Fractions: Addition and Multiplication
To add fractions, they must have a common denominator.
- Find the Least Common Denominator (LCD): The smallest multiple that both denominators share.
- Convert Fractions: Multiply the numerator and denominator of each fraction by the number that makes the denominator equal to the LCD.
- Add Numerators: Add the numerators of the fractions with the common denominator.
- Simplify: Reduce the resulting fraction to its simplest form.
|
Example:
Add \frac{1}{3} and \frac{1}{4}
- LCD of 3 and 4 is 12.
- Convert: \frac{1}{3} = \frac{1 \times 4}{3 \times 4} = \frac{4}{12} and \frac{1}{4} = \frac{1 \times 3}{4 \times 3} = \frac{3}{12}
- Add: \frac{4}{12} + \frac{3}{12} = \frac{7}{12}
- Simplify: \frac{7}{12} is already in simplest form.
|
Adding mixed numbers example:
2\frac{1}{2} + 1\frac{1}{3} = ?
\frac{5}{2} + \frac{4}{3} = ?
\frac{15}{6} + \frac{8}{6} = \frac{23}{6}
So the answer is: 3\frac{5}{6}
|
Multiplying fractions is straightforward:
- Multiply Numerators: Multiply the numerators of the fractions.
- Multiply Denominators: Multiply the denominators of the fractions.
- Simplify: Reduce the resulting fraction to its simplest form.
|
Example:
Multiply \frac{2}{5} and \frac{3}{4}
- Multiply Numerators: 2 \times 3 = 6
- Multiply Denominators: 5 \times 4 = 20
- Result: \frac{6}{20}
- Simplify: \frac{6}{20} = \frac{3}{10}
|
Multiplying mixed numbers example:
2\frac{1}{2} * 1\frac{1}{3} = ?
\frac{5}{2} * \frac{4}{3} = \frac{20}{6}
So the answer is: 3\frac{2}{6} or 3\frac{1}{3}
|
Calculating Expenses: Weekly, Monthly, Yearly
Tracking weekly expenses helps in budgeting.
- List Expenses: Identify all expenses for the week.
- Calculate Total: Sum up all the expenses.
|
Example:
Groceries: $50
Transportation: $20
Entertainment: $30
Total Weekly Expenses: $50 + $20 + $30 = $100
|
Monthly expenses provide a broader view of spending.
- List Expenses: Include all fixed and variable monthly expenses.
- Calculate Total: Sum up all the expenses.
|
Estimating from Weekly:
If weekly expenses are $100, then monthly expenses ≈ $100 \times 4 = $400
Important Note: Some months have more than 4 weeks, so a more accurate calculation is $100 * 52 / 12 ≈ $433.33
|
Yearly expenses give a long-term perspective on finances.
- List Expenses: Include all annual expenses.
- Calculate Total: Sum up all the expenses.
|
Estimating from Monthly:
If monthly expenses are $400, then yearly expenses = $400 \times 12 = $4800
|
Cost Price, Sales Price, and GST
The cost price is the original price of an item before any profit or loss.
Formula:
Cost Price = Purchase Price + Additional Expenses (e.g., transportation, repairs)
|
Example:
A shopkeeper buys a book for $50 and spends $10 on transportation. The cost price is $50 + $10 = $60
|
The sales price is the price at which an item is sold.
Formula:
Sales Price = Cost Price + Profit OR Sales Price = Cost Price - Loss
|
Example:
If the shopkeeper sells the book (with a cost price of $60) for $80, the sales price is $80. The profit is $80 - $60 = $20.
|
GST is a consumption tax added to the price of goods and services.
Formula:
GST Amount = (Original Price \times GST Rate) / 100
Sales Price with GST = Original Price + GST Amount
|
Example:
If an item costs $100 and GST is 10%:
GST Amount = ($100 \times 10) / 100 = $10
Sales Price with GST = $100 + $10 = $110
|
