Calculating Percentage Values

The question asks us to find the value of a mathematical expression involving percentages. The expression is: 9% of 5500 + 2.4% of 1100 - 40% of 1600.

To solve this, we need to calculate each part of the expression separately and then combine them according to the given operations.

Step 1: Calculate 9% of 5500

To find a percentage of a number, we convert the percentage to a decimal or a fraction and multiply it by the number. 9% can be written as $\frac{9}{100}$ or 0.09.

So, 9% of 5500 is calculated as:

$\frac{9}{100} \times 5500$

We can simplify this calculation:

$9 \times \frac{5500}{100} = 9 \times 55 = 495$

So, 9% of 5500 is 495.

Step 2: Calculate 2.4% of 1100

Similarly, 2.4% can be written as $\frac{2.4}{100}$ or 0.024.

So, 2.4% of 1100 is calculated as:

$\frac{2.4}{100} \times 1100$

We can simplify this calculation:

$2.4 \times \frac{1100}{100} = 2.4 \times 11$

Multiplying 2.4 by 11:

$2.4 \times 11 = (2 + 0.4) \times 11 = 2 \times 11 + 0.4 \times 11 = 22 + 4.4 = 26.4$

So, 2.4% of 1100 is 26.4.

Step 3: Calculate 40% of 1600

40% can be written as $\frac{40}{100}$ or 0.40.

So, 40% of 1600 is calculated as:

$\frac{40}{100} \times 1600$

We can simplify this calculation:

$40 \times \frac{1600}{100} = 40 \times 16$

Multiplying 40 by 16:

$40 \times 16 = 640$

So, 40% of 1600 is 640.

Step 4: Combine the results

Now we substitute the calculated values back into the original expression:

(9% of 5500) + (2.4% of 1100) - (40% of 1600)

becomes

$495 + 26.4 - 640$

First, add the first two terms:

$495 + 26.4 = 521.4$

Now, subtract the third term from this sum:

$521.4 - 640$

Since 640 is larger than 521.4, the result will be negative. We calculate the difference between 640 and 521.4:

$640 - 521.4 = 118.6$

Therefore, $521.4 - 640 = -118.6$.

The value of the expression is -118.6.

Summary of Calculations

The final value of the expression is -118.6.

Revision Table: Percentage Calculation Practice

Additional Information: Working with Percentages

Percentages are a fundamental concept in mathematics used to represent a part of a whole in terms of 100. They are widely used in various fields like finance, statistics, and everyday calculations.

• Understanding the Base: When calculating a percentage, it's important to understand what the percentage is 'of'. This number is the base or the whole. In our question, the bases were 5500, 1100, and 1600 for the respective percentage calculations.
• Percentage Increase/Decrease: Percentages are also used to describe changes. A percentage increase or decrease is calculated relative to the original value.
• Percentage Points vs. Percentage Change: It's crucial not to confuse a change in percentage points with a percentage change. For example, if an interest rate goes from 4% to 5%, that's a 1 percentage point increase, but a 25% increase in the rate itself ($\frac{5-4}{4} \times 100\% = 25\%$).

Being comfortable with percentage calculations is essential for solving many mathematical problems and understanding real-world data.