Practice Numerical Reasoning Test

# How to Calculate Ratios: A Step-By-Step Guide

Updated May 17, 2022

## What Are Ratios?

A ratio is a mathematical term used to describe how much of one thing there is in comparison to another thing.

Ratios are usually written in the following formats:

• 2:1
• 2 to 1
• 2/1

Used in mathematics and everyday life, you may have come across ratios without knowing it – for example in scale drawings or models, in baking and cooking, and even when converting currency for a holiday abroad.

Ratios are useful when you need to know how much of one thing there needs to be in comparison with another thing.

Example 1:

In a bag of 20 sweets, the ratio of blue to pink might be 2:3

The use of ratio in this example will inform us that there would be 8 blue sweets and 12 pink sweets. (This question and the way to work it out is detailed below).

Example 2:

If you are making a cake, and you require 3 cups of flour and 2 cups of sugar to make enough to feed 10 people, then you can express that as the ratio 3:2.

To scale the ingredients up to feed 20 people (to double the recipe size) you need to double the ingredients – so you would need 6 cups of flour and 4 of sugar (or 6:4).

## Key Ratio Facts

• Ratios can describe quantity, measurements or scale.

• When describing a ratio, the first number is known as the ‘antecedent’ and the second is the ‘consequent’. So, in the ratio 3:1, the antecedent is 3 and the consequent is 1.

• Ratios should always be presented in their simplified form. You can simplify a ratio by dividing both sides by the highest common factor. For example, 12:4 simplified would be 3:1 – both sides of the ratio divided by 4.

• Equivalent ratios can be divided and/or multiplied by the same number on both sides, so as above, 12:4 is an equivalent ratio to 3:1.

• Ratios can inform you of the direct proportion of each number in comparison to the other. For example, when a pair of numbers increase or decrease in the same ratio, they are directly proportional.

• When expressing ratios, you need to ensure that both the antecedent and the consequent are the same units – whether that be cm, mm, km. This makes it easier to use the ratio to inform your calculations.

• Ratios are used in maps to provide scale. Usually expressed as 1:10,000 or similar, this tells you that for every 1 unit on the map, the real distance is 10,000 units. If you measure 1 cm on the map, the real distance would be 10,000 cm (or 100 m).

• Ratios are also used in drawings, such as architectural designs, to show perspective and relative size on a smaller scale, and in models. For example, a model car might have a ratio of 1:20 – so 1 cm on the model would be 20 cm on the actual car.

## Sample Questions and Their Solutions

Understanding how to work out ratios is an important skill and can be particularly useful when applying for jobs where a good understanding of mathematics is required.

It is a good idea to revise skills like this before taking numerical reasoning or other math-based aptitude tests.

Here are the key ratio skills that you need to master:

### 1. How to Find the Ratio of Two Things

Example Question

Question:

In a bag of 20 sweets, there are 8 blue sweets and 12 pink sweets. What is the ratio of blue to pink sweets?

### 2. How to Convert Ratios With Different Units

Example Question

Question:

How should the scale factor of 3 cm : 15 m be expressed as a simplified ratio?

Example Question

Question:

Simplify 10:2.5

### 4. Using Ratios to Work out the Direct Proportions of Quantity

Example Question

Question:

If you go to the shop and buy 4 apples for £0.64, how much would 11 apples cost?

### 5. How to Divide a Number by a Ratio

Example Question

Question:

Andrew and James have 400 sweets and they need to share them in the ratio 5:3. How many sweets does each of them receive?

### 6. How to Use Ratios to Find an Unknown Number

Example Question

Question:

The sweet company likes to put uneven numbers of sweets in their bags. They are currently creating a bag of blue and pink sweets in the ratio 4:6.

If you get a bag with 12 blue sweets in it, how many will there be in total?

The formula you use for calculating ratