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Study Guide: UK K12 GCSE/A-Level: Year 6 KS2 Mathematics - Ratio and Proportion
Source: https://www.fatskills.com/key-stage-2-ks2/chapter/uk-k12-gcse-a-level-year-6-ks2-mathematics-ratio-and-proportion

UK K12 GCSE/A-Level: Year 6 KS2 Mathematics - Ratio and Proportion

By Fatskills Exam Guides Team — the exam nerds behind 28,500+ quizzes and 2.1M practice questions across 500+ global exams.

⏱️ ~4 min read

Learning Objectives

By the end of this topic, students will be able to:

  • Understand the concept of ratio and proportion, and their applications in real-life situations
  • Identify and write ratios in simplest form
  • Compare and order ratios using vocabulary such as 'greater than', 'less than', and 'equal to'
  • Use ratio and proportion to solve problems involving measurement, scaling, and similarity
  • Apply ratio and proportion to everyday contexts, such as cooking and design

Core Concepts

A ratio is a way of comparing two or more numbers. It is often written as a fraction or a colon, and can be represented as a part-to-part comparison (e.g. 3:4) or a part-to-whole comparison (e.g. 3/4). A proportion is a statement that two ratios are equal.

For example, if a recipe requires 3 parts of sugar to 4 parts of flour, the ratio of sugar to flour is 3:4. If we want to make a larger batch of the recipe, we can multiply both parts of the ratio by the same number, for example 6:8. This is an example of scaling.

Another example of ratio and proportion is in design. Imagine a picture of a house that is 3 cm wide and 4 cm tall. If we want to make the picture 6 cm wide, we need to find the corresponding height. We can use the ratio of width to height to find the new height: 6:4 = 3:2. Therefore, the new height is 3 cm x 2 = 6 cm.

Worked Examples

Example 1: Writing Ratios in Simplest Form

A recipe for making a cake requires 2 cups of flour and 3 cups of sugar. What is the ratio of flour to sugar in simplest form?

To find the ratio in simplest form, we need to find the greatest common divisor (GCD) of 2 and 3, which is 1. Therefore, the ratio of flour to sugar is 2:3.

Example 2: Comparing Ratios

Which ratio is greater, 3:4 or 2:3?

To compare the ratios, we can convert them to equivalent fractions. 3:4 is equal to 3/4, and 2:3 is equal to 2/3. Since 3/4 is greater than 2/3, the ratio 3:4 is greater than 2:3.

Example 3: Using Ratio and Proportion to Solve a Problem

A bookshelf is 3 meters long and 2 meters high. If we want to make the bookshelf 6 meters long, how tall will it be?

We can use the ratio of length to height to find the new height: 6:2 = 3:1. Therefore, the new height is 3 meters x 1 = 3 meters.

Common Misconceptions

  • Students may confuse ratio and proportion, thinking they are the same thing.
  • Students may not simplify ratios in simplest form, leading to incorrect answers.
  • Students may not use the correct vocabulary when comparing ratios, such as 'greater than', 'less than', and 'equal to'.

Exam Tips

  • Make sure to simplify ratios in simplest form.
  • Use the correct vocabulary when comparing ratios.
  • Read the question carefully and make sure you understand what is being asked.
  • Use diagrams and visual aids to help you solve problems.

MCQs

MCQ 1: [F]

What is the ratio of flour to sugar in the recipe? A) 2:3 B) 3:2 C) 1:1 D) 4:5

Answer: A) 2:3 Why the distractors fail: B) 3:2 is the inverse of the correct answer, C) 1:1 is a ratio where the two parts are equal, and D) 4:5 is a different ratio altogether.

MCQ 2: [H]

Which ratio is greater, 5:6 or 4:5? A) 5:6 B) 4:5 C) 2:3 D) 3:4

Answer: A) 5:6 Why the distractors fail: B) 4:5 is the inverse of the correct answer, C) 2:3 is a different ratio altogether, and D) 3:4 is a ratio where 3 is greater than 4, but 5 is not greater than 4.

MCQ 3: [F]

What is the ratio of width to height in the picture of the house? A) 3:4 B) 4:3 C) 2:3 D) 1:1

Answer: A) 3:4 Why the distractors fail: B) 4:3 is the inverse of the correct answer, C) 2:3 is a different ratio altogether, and D) 1:1 is a ratio where the two parts are equal.

MCQ 4: [H]

A recipe for making a cake requires 2 cups of flour and 3 cups of sugar. If we want to make a larger batch of the recipe, what is the new ratio of flour to sugar? A) 4:6 B) 6:8 C) 3:4 D) 2:3

Answer: B) 6:8 Why the distractors fail: A) 4:6 is a different ratio altogether, C) 3:4 is the original ratio, and D) 2:3 is the original ratio.

MCQ 5: [F]

A bookshelf is 3 meters long and 2 meters high. If we want to make the bookshelf 6 meters long, how tall will it be? A) 2 meters B) 3 meters C) 6 meters D) 1 meter

Answer: B) 3 meters Why the distractors fail: A) 2 meters is the original height, C) 6 meters is the new length, and D) 1 meter is not related to the problem.

Short-answer Questions

Question 1

Write the ratio of 6:8 in simplest form.

Answer: 3:4

Question 2

Compare the ratios 3:4 and 2:3. Which ratio is greater?

Answer: 3:4 is greater than 2:3.

Question 3

A recipe for making a cake requires 2 cups of flour and 3 cups of sugar. If we want to make a larger batch of the recipe, what is the new ratio of flour to sugar?

Answer: 4:6

Question 4

A bookshelf is 3 meters long and 2 meters high. If we want to make the bookshelf 6 meters long, how tall will it be?

Answer: 3 meters

Question 5

Write the ratio of width to height in the picture of the house.

Answer: 3:4