> ## Content Index > Fetch the complete content index at: https://www.esheets.io/llms.txt > Use this file to discover other available public pages before exploring further. # Writing Ratios as Fractions - URL: https://www.esheets.io/writing-ratios-as-fractions/ - Published: 2026-08-11T13:18:46.000Z - Updated: 2026-08-11T13:18:46.000Z - Author: Richard Linnington - Tags: Maths, Ratio and proportion Ratios describe how parts of a total relate to each other. Understanding how to turn these ratio parts into fractions of a whole is an essential mathematical skill. This worksheet practises converting between two-part or three-part ratios and fractions, finding the fraction for a combination of parts, and reversing the process to write fractions as ratios. [Jump to the questions](#practise-now) ## Practise now Worksheet preview and key skills ### Worksheet preview This worksheet provides targeted practice on converting between ratios and fractions. It begins with simple two-part ratios and progresses through to three-part ratios and reverse conversions. The final questions challenge you to apply your reasoning to multi-stage problems involving subgroups. #### What you’ll practise - Writing one part of a two-part ratio as a fraction of the total. - Writing one part of a three-part ratio as a fraction of the total. - Finding the fraction represented by combined parts (e.g. “not blue”). - Simplifying fractions derived from ratios where necessary. - Reversing the process: using a fraction of a total to write a two-part ratio. - Using two given fractions to construct a three-part ratio in simplest form. - Applying these skills to harder contextual problems. Use the interactive worksheet below, or read the [Topic guide](#topic-guide) for the method and worked example. ## Writing ratios as fractions Convert between ratios and fractions. Give your answer in its simplest form when asked. ## Topic guide A ratio shows how a total is split into parts. By finding the total number of parts, you can write any part of the ratio as a fraction of the whole. ### Converting a two-part ratio to a fraction If a ratio has two parts, the denominator of the fraction is the sum of those parts. For example, if the ratio of boys to girls is **2:3**: - The number of parts for boys is 2. - The number of parts for girls is 3. - The total number of parts is 2 + 3 = **5**. Therefore, boys make up **2/5** of the total, and girls make up **3/5** of the total. ### Converting a three-part ratio to a fraction The same logic applies when a ratio has three or more parts. Add all the parts together to find the total. For example, if red, blue and green counters are in the ratio **4:1:3**: - Total parts = 4 + 1 + 3 = **8**. - Red counters are **4/8** (which simplifies to 1/2) of the total. - Blue counters are **1/8** of the total. - Green counters are **3/8** of the total. ### Combining parts to find a fraction Sometimes you need to find the fraction for a combination of groups, such as "not red". Simply add the relevant parts together to find your numerator. Using the 4:1:3 ratio above, the counters that are "not red" are the blue and green counters. - Blue parts + green parts = 1 + 3 = **4** parts. - The fraction of counters that are not red is **4/8**, which simplifies to **1/2**. ### Reversing a fraction into a ratio If you know the fraction for one part, you can work backwards to find the ratio. If **3/7** of the students walk to school, that means 3 out of every 7 parts walk. The remaining students do not walk. - Total parts = 7. - Walking parts = 3. - Not walking parts = 7 − 3 = **4**. The ratio of those who walk to those who do not walk is **3:4**. ### Worked example: Finding a fraction from nested ratios Sometimes a group is split into a ratio, and one of those subgroups is split again. *Example: In a sports club, the ratio of adults to children is 3:2\. Among the children, the ratio of boys to girls is 1:4\. What fraction of everyone in the club are girls?* 1. The fraction of people who are children is **2/5** (since 3 + 2 = 5 total parts). 2. The fraction of children who are girls is **4/5** (since 1 + 4 = 5 total child parts). 3. To find the fraction of everyone who are girls, multiply these fractions together: **2/5** × **4/5** \= **8/25**. So, 8/25 of the people in the club are girls. ### Common mistakes to avoid - **Using the wrong denominator:** The most common mistake is treating a ratio of 2:3 as meaning 2/3 of the total. Remember that the total parts are 2 + 3 = 5, so the fraction is 2/5. - **Taking the wrong numerator:** Ensure you are selecting the part of the ratio that matches the group asked for in the question. Order matters! - **Forgetting a part:** In a three-part ratio, make sure you add *all three* numbers to find the total denominator. - **Reversing the ratio:** When turning a fraction back into a ratio, check that the parts are written in the correct order requested. - **Failing to simplify:** Always check if your final fraction or ratio can be simplified by dividing both numbers by a common factor.