Loading…
Free Content10 MCQs
Imagine you have a messy toy box with all your toys mixed up. Simplification is like organizing that toy box, putting everything in its right place to make it neat and easy to understand. In math, it means making a big, complicated number problem small and simple. This helps us find the right answer quickly, especially when you're calculating your total grocery bill with different discounts and taxes!
When you need to multiply a number by a slightly bigger or smaller number, break the second number into simpler parts. This is called the distributive property. It makes mental multiplication super fast!
Think of it like sharing your tiffin box (the first number) with two friends (the broken-down parts of the second number). You give some to the first friend, and some to the second, then add up what they got.
Want to quickly find the square of any number ending with 5? Here's a cool trick! Just remember, the last two digits will always be 25. For the front part, take the first digit(s), multiply it by the next consecutive number (the number just after it), and put that result in front of 25.
Multiplying by numbers like 5, 25, or 125 can be tricky, but there's an easy way! Think of them as fractions of 10, 100, or 1000. This turns multiplication into division, which is often easier.
Usually, we add numbers from right to left (starting with the ones place). But in competitive exams, you can speed up by adding from left to right, especially with bigger numbers. This helps you keep track of the sums in your head.
Imagine you have ₹450 and someone gives you ₹320. You first add the hundreds (400+300 = 700), then tens (50+20 = 70), then combine (700+70 = 770).
Adding fractions with different bottom numbers (denominators) can be tricky. Use the 'Butterfly Method' for two fractions! You cross-multiply and then multiply the bottom numbers. It's like drawing a butterfly!
It works like this: For a/b + c/d, the top number (numerator) becomes (a×d) + (c×b), and the bottom number (denominator) becomes (b×d).
Simplification is simply finding the final value of a mathematical expression (a math sentence with numbers and symbols). It's like solving a puzzle where you have many pieces, and you need to put them in the correct order to see the full picture. When you see a problem like 5 + 3 × 2 - (6 ÷ 3), it looks confusing. Simplification gives us a clear path to solve it step-by-step.
The most important rule in simplification is BODMAS. It's an acronym (a word made from the first letters of other words) that tells you the correct order to do math operations. Think of it as a roadmap for solving complex problems. If you don't follow this order, you might get the wrong answer!
Without BODMAS, everyone might solve a problem differently. For instance, in 2 + 3 × 4, if you add first (2+3=5, then 5×4=20), you get 20. But if you multiply first (3×4=12, then 2+12=14), you get 14. BODMAS tells us multiplication comes before addition, so 14 is the correct answer. This rule makes sure we all speak the same math language and get the same right answer every time!
Simplification problems can also involve fractions (like 1/2) and decimals (like 0.5). The BODMAS rule still applies. When dealing with fractions, you might need to find a common denominator (a common bottom number) for addition or subtraction. For multiplication, you multiply the top numbers and bottom numbers. For division, you flip the second fraction and then multiply. Decimals are handled just like whole numbers, but you need to be careful with the decimal point in the final answer.
BODMAS Rule
Bracket → Order → Division → Multiplication → Addition → SubtractionAlgebraic Identity 1
(a + b)² = a² + b² + 2abAlgebraic Identity 2
(a - b)² = a² + b² - 2abAlgebraic Identity 3
a² - b² = (a - b)(a + b)Algebraic Identity 4
(a + b)³ = a³ + b³ + 3ab(a + b)| Operation | Order in BODMAS | Example |
|---|---|---|
| Brackets | 1st Priority | (5 + 2) = 7 |
| Orders (Powers/Roots) | 2nd Priority | 3² = 9, √16 = 4 |
| Division | 3rd Priority (L→R with Multiplication) | 10 ÷ 2 = 5 |
| Multiplication | 3rd Priority (L→R with Division) | 5 × 3 = 15 |
| Addition | 4th Priority (L→R with Subtraction) | 7 + 4 = 11 |
| Subtraction | 4th Priority (L→R with Addition) | 12 - 5 = 7 |
Q: Simplify: 18 - 4 × 3 + (15 ÷ 5)
Q: Simplify: 25 + [36 ÷ {9 - (2 + 1)}]
Q: Simplify: 1/4 of (20 + 4²) - 5
Q: Simplify: 0.5 × 12 + (1.2 ÷ 0.4) - 2.5
You're at the supermarket. You buy 3 packets of biscuits for ₹20 each, and 2 bottles of juice for ₹35 each. There's a special offer: get ₹10 off your total bill. How much do you pay?
In your favorite video game, you scored 150 points. Then, you completed a bonus level, multiplying your score by 2. But you also lost 20 points for a mistake. What's your final score?
Your cricket team scored 180 runs in the first innings. In the second innings, they scored half of the first innings' runs. If 15 runs were penalty runs, what was the total score?
You ordered a pizza cut into 8 slices. You ate 3 slices. Your friend ate 2 slices. If there were 2 pizzas initially, how many slices are left?
What is the value of 5 + 5 × 5 - 5 ÷ 5?
Simplify: 120 ÷ 4 × (1/2 + 1/4)
What is the value of 8 + 8 × 8 - 8 ÷ 8 + 8?
If 'P' means '+', 'Q' means '×', 'R' means '÷', and 'S' means '-', then 18 Q 12 R 4 P 5 S 6 = ?
1Simplify: 100 - [80 ÷ (4 × 5)]
2What is the value of 7 + 7 × 7 - 7?
3Simplify: (60 ÷ 10) × 4 - 8
4Calculate: 1/2 + 3/4 - 1/8
5If A = 5, B = 2, then what is the value of (A + B)² - (A - B)²?
6Simplify: 121 ÷ 11 × 3 - 5 + 2
7Value of (0.2)² + (0.3)²
8Simplify: 50 + 50 ÷ 50 × 2 - 10
9Which operation should be performed first in 15 - (3 + 4) × 2?
10Simplify: 144 ÷ 12 + 8 × 2
When you need to multiply a number by a slightly bigger or smaller number, break the second number into simpler parts. This is called the distributive property. It makes mental multiplication super fast!
Think of it like sharing your tiffin box (the first number) with two friends (the broken-down parts of the second number). You give some to the first friend, and some to the second, then add up what they got.
Want to quickly find the square of any number ending with 5? Here's a cool trick! Just remember, the last two digits will always be 25. For the front part, take the first digit(s), multiply it by the next consecutive number (the number just after it), and put that result in front of 25.
Multiplying by numbers like 5, 25, or 125 can be tricky, but there's an easy way! Think of them as fractions of 10, 100, or 1000. This turns multiplication into division, which is often easier.
Usually, we add numbers from right to left (starting with the ones place). But in competitive exams, you can speed up by adding from left to right, especially with bigger numbers. This helps you keep track of the sums in your head.
Imagine you have ₹450 and someone gives you ₹320. You first add the hundreds (400+300 = 700), then tens (50+20 = 70), then combine (700+70 = 770).
Adding fractions with different bottom numbers (denominators) can be tricky. Use the 'Butterfly Method' for two fractions! You cross-multiply and then multiply the bottom numbers. It's like drawing a butterfly!
It works like this: For a/b + c/d, the top number (numerator) becomes (a×d) + (c×b), and the bottom number (denominator) becomes (b×d).
Bracket → Order → Division → Multiplication → Addition → Subtraction(a + b)² = a² + b² + 2ab(a - b)² = a² + b² - 2ab+2 more formulas below