This page focuses on sharing in ratios and finding fractional proportions.

Sharing in ratios involves dividing a total amount proportionally based on given ratio parts. For example, sharing £24 in a 1:2 ratio would result in £8 and £16.

Example: Sharing £24 in a 7:5 ratio results in £14 and £10

The page also covers finding fractional proportions, which involves calculating parts of a whole based on given ratios.

Vocabulary: Equivalent fractions are fractions that represent the same value, such as 1/2 and 3/6

Combining ratios is introduced, showing how to work with multiple related ratios. An example is given of a car dealership with three types of cars: diesel, petrol, and electric. The ratios between these types are combined to form a single ratio representing all three types.

Highlight: When combining ratios, multiply the terms of one ratio by the other ratio to find the equivalent combined ratio

This concept is crucial in various real-world applications, such as resource allocation, financial planning, and statistical analysis.

This page delves into more advanced topics related to combining and expanding complex ratios.

The page starts with an example of expanding and simplifying ratios involving squares and triangles. It demonstrates how to manipulate ratios with different geometric shapes.

Example: A ratio of squares to triangles 3:4 can be expanded to 15:20:4 when considering rectangles as well

Complex ratios involving square roots are introduced. These ratios require more sophisticated simplification techniques.

Vocabulary: LCM (Least Common Multiple) is often used in simplifying complex ratios

The page provides step-by-step guidance on simplifying complex ratios involving square roots. It shows how to expand, factorize, and simplify these ratios.

Highlight: When working with square roots in ratios, it's often helpful to simplify the square roots first before combining terms

The final example demonstrates how to combine three complex ratios (a:b, b:c, and a:c) into a single simplified ratio. This process involves careful manipulation of square roots and fractions.

These advanced ratio techniques are particularly useful in higher-level mathematics, physics, and engineering applications where precise proportions involving complex numbers are required.

This page covers techniques for simplifying ratios and working with scale models.

Simplifying ratios involves reducing them to their lowest terms by dividing both sides by their greatest common factor. For example, 2:4 simplifies to 1:2, and 3:63 simplifies to 1:21.

Example: The ratio 123:369 simplifies to 1:3

The page also covers currency conversions using ratios. For instance, if £1 is worth $1.14, then$291.84 would be equivalent to £256.

Scale models are introduced, showing how ratios are used to represent real-world measurements:

Highlight: Common scale conversions include:

• 1 cm = 10 mm
• 1 m = 1000 mm
• 1 m = 100 cm
• 1 km = 1000 m
• 1 km = 1,000,000 mm

These scale conversions are essential in fields like architecture, engineering, and cartography where accurate representations of large objects or distances are needed.