3.3.1 Increasing by a percentage

Our everyday experience of percentages includes percentage increases (like VAT at %, or a service charge of 15%) and percentage decreases (such as a discount of 15%).

For example, Â£8 plus

## Activity 20

Convert each of the following to percentages. Round off the percentages to whole numbers.

(a)

(i) 0.8

(ii) 0.

3.2 Converting to a percentage

Fractions and decimals can also be converted to percentages, by multiplying by 100%.

So, for example, 0.17, 0.3 and can be expressed as percentages as follows:

Â Â 0.17 Ã— 100% = 17%;

<## Activity 17

Express each of the following percentages as fractions:

(a) 40%

(b) 8%

(c) 70%

(d)

Percentages are used, particularly in newspaper articles, to indicate fractions (as in â€˜64% of the population votedâ€™) or to indicate changes (as in â€˜an increase of 4%â€™).

Percentages often indicate proportions. For example, labels in clothes indicate the various proportions of different yarns in the fabric. â€˜Per centâ€™ means â€˜per hundredâ€™ and is denoted by the symbol %. 100% is the same as the whole, or one hundred per hundred.

## Activity 14

A piece of computer software is to be developed by a team of programmers. It is estimated that a team of four people would take a year. Which of the following times is the length of time taken by three program

In Section 2.2 you saw that direct proportion described relationships between two quantities, where as one increased, so did the other. Sometimes as one quantity increases the other decreases instead of increasing. This is called indirect proportion. Team tasks are often an example of this. The ti

## Activity 12

A recipe for four people calls for Author(s):

In a recipe the quantity of each ingredient needed depends upon the number of portions. As the number of portions increases, the quantity required increases. The quantity per portion is the same. This is called direct proportion. The quantity is said to be **directly proportional** to the number of portions. If 2 potatoes are required for one portion, 4 will be required for two portions etc. A useful method for direct proportion problems is to find the quantity for one and multiply by the

## Activity 5

Convert each of the following fraction ratios to decimal ratios.

(a) Author(s):

1.4 Converting ratios from fractions to decimals

Although ratios are often given as fractions, they can also be expressed as decimals. You need to deal with a mixture of fractions and decimals, and to compare ratios given in either form, so you need to be able to convert between the two forms.

## Example 4

The ratio of the circ

## Activity 3

A local supermarket sells a popular breakfast cereal in a â€˜Large Packâ€™ and â€˜New Extra Large Packâ€™. They are both being sold at â€˜knock downâ€™ prices. The large pack contains 450 g of cereal priced at Â

To make short crust pastry, one recipe book says â€˜use one part of fat to two parts of flourâ€™; another recipe says â€˜use fat and flour in the ratio of one to twoâ€™; and yet another says â€˜use half as much fat as flourâ€™. These are different ways of expressing the same ratio. Ratios are often expressed as fractions. So in this case:

After studying this course, you should be able to:

work with simple ratios

convert between fractions, decimals and percentages

explain the meaning of ratio, proportion and percentage

find percentages of different quantities

calculate percentage increases and decreases.

The content acknowledged below is Proprietary (see and conditions made available under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 Licence) and used under licence.

Course image: rod

*Better Mathematics*, London, HMSO.

*Key Stage 3 National Strategy: Framework for Teaching Mathematics: Years 7, 8 and 9*, London, DfEE.

*Curriculum and Evaluation Standards for School Mathematics*Reston VA, National Council of Teachers of Mathematics.

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In this course you have been introduced to the difference between mathematical content and processes. You have worked on the *doâ€“talkâ€“record* (DTR) framework for learning mathematics.

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problem-solving (including investigating);

mathematical modelling;

reasoning;

communicating;

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using tools.

Each of the six processes listed here repre

1.1 Experiences of learning mathematics

You will come to this course with many memories of mathematics, both as a teacher and a learner. It may help if you start by recalling memories of learning mathematics and making a record of them in your notebook.

When you work on a task, get into the habit of having your notebook to hand to record your thinking. Use the notebook in any way that helps you to think about the work you have done. Some people find it helpful to divide a page into two columns using the left-hand side to reco