Problem 27 - Basic Engineering Mathematics

Question

\text { Find } 12.5 \% \text { of } £ 378

Step-by-Step Solution

Answer

£47.25

Step 1: Understand the Problem

The task involves finding a certain percentage (12.5%) of a given amount (£378). To solve this, we will use the percentage formula.

Step 2: Convert Percentage to Decimal

To find 12.5% of a number, first convert the percentage to a decimal by dividing by 100: \(12.5\% = \frac{12.5}{100} = 0.125\).

Step 3: Multiply to Find the Amount

Multiply the decimal by the total amount to find 12.5% of £378: \(0.125 \times 378 = 47.25\).

Step 4: Write the Result

The value of 12.5% of £378 is £47.25.

Key Concepts

Conversion of Percentage to Decimal

In mathematics, converting a percentage to a decimal is a simple yet crucial task. This conversion helps in performing accurate calculations, especially when dealing with percentages of amounts. To convert a percentage to a decimal, you simply divide the percentage by 100. This is because percent means "per hundred," so you need to shift the decimal two places to the left. For example, to convert 12.5% to a decimal:

• Take the percentage value: 12.5%
• Divide by 100: \( \frac{12.5}{100} \)
• The decimal form is 0.125

Once in decimal form, percentages become easier to multiply by any given number. This conversion lays the groundwork for precise operations in further calculations.

Multiplying Decimals

Once you have converted a percentage to a decimal, the next step often involves multiplying that decimal with a given number. This operation is common in percentage calculations, helping us find the part of a whole.When you multiply decimals, it's important to remember:

• Align the numbers based on the rightmost digit, not the decimal point.
• Ignore the decimal points during multiplication, and just multiply the numbers as if they were whole numbers.
• Count the total number of decimal places in the factors. After multiplying, place the decimal point in the result, so it reflects the same number of decimal places.

Let's apply this to our example of finding 12.5% of £378:

• First convert 12.5% to decimal form: 0.125
• Multiply: \( 0.125 \times 378 = 47.25 \)

Thus, by multiplying decimals effectively, you determine that 12.5% of £378 is indeed £47.25.

Word Problems in Mathematics

Word problems are a staple in mathematics, challenging students to apply their numerical knowledge linguistically. In our example, the word problem asks: "Find 12.5% of £378." Solving word problems demands a clear strategy:

• Read the problem carefully to understand what is being asked.
• Identify the key values and operations needed for the solution.
• Break down the problem into manageable steps, applying relevant mathematical rules.

In the given problem, we first needed to convert the percentage into a decimal. Then, we used multiplication to find the specified percentage of the given amount. Each of these steps ties back to the text of the problem, ensuring you answer the question asked succinctly and accurately. This method not only aids in solving the word problem at hand but also strengthens overall problem-solving skills. Understanding how to interpret and dissect word problems is key to success in mathematics.