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Multiplying fractions, decimals and percentages

Multiplying fractions, decimals and percentages
MICHAEL ANDERSON: Hello, and welcome to week 3.
PAULA KELLY: Last week, we saw how to express a fraction in many different ways, including as a decimal and a percentage. We also explored the different methods when converting between fractions, decimals, and percentages.
MICHAEL ANDERSON: This week we’ll be concentrating on multiplication. We’ll discover what it means to multiply a number by a fraction, decimal, or a percent. We’ll also work through a range of multiplication methods and the ideas behind them.
PAULA KELLY: We’ll look at different strategies that can be employed when multiplying with decimals and fractions, and how to find a percentage of an amount– for example, how to find 60% of 25.
MICHAEL ANDERSON: As we go through each step, you’ll find a range of examples, as well as questions for you to try yourself. We’ve also linked to some traditional classroom-based resources you may wish to explore in your own teaching.
PAULA KELLY: Don’t forget to join in the discussion, post your answers thoughts and questions in the sections below each step.
This week we’ll be looking at multiplying fractions, decimals and percentages. This allows us to answer questions such as:
  • What is \(\frac{2}{3}\) of \(\frac{4}{5}\)?
  • What is 60% of 25?
There are many different ways to find the product of two or more numbers. Finding the product is what we mean by finding the answer when two or more numbers are multiplied together. Some methods are more efficient than other methods.
By the end of this week you’ll have practised a range of methods and will be able to choose methods for multiplying fractions, decimals and percentages. Importantly, we’ll be highlighting the issues with relying on ‘trick’ methods.
You can download this week’s problem sheet questions at the bottom of this first unit.

Starter Activity

Without using a calculator, find the product of 62 and 31. In other words perform the calculation: \(62 \times 31\).
When you have an answer you may like to check it using a calculator.
Now think of a different method of multiplying these numbers together.
Can you talk through the different methods you’ve used and explain each of the methods?
Now look back at the different methods used. Do you think the method you used can be extended to help you perform the calculation \(0.62 \times 0.31\)?
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Maths Subject Knowledge: Fractions, Decimals, and Percentages

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