**5.1- Introduction**

Express one quantity as a fraction of another, where the fraction is less than 1 or greater than 1

Use ratio notation, including reduction to simplest form divide a given quantity into two parts in a given part:part or part:whole ratio; express the division of a quantity into two parts as a ratio; apply ratio to real contexts and problems (such as those involving conversion, comparison, scaling, mixing, concentrations)

Express a multiplicative relationship between two quantities as a ratio or a fraction

**5.2- Fractions and Percentages**

• Calculate a given percentage of a quantity

• Express one quantity as a percentage of another

• Calculate percentage increase or decrease

• Carry out calculations involving reverse percentages

e.g. finding the cost price given the selling price and the percentage profit

Define percentage as ‘number of parts per hundred’; interpret percentages and percentage changes as a fraction or a decimal, and interpret these multiplicatively ; express one quantity as a percentage of another ; compare two quantities using percentages; work with percentages greater than 100% ; solve problems involving percentage change, including percentage increase/decrease and original value problems, and simple interest including in financial mathematics

**5.3-Calculations with fractions**

Adding and Subtracting Fractions

To add two fractions, the bottom (denominator) of the two fractions must be the same. \(\frac{1}{2}+ \frac{3}{2}\) = \(\frac{4}{2}\);\(\frac{1}{10}+ \frac{3}{10}+ \frac{5}{10}\) = \(\frac{9}{10}\). If the denominators are not the same, multiply the top and bottom of one (or more) of the fractions by a number to make the denominators the same.

Multiplying Fractions

This is simple : just multiply the two numerators (top bits) together, and the two denominators together :

\(\frac{3}{5}×\frac{4}{7}\) = \(\frac{12}{35}\)

**5.4- Fractions, decimals and percentages**

A percentage is a fraction whose denominator (bottom) is 100. So if we say 50%, we mean \(\frac{50}{100}\) = \(\frac{1}{2}\) (after cancelling). So 50% means ½. If want to find 10% of something, ‘of’ just means ‘times’. So 10% of 150

= \(\frac{10}{100}× 150\) = 15.

If you have to turn a percentage into a decimal, just divide by 100. For example, 25% = \(\frac{25}{100}\) = 0.25. To change a decimal into a percentage, multiply by 100. So 0.3 = 0.3 × 100 =30% .

Percentage Change

% change =\(\frac{new value-original value}{original value}× 100\)

**5.5- Summary and Review**

**5.6- Assessment 5**

**Question 1 :**

\(\frac{4}{9}+ \frac{5}{3} - \frac{1}{4}÷ \frac{2}{3}\) ?

**Question 2 :** Work out 25.68 divided by 12?

**Question 3 :** A shop sells two brands of battery. Brand “Auchan” powers a toy for 5 hours, and is sold in packs of 8 for £3.60. Brand “Red dragon “ battery powers the same toy for 5-and-a-half hours, and sells in packs of 6 for £2.94. Which brand is better value?

**Question 4 :** The value of a new car is £18,000. The value of the car decreases by 25% in the first year and 12% in each of the next 4 years. Calculate the value of the car after 5 years ?

**5.7- Lifeskills 1 : The business plan**

-Use given data to solve problems on personal and small business finance involving earnings, simple interest and compound interest

•Use given data to solve problems on personal and small business finance involving earnings, simple interest and compound interest

• extract data from tables and charts

-Includes discount, and profit and loss (as an amount or a percentage).

Knowledge of compound interest formula given below is required:

Value of investment = \(P(1+\frac{r}{100})^n\)

where P is the amount invested,

r is the percentage rate of interest and

n is the number of years of compound interest.

**Question 1.** Norbert has £5 to buy pencils and rulers. Pencils are 8p each. Rulers are 30p each. She says “I will buy 15 pencils. Then I will buy as many rulers as possible. With my change I will buy more pencils.” How many pencils and how many rulers does she buy?

**Question 2 .** Andy wants to buy these tickets for a show. 4 adult tickets at £15 each and 2 child tickets at £10 each. A 10% booking fee is added to the ticket price. 3% is then added for paying by credit card. Calculate the total charge for these tickets when paying by credit card ?