In this section, we explore the practical applications of the fundamental arithmetic operations—addition, subtraction, multiplication, and division—especially focusing on their use with negative numbers, improper fractions, mixed numbers, and temperature changes. These skills are not only essential for the Cambridge IGCSE curriculum but also for solving real-world problems.

Understanding the Four Operations

A solid understanding of the basic operations is crucial for tackling more complex problems. These operations are the building blocks of all mathematical calculations.

Addition and Subtraction

Addition combines quantities, while subtraction finds the difference. Working with negative numbers is crucial in these operations, especially in contexts like temperature changes or financial transactions.

Multiplication and Division

Multiplication is essentially repeated addition, and division breaks a number into equal parts. Mastery over fractions and decimals is necessary for these operations, particularly in practical applications.

Practical Applications

Working with Negative Numbers

Example 1: Temperature Changes

Calculate the total temperature change when the temperature drops from 0°C to -3°C.

Solution:

• Initial temperature = 0°C
• Final temperature = -3°C
• Change in temperature = Final temperature - Initial temperature
• Change in temperature = (-3) - 0 = -3°C

This means the temperature has decreased by 3°C.

Dealing with Fractions and Mixed Numbers

Fractions and mixed numbers are common in practical situations, such as measurements and financial calculations.

Example 2: Adding Mixed Numbers

Add $3\frac{1}{4}$ and $2\frac{3}{4}$.

Solution:

Convert mixed numbers to improper fractions:

Now add the fractions:

Thus, the sum of $3\frac{1}{4}$and $2\frac{3}{4}$ is 6.

Applications in Practical Situations

Budgeting and Finance

Example 3: Calculating Expenses

Calculate the total expenditure if you spend £250 on rent, £75.50 on groceries, and £48.25 on utilities.

Solution:

• Total expenditure = Rent + Groceries + Utilities
• Total expenditure = £250 + £75.50 + £48.25 = £373.75

Therefore, the total expenditure is £373.75.

Temperature Changes

Example 4: Understanding Temperature Fluctuations

If the temperature at midday is 15°C and it drops by 7°C by evening, what is the evening temperature?

Solution:

• Midday temperature = 15°C
• Temperature drop = 7°C
• Evening temperature = Midday temperature - Temperature drop
• Evening temperature = 15 - 7 = 8°C

Therefore, the temperature in the evening is 8°C.

Correct Operation Ordering and Bracket Usage

Understanding the order of operations is crucial for correctly solving mathematical problems.

Example 5: Applying BODMAS

Evaluate $2 + 3 \times (6 - 4)^2$.

Solution:

Follow BODMAS: Brackets, Orders (powers and roots), Division and Multiplication, Addition and Subtraction.

1. Solve inside the bracket: $6 - 4$

2. Square the result: $(...)^2$

3. Multiply by 3.

4. Finally, add 2

Following the correct order of operations gives us a result of 14.

Strategies for Problem-Solving

• Contextual Understanding: Grasp the real-life context of a problem to select the correct operation.
• Real Data Practice: Engage with actual data for practice.
• Review Calculations: Always double-check your work, particularly with negatives and fractions.