Multiplication of Large Numbers: Try All Tricks For Advanced Math

Just like in page 1, you have learnt almost all the tricks in multiplication but in examples, we have only solved short numbers, but here we will solve big numbers. The pattern, the steps, and the methods will all be the same, no change what so ever.

Example: 468 × 257 = 120276.

$\begin{array}{r} *\ \ 11 \\ *\ \ 34 \\ *\ \ 45 \\ \ \ \ \ \ \ \ \ 468 \\ × \ \ \ 257 \\ \hline \ \ \ \ \ 3276 \\ \ \ \ 2340{×} \\ \ \ \ \ 936{×}{×} \\ \hline * \ 11\ \ \ \ \ \ \ \ \ \ \\ \ 120276 \end{array}$

Step-by-step:
468 × 7 = 3276
468 × 50 = 23400
468 × 200 = 93600
Add all:
3276 + 23400 + 93600 = 120276. This is long multiplication with place value.

Another example: 758 × 406 = 307,748.

$\begin{array}{r} *\ \ 23 \\ *\ \ 34 \\ \ \ \ \ \ \ \ \ 758 \\ × \ \ \ 406 \\ \hline \ \ \ \ \ 4548 \\ \ \ \ \ \ \ 000{×} \\ \ \ 3032{×}{×} \\ \hline \ 307748 \end{array}$

Step-by-step:
758 × 6 = 4548
758 × 00 = 000
758 × 400 = 303200
Add all:
4548 + 0 + 303200 = 307748. This is another long multiplication with place value. Just like that you can try any multiplication.

Multiplication by Place Value

You can multiply by breaking numbers into hundreds, tens, and ones like we have done in page 1, it is exactly the same.
Example: 124 × 36
124 × 30 = 3720
124 × 6 = 744
Total: 3720 + 744 = 4464.
This is often faster than one large vertical sum if you are strong mentally.

Multiplication of Decimals

Decimal multiplication works by multiplying as whole numbers first, then placing the decimal point. This is the best approach. In order to be accurate, you must place the decimal on the same spot again later. Once misstep can cause incorrect solution.
Example: 3.2 × 4
First do it without decimal: 32 × 4 = 128
Since 3.2 has 1 decimal place, the answer is: 12.8

2nd Example: 2.5 × 1.4
25 × 14 = 350
There are 2 decimal places total, so: 3.50 = 3.5
Answer: 3.5

3rd Example: 32.9 × 4.872
3290 × 4872 = 16,028,880
To put zero or not with 329 is your choice. If you do not put zero then there are 4 decimal places. However the moment, you put Zero, there are 5 decimal places now like below.
There are 5 decimal places total, so the correct answer is: 160.2888
OR
4872 × 329 = 16,028,88
There are 4 decimal places total, the correct answer is still: 160.2888

Multiplication of Fractions

Fractions multiply very cleanly. Like addition or subtract, the multiplication of fraction is very easy.
Rule: Multiply numerators together and denominators together.
Example:
$\frac23 \times \frac35 = \frac{2×3}{3×5} = \frac{6}{15} = \frac25$

Another example: 1/2 × 4/7 = 4/14 = 2/7
$\frac12 × \frac47 = \frac{1×4}{2×7} = \frac{4}{14} = \frac27$

Mixed Numbers

Just like fraction, mixed number is a mix of a digit with fraction like below. The multiplication looks different but it is kind of same like addition and subtraction.
Example:
$1\frac12 × 2 = 3$
First we convert mixed number $a\frac{b}{c}$ into fraction value $\frac{b + (a × c)}{c}$:
Let’s put the above numbers:
$1\frac12 = \frac{1 + (1 × 2)}{2} = \frac{1+2}{2} = \frac32$
Then:
$\frac32 × 2 = 3$. That is how we do mixed number into fraction and then multiply

Another example:
$3\frac46 × 8 = \frac{88}{3}$
First we convert mixed number $a\frac{b}{c}$ into fraction value $\frac{b + (a × c)}{c}$:
Let’s put the above numbers:
$3\frac46 = \frac{4 + (3 × 6)}{6} = \frac{4+18}{6} = \frac{22}{6} = \frac{11}{3}$
Then:
$\frac{11}{3} × 8 = \frac{11 × 8}{3} = \frac{88}{3}$ .

Multiplication of Negative Numbers: Very Important Math Skill

Sign rules are essential. Once of most used math skill in algebra. Most of beginner learners make mistakes at some point. This could cause the fall of whole question.

