Converting Fractions, Decimals, and Percentages

Welcome to your first lesson! I'm excited to start this journey with you as we work together to build a strong foundation for your success in Year 9. This course will cover a wide range of subjects, from Maths and Science to English and Spanish, all aligned with the New Zealand curriculum to get you well-prepared for the year ahead.

Today, we're kicking things off with a fundamental mathematics topic: converting between fractions, decimals, and percentages. You've likely seen these before, but mastering them is crucial. They are different ways of describing parts of a whole, and you'll use them everywhere – from calculating discounts in shops and understanding statistics in the news, to figuring out your score on a test. In this lesson, we will explore what each of these forms represents and learn the clear, step-by-step methods to convert between them.

The Big Idea: Three Languages, One Meaning

Before we dive into the rules, it's important to understand that fractions, decimals, and percentages are simply different ways of representing the same value. Think of it like saying "hello" in different languages: "hello," "hola," and "bonjour" all mean the same thing. In the same way, $\frac{1}{2}$, $0.5$, and $50\%$ all represent the exact same amount – half of something.

The key to easy conversions is to understand how each form relates to the others. We'll explore a handy strategy: using decimals as a central 'hub' to help us convert between fractions and percentages.

To get a quick visual overview of how these three concepts are connected, the following video provides a great introduction.

The Conversion Pathways

There are six conversion paths in total. We'll break them down into simple, manageable steps. This diagram illustrates the main pathways. The most direct routes are shown with solid lines, while conversions that often involve an extra step are shown with a dashed line.

Let's work through each of these pathways.

Converting To and From Decimals

Decimals are often the easiest form to work with for conversions. Let's start by mastering the conversions between decimals and the other two forms.

Converting Between Fractions and Percentages

Now for the final two pathways. While you can convert directly, it's often easiest to use decimals as a middle step for converting a fraction to a percentage.

For any fraction, the most reliable method is the two-step process we talked about:

• Step 1: Convert the fraction to a decimal (divide the numerator by the denominator).
• Step 2: Convert that decimal to a percentage (multiply by 100).

For example, to convert $\frac{3}{8}$ to a percentage:

1. $3÷8=0.375$
2. $0.375\times 100=37.5\%$

This two-step method will always work!

Practice Time

You've now covered all six conversion types. The best way to lock in this knowledge is to practise. Let's use the test section from the BBC Bitesize article you read earlier.

Key Takeaways

Well done on completing your first lesson! You've taken a great step in preparing for Year 9. Let's summarise what we covered:

• Fractions, decimals, and percentages are three different ways to represent a part of a whole.
• Decimals can be used as a 'hub' to make converting between fractions and percentages easier.
• The key conversion rules are:
  • To get a Percentage: Multiply by 100.
  • From a Percentage: Divide by 100.
  • Fraction to Decimal: Divide the numerator by the denominator.
  • Decimal to Fraction: Use place value to make a fraction over 10, 100, or 1000, then simplify.
  • Percentage to Fraction: Put the number over 100, then simplify.

In our next lesson, we will continue to build your core number skills by learning how to calculate with positive and negative integers using the correct order of operations. This is another essential building block for tackling more complex algebra and other maths topics in the future.