How to Work out a Fraction of an Amount

In today’s blog post, we are going to explore how to calculate fractions of an amount. This is a fundamental math skill that will be useful for various real-life applications. It’s not a tricky task, but you need to follow a series of steps to arrive at the correct answer. Let’s dive right in with a straightforward example.

Understanding Fractions of an Amount

Let’s start with a really simple question: Three quarters of 80. What does that mean? When we say we want to work out three quarters of 80, we’re essentially breaking down the number 80 into equal parts and then taking three out of those four parts.

Visual Representation

Imagine a bar that represents the number 80.

Now, if we want to find out what one quarter of this bar is, we need to divide the bar into four equal parts. Each part will represent one quarter of the bar.

Step-by-Step Calculation

Step 1: Find One Quarter

To calculate one quarter of 80, we need to divide 80 by 4 (since a quarter is one part out of four equal parts).

80 ÷ 4 = 20

So, one quarter of 80 is 20.

Step 2: Find Three Quarters

Since three quarters is three times one quarter, we simply multiply one quarter by three.

3 × 20 = 60

Therefore, three quarters of 80 is 60.

“Understanding the reasoning behind each step makes solving these problems much simpler.”

Why We Divide and Multiply

You might wonder why we divide by 4 and multiply by 3. The number 4 is significant because it’s the denominator in our fraction (three quarters). It represents the four equal parts of the whole (80 in this case). We divide by 4 to find the value of one part and then multiply by 3 (the numerator) because we want three of those parts.

Another Example: Two Fifths of 125

Let’s try another example. What is two fifths of 125?

Step 1: Find One Fifth

First, we need to divide 125 by 5 (since we are working with fifths, or five equal parts).

125 ÷ 5 = 25

One fifth of 125 is 25.

Step 2: Find Two Fifths

Next, we multiply that one fifth by 2 because we want two of those parts.

2 × 25 = 50

So, two fifths of 125 is 50.

Visualizing the Calculation

Visual aids can significantly help in understanding how fractions work. Let’s represent 125 as a bar divided into five equal parts.

By dividing 125 by 5, each part equals 25. Therefore, two out of these five parts equal 50.

A Quick Exercise: Five Eighths of 40

Now, it’s your turn! Try to calculate five eighths of 40 on your own. Pause here, grab a piece of paper, and see if you can work it out. Once done, continue reading to check your answer.

Step 1: Find One Eighth

Divide 40 by 8.

40 ÷ 8 = 5

One eighth of 40 is 5.

Step 2: Find Five Eighths

Now, multiply that one eighth by 5.

5 × 5 = 25

Therefore, five eighths of 40 is 25.

By visualising, we can see that breaking 40 into eight equal parts gives us 5 per part, and five of these parts total 25.

Here is the breakdown:

• Each eighth = 5
• Five eighths = 5 × 5 = 25

Conclusion

Calculating fractions of an amount is all about understanding how to break a whole number into equal parts and then multiplying those parts based on the fraction you need. Here’s a quick summary:

1. Divide the total amount by the denominator to find one part.
2. Multiply that one part by the numerator to find the fraction you need.

Feel free to practice with more examples and let us know how you get on in the comments below! Understanding these steps will make working with fractions a lot simpler, and you’ll be able to apply it to many different scenarios.

Happy calculating!