Solving Percentage Problems: Finding a Fraction of a Number

This problem involves understanding and applying percentage calculations. We are given a relationship between a number and a percentage of it, and then asked to find a percentage of a percentage of that same number. Let's break it down step-by-step.

Step 1: Find the Original Number

We are told that 80% of a certain number is equal to 768. Let's call the original number 'x'. We can write this information as an equation:

$$\text{80% of } x = 768$$

To solve for x, we convert the percentage to a decimal (80% is 0.80) and set up the equation:

$$0.80 \times x = 768$$

Now, we isolate x by dividing both sides of the equation by 0.80:

$$x = \frac{768}{0.80}$$

To make the division easier, we can remove the decimal by multiplying the numerator and denominator by 100:

$$x = \frac{768 \times 100}{0.80 \times 100} = \frac{76800}{80}$$

Simplify the fraction:

$$x = \frac{7680}{8} = 960$$

So, the original number is 960.

Step 2: Calculate 5% of the Original Number

Next, we need to find 5% of the number we just found, which is 960. Again, we convert the percentage to a decimal (5% is 0.05) and multiply:

$$5\% \text{ of } 960 = 0.05 \times 960$$

$$0.05 \times 960 = 48$$

So, 5% of the original number (960) is 48.

Step 3: Calculate 40% of the Result from Step 2

Finally, we need to find 40% of the result from Step 2, which is 48. Convert 40% to a decimal (0.40 or 0.4) and multiply:

$$40\% \text{ of } 48 = 0.40 \times 48$$

$$0.4 \times 48 = 19.2$$

Therefore, 40% of 5% of the original number is 19.2.

Summary of Percentage Calculation Steps

Here’s a quick look at the calculations:

Final Answer Determination

Following the steps, 40% of 5% of the number is 19.2.

Revision Table: Key Percentage Concepts

Additional Information: Applying Percentages

Percentage calculations are fundamental in many areas, including finance, statistics, and everyday shopping. Understanding how to convert percentages to decimals or fractions and how to find a part of a whole or the whole from a part is crucial.

• Percentages can be greater than 100% (e.g., 120% means 1.2 times the number).
• Finding 'a% of b% of a number' involves sequential multiplication: (a/100) * (b/100) * number.
• It's often helpful to estimate the answer before calculating. For example, 5% of 960 is roughly 5 times 10 (since 960 is close to 1000/100), which is 50. 40% of 50 is 0.4 * 50 = 20. Our answer 19.2 is close to 20, suggesting our calculation is likely correct.