don't multiply everything! Just multiply the last digits of each number. The last digit of that small product will be the last digit of your big answer.
Finding HCF or LCM of fractions (like 1/2, 3/4) looks tough, but it's not! To find the HCF of fractions, find the HCF of the top numbers (numerators) and LCM of the bottom numbers (denominators). For LCM of fractions, do the opposite: LCM of numerators / HCF of denominators.
Do you need to square a number that ends with 5, like 25 or 65? It's super fast! Take the digit before the 5 (e.g., for 25, it's 2). Multiply this digit by the next counting number (2 × 3 = 6). Then, just put 25 at the end. That's your answer!
If you want to quickly add up the first few odd numbers (like 1+3+5), there's a neat trick! Just count how many odd numbers you are adding (let's say 'n' numbers). The sum will always be n multiplied by itself (n²). It's like building a perfect square with numbers!
A number is divisible by 2 if its last digit is 0, 2, 4, 6, or 8.A number is divisible by 3 if the sum of its digits is divisible by 3.Numbers greater than 1 that have only two factors: 1 and themselves.+2 more formulas below