Ratios in the form of 1 to n
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
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.