Positive × positive = positive ( + , + = +)
Negative × negative = positive (- , – = +)
Positive × negative = negative (+ , – = -)
Negative × positive = negative (- , + = -)

Examples: We normally do not show positive sign. When you do not see any sign means, it is positive.
3 × 4 = 12
3 × (-4) = -12
(-3) × 4 = -12
(-3) × (-4) = 12
This is one of the most important sign rules in algebra.

Multiplication in Algebra: Learn The Basics Here

Multiplication is everywhere in algebra. It doesn’t work like addition or subtraction. The multiplication could turn into exponent or power value.
Example:

• 3x × 4 = 12x
• 2a × 3b = 6ab
• 2a × 3b × c = 6abc
• x × x = x²
• x × x × x = x³
• 2x × 5x = 10x²

Multiplying Brackets

It is an important part, in addition and subtraction, you have seen a plus or minus sign between two or more brackets but here you do not see any sign because it is multiplying.
Example: (x + 3)(x + 2)
Multiply each term:
The x from left side with x from right side: x × x = x²
Same x from left side with 2 from right side: x × 2 = 2x
Now the 3 from left side with x from right side: 3 × x = 3x
The same 3 from left side with 2 from right side: 3 × 2 = 6
So:
(x + 3)(x + 2) = x² + 5x + 6
This is a very important algebraic multiplication skill.

Fast Multiplication Tricks for Competitive Exams: Must Look

Here are the strongest speed techniques which I have already given above to you but just for revision take a look and try to remember what they were and how they were. Below are some useful examples.

1. Use distributive property to break numbers.
2. Multiply by 5, 9, 10, 11, 25, 50, and 100 using shortcuts.
3. Use round-number adjustment.
4. Reorder factors to make life easier.
5. Memorize core tables deeply.
6. Use patterns for 11 and 9.
7. Estimate first to catch mistakes.

1st Example: 98 × 7
100 × 7 = 700
700 – 14 = 686
So:
98 × 7 = 686.
A smarter mental method is often faster than the formal one.

2nd Example Type: Numbers ending in 5 Hack

This trick is for all numbers which ends with 5 whether the numbers are two digit, four, eight and even larger, it doesn’t matter. The patter – the trick stays the same.
35 × 35 = 1225
45 × 45 = 2025
55 × 55 = 3025

Rule: n5 × n5 = n(n+1)25
Example:
65 × 65
6 × 7 = 42
Add 25, why? Because 5 × 5 = 25.
Answer: 4225.

Another example:
95 × 95
9 × 10 = 90
Add 25, why? Because 5 × 5 = 25.
Answer: 9025.

One more to look at:
945 × 945
The first step: 94 × 95 = 8930
Add 25
Answer: 893,025

3rd Example Type: Multiply by 101 Trick (Awesome Trick)

Just like the above hack, this trick is also limitless, no matter how many digits multiplied by 101, the pattern stays the same.
37 × 101 = 3737
Because:
37 × (100 + 1) = 3700 + 37 = 3737

Let’s see some others:
46 × 101 = 4646
88 × 101 = 8888
97 × 101 = 9797

But the three digits works slightly different:
212 × 101 = 21412
Because: 212+212
2 + 2 = 4
Answer: 21412

Let’s see some more three digits:
498 × 101 = 50298
Same way here: 498+498
8 + 4 = 12
So 1 carries to 49 thousand: 49 + 1 = 50
Answer: 50298.

How about trying 4 digits:
1746 × 101 = 176,346
Same trick: 1746+1746
46 + 17 = 63
Easy right, the answer: 176346.

These are powerful genius-level shortcuts. Try 5 digit and answer the pattern in the comment section.

Conclusion

Multiplication is not just a table to memorize. It is a deep mathematical tool for building, scaling, combining, and solving. From simple equal groups to advanced algebraic products, multiplication rewards understanding. Once you learn the patterns, tricks, and structure behind it, you can calculate faster, reason better, and solve more advanced math with confidence.

Why Multiplication Matters in Real Life

Because it is used in:

• Shopping and prices
• Area and geometry
• Time and speed
• Science formulas
• Statistics
• Coding and algorithms
• Business calculations
• Fractions and algebra

Whenever equal groups, repeated scaling, or repeated structure appears, multiplication is there. Master the basics, then train the shortcuts. That is how multiplication becomes effortless and powerful.

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