Numeracy

Basics of Division '÷'





Key Points About Division

  1. Definition: Division splits a number into equal parts or groups.
  2. Symbols:
  3. ÷: Common symbol.
  4. /: Used in computers and spreadsheets.
  5. Opposite of Multiplication: Example: If (5 * 4 = 20), then (20 \div 5 = 4).

Rules of Division

  1. Dividing 0:
  2. (0 \div {any number} = 0).
  3. ({any number} \div 0): Undefined.
  4. Dividing by 1: Result is the number itself. Example: (8 \div 1 = 8).
  5. Halving: Dividing by 2 is the same as halving.
  6. Same Number: A number divided by itself equals 1. Example: (10 \div 10 = 1).
  7. Order Matters: Division is not commutative. Example: (10 \div 2 = 5), but (2 \div 10 = 0.2).
  8. Fractions Are Division: ( \frac{1}{2} ) means (1 \div 2).

Examples of Division

  1. Simple Division:
  2. (10 \div 2 = 5) (e.g., splitting 10 sweets among 2 kids).

  3. Multiple Subtractions:

  4. (10 \div 2): Subtract 2 repeatedly (10 8 6 4 2 0).
  5. Total subtractions = 5.

  6. Using Multiplication Tables:

  7. 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

  1. Use a calculator for large numbers but practice manual division to strengthen understanding.
  2. Memorize the multiplication table to simplify division.
  3. 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!


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