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# Ratios in the form of 1 to n
- URL: https://www.esheets.io/ratios-in-the-form-of-1-to-n/
- Published: 2025-02-27T18:24:47.000Z
- Updated: 2026-06-21T18:33:51.000Z
- Author: Richard Linnington
- Tags: Maths, Ratio and proportion

Ratios are everywhere—from mixing drinks to reading maps! Simplifying ratios in the form of 1:n helps compare quantities more easily. For example, if a recipe calls for 3 parts water to 9 parts juice, simplifying to 1:3 makes it clear that for every 1 part of water, you need 3 parts of juice. This skill is especially useful in scaling recipes, designing models, and understanding real-world proportions! [Jump to the questions](#practise-now)

## Practise now

Worksheet preview and key skills 

### Worksheet preview

Practise ratios in the form of 1 to n 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 first part.
- Making the first part equal to 1.
- Writing the second 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 1 : n.

## Topic guide

### What this worksheet practises

This worksheet focuses on simplifying ratios into the specific format "1 : n". This means the left-hand side of the ratio must be exactly the number 1, and the right-hand side ('n') will be whatever decimal or fraction is required to make it balance. This is very common in map scales and exchange rates.

### Key method

You must force the left-hand number to become a 1, regardless of how messy it makes the right-hand side.

- Look at the number on the left side of the ratio.
- Divide both sides of the entire ratio by this exact number.
- The left side will automatically become 1 (because any number divided by itself is 1).
- Calculate the new value for the right side. This might be a whole integer, a decimal, or a fraction.

### Worked example

**1) Write the ratio 5 : 15 in the form 1 : n.** 
**2) Write the ratio 4 : 10 in the form 1 : n.**

Example 1: (5 : 15)

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

Left side: 5 ÷ 5 = 1.

Right side: 15 ÷ 5 = 3.

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

Example 2: (4 : 10)

Step 1: The left number is 4\. We must divide both sides by 4.

Left side: 4 ÷ 4 = 1.

Right side: 10 ÷ 4 = 2.5.

Final Answer: **1 : 2.5**. (Here, n = 2.5).

### Common mistakes to avoid

The most common mistake is simplifying the ratio normally (e.g. turning 4 : 10 into 2 : 5) and stopping there. While 2 : 5 is fully simplified, it is not in the specific format requested. The question demands the left side is exactly 1\. You must keep dividing until you achieve this.

### Things to remember

It is perfectly acceptable, and very common, to have decimals or fractions in an "1 : n" ratio. In standard ratio simplification, decimals are forbidden, but this specific format is the major exception to that rule.