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This content is taken from the National STEM Learning Centre's online course, Maths Subject Knowledge: Fractions, Decimals, and Percentages. Join the course to learn more.
4.1

## National STEM Learning Centre

Skip to 0 minutes and 7 seconds PAULA KELLY: Hello, and welcome to the fourth week of our course, exploring fractions, decimals, and percentages.

Skip to 0 minutes and 13 seconds MICHAEL ANDERSON: Last week, we looked at multiplication. We hope you managed to solve our discount problem from the last step. Was the answer one you expected? How could you explain this to your students?

Skip to 0 minutes and 23 seconds PAULA KELLY: This week, we’ll look at methods for comparing fractions, decimals, and percentages in more detail. We’ll consider the role of addition and subtraction when considering how much larger or smaller one quantity is when we’re comparing another dealing with fractions, decimals, and percentages.

Skip to 0 minutes and 40 seconds MICHAEL ANDERSON: As usual, this week will contain a mixture of videos, examples, worked questions, and questions for you to have a go at yourself.

# Adding and subtracting fractions, decimals and percentages

This week we compare fractions, decimals, and percentages in more detail. To begin with, we’ll look at the methods for comparing fractions, decimals, and percentages.

In week one we asked you to compare two fractions to determine which fraction was the largest. We take this idea further by not only asking which value is the largest but how much larger is one value than the other. One way of deciding how much larger one value is than another is to perform the relevant subtraction calculation. The techniques required to subtract can also be used to add fractions, decimals, and percentages.

You can download this week’s problem worksheet at the end of this unit.

## Solution to last week’s question

At the end of last week we asked you the following question:

In a sale, all items are half price. You also have a loyalty card that gets you $$\frac{1}{10}$$th off any purchase. As you take your item to the cashier they ask you which discount you would like to apply first.

Hopefully, you’ll have spotted this is a multiplication problem, and that it doesn’t matter which order the discounts are applied.

The commutative property of multiplication is useful. This week we explore whether this commutative property holds for addition and subtraction.

## Identifying misconceptions

Over the next three steps, we’ll look at how to compare percentages, decimals and fractions, and the common misconceptions students have. At this point now, what are the common misconceptions or issues that you have identified when students make comparisons between amounts represented as fractions, decimals or percentages? Share in the comments below.