11 Plus Ratio and Proportion

Ratio

A ratio compares two or more quantities, showing how many times one value contains or is contained within the other.

It is often written in the form ‘a:b’

Key Concepts:

The order of terms in a ratio is important. For example, a ratio of 2:3 means 2 parts of the first quantity for every 3 parts of the second quantity.
Ratios can be simplified by dividing both terms by their greatest common divisor (GCD). For example, the ratio 8:12 can be simplified to 2:3 by dividing both terms by 4 (the GCD).
Ratios that express the same relationship are called equivalent ratios. For example, the ratio 4:6 is equivalent to 2:3 because both simplify to the same ratio.
Ratios can be scaled up or down by multiplying or dividing both terms by the same number. For example, scaling up the ratio 2:3 by multiplying both terms by 2 gives 4:6.

A proportion is an equation that states that two ratios are equivalent. It shows that two ratios are in balance.

Key Concepts:

To set up a proportion, we write two ratios as fractions and set them equal to each other. For example, ‘a/b = c/d’.
Use cross-multiplication to solve proportions. Cross-multiplication can be used to solve proportions. If ‘a/b = c/d’, then ‘a * d = b * c’.
Direct Proportion: When one quantity increases, the other increases at the same rate.
Inverse Proportion: When one quantity increases, the other decreases at the same rate.

Example 1:

Example 2:

Tips for Solving Ratio and Proportion Problems:

Always simplify ratios if possible.
Check if ratios are equivalent by cross-multiplying.
For word problems, carefully identify the quantities and set up the ratios or proportions correctly.
Practice a variety of problems to become familiar with different types of ratio and proportion questions.
Make sure you understand what ratios and proportions are and how they are used to compare quantities.
Work on simplifying ratios by finding the GCD of the terms.
Practice setting up and solving proportion problems using cross-multiplication.
Apply your knowledge to real-life scenarios, such as cooking recipes, map reading, and distance-time problems.
Diagrams and models can help visualize ratio and proportion problems, making them easier to understand.