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# Ratios in the form of n to 1
- URL: https://www.esheets.io/ratios-in-the-form-of-n-to-1/
- Published: 2025-02-27T19:04:55.000Z
- Updated: 2026-06-21T18:37:41.000Z
- Author: Richard Linnington
- Tags: Maths, Ratio and proportion

Ratios help us compare quantities, and simplifying them in the form of n:1 makes it easier to understand relationships. For example, if a map scale is 8 cm to 2 km, simplifying to 4:1 shows that every 4 cm on the map represents 1 km in real life. This method is useful in engineering, architecture, and scaling models accurately! [Jump to the questions](#practise-now)

## Practise now

Worksheet preview and key skills 

### Worksheet preview

Practise ratios in the form of n to 1 with this self-marking maths worksheet.

The interactive worksheet below generates questions, gives instant feedback, and lets students record their score.

#### What you’ll practise

- Dividing both parts of the ratio by the second part.
- Making the second part equal to 1.
- Writing the first part as a number or decimal.
- Keeping the ratio in equivalent form.

Use the interactive worksheet below, or read the [Topic guide](#topic-guide) for the method and worked example.

Simplify the given ratios fully into the form n : 1.

## Topic guide

### What this worksheet practises

This worksheet provides practice on converting ratios into the specific format "n : 1". This means the right-hand side of the ratio must be exactly the number 1, and the left-hand side ('n') will be the resulting value, often a decimal or fraction. This is used frequently to calculate "unit costs" (how much you get for £1).

### Key method

You must force the right-hand number to become a 1.

- Look at the number on the right side of the original ratio.
- Divide both sides of the entire ratio by this exact number.
- The right side will automatically become 1.
- Calculate the new value for the left side. Do not worry if it is a decimal.

### Worked example

**1) Write the ratio 18 : 6 in the form n : 1.** 
**2) Write the ratio 7 : 5 in the form n : 1.**

Example 1: (18 : 6)

Step 1: The right number is 6\. We must divide both sides by 6.

Right side: 6 ÷ 6 = 1.

Left side: 18 ÷ 6 = 3.

Final Answer: **3 : 1**. (Here, n = 3).

Example 2: (7 : 5)

Step 1: The right number is 5\. We must divide both sides by 5.

Right side: 5 ÷ 5 = 1.

Left side: 7 ÷ 5 = 1.4\. (You can use a calculator or write it as 7/5).

Final Answer: **1.4 : 1**. (Here, n = 1.4).

### Common mistakes to avoid

A very common error is mixing up the format. A student asked to find "n : 1" will often calculate "1 : n" instead. Always pay close attention to the position of the '1' in the question. If the 1 is on the right, you must divide by the number on the right.

### How to check your answer

If the original ratio is "top-heavy" (the left number is bigger, like 18:6), your 'n' value will always be greater than 1\. If the original ratio is "bottom-heavy" (the left number is smaller, like 2:8), your 'n' value will always be a decimal starting with "0.".