Key Points About Division
- Definition: Division splits a number into equal parts or groups.
- Symbols:
- ÷: Common symbol.
- /: Used in computers and spreadsheets.
- Opposite of Multiplication: Example: If (5 * 4 = 20), then (20 \div 5 = 4).
Rules of Division
- Dividing 0:
- (0 \div {any number} = 0).
- ({any number} \div 0): Undefined.
- Dividing by 1: Result is the number itself. Example: (8 \div 1 = 8).
- Halving: Dividing by 2 is the same as halving.
- Same Number: A number divided by itself equals 1. Example: (10 \div 10 = 1).
- Order Matters: Division is not commutative. Example: (10 \div 2 = 5), but (2 \div 10 = 0.2).
- Fractions Are Division: ( \frac{1}{2} ) means (1 \div 2).
Examples of Division
- Simple Division:
-
(10 \div 2 = 5) (e.g., splitting 10 sweets among 2 kids).
-
Multiple Subtractions:
- (10 \div 2): Subtract 2 repeatedly (10 8 6 4 2 0).
-
Total subtractions = 5.
-
Using Multiplication Tables:
- To calculate (56 \div 8): Locate (8 * = 56). Answer: (7).
Dividing Larger Numbers
Example:
- Problem: (480 \div 5)
- Steps:
- Divide (48) (from 480) by (5).
- (5) goes into (48) nine times (remainder: (3)).
- Bring down the (0) (30).
- (5) goes into (30) six times (no remainder).
- Answer: (96). Each tyre costs $96 if $480 is split among 5 tyres.
Real-Life Division Examples
Recipe Scaling:
- Problem: Ingredients for 24 cakes need adjusting for 8 cakes.
- Solution:
- Divide each ingredient by (3) ((24 \div 8 = 3)).
- Example:
- (120 \, {g butter} \div 3 = 40 \, {g butter}).
- (3 \, {eggs} \div 3 = 1 \, {egg}).
- (1 \, {tsp vanilla extract} \div 3 = \frac{1}{3} \, {tsp}).
Pro Tip: Convert units for accuracy (e.g., (1 \, {tsp} = 5 \, {ml})).
Practical Tips
- Use a calculator for large numbers but practice manual division to strengthen understanding.
- Memorize the multiplication table to simplify division.
- Estimate to verify results (e.g., check if the answer is reasonable by rounding numbers).
Division may seem tricky, but understanding the process can make it logical and straightforward!