What is Multiplication?
- Multiplication is adding a number to itself repeatedly.
Example: ( 4 * 3 = 4 + 4 + 4 = 12 ).
- Common Symbols:
- ‘×’ for written math.
- ‘*’ in spreadsheets or coding.
Key Rules of Multiplication
- Any number × 0 = 0: ( 200 * 0 = 0 ).
- Any number × 1 = Same number: ( 200 * 1 = 200 ).
- Doubling (×2): Multiply by 2 to double the number.
- Multiplying by 10, 100, etc.:
- Add the same number of zeros as in the multiplier.
- ( 4 * 2000 = 4 * 2 = 8 ), then add 3 zeros: 8000.
Multiplication Table
The times table (1–10) helps find answers quickly. Example:
- To find ( 4 * 6 ), locate 4 in the top row and 6 in the left column. The intersection is 24.
- Order doesn't matter: ( 4 * 6 = 6 * 4 ).
Real-World Example:
- Cinema Tickets:
- 4 tickets at $8 each: ( 4 * 8 = 32 ).
- Total cost: $32.
Steps for Multiplying Larger Numbers:
Example: ( 23 * 14 )
- Set up columns (hundreds, tens, units).
- Multiply each digit in the bottom number with the digits in the top number, starting from the right.
- Add intermediate results:
- ( 4 * 3 = 12 ) Write 2 in units, carry over 1 to tens.
- ( 4 * 20 = 80 ).
- ( 10 * 3 = 30 ).
- ( 10 * 20 = 200 ).
- Add ( 12 + 80 + 30 + 200 = 322 ).
Multiplying More Than Two Numbers:
- Multiply the first two numbers.
- Multiply the result by the next number.
Example: ( 7 * 5 * 4 ).
- Step 1: ( 7 * 5 = 35 ).
- Step 2: ( 35 * 4 = 140 ).
Negative Numbers in Multiplication
- Positive × Negative = Negative:
- ( 15 * (-4) = -60 ).
- Negative × Negative = Positive:
- ( (-15) * (-4) = 60 ).
Quick Calculation Tips:
- Break down large numbers:
- ( 12 * 140 = (10 * 140) + (2 * 140) = 1400 + 280 = 1680 ).
- Use patterns: Memorize tables and repeat similar calculations for speed.
Master these steps, and multiplication becomes straightforward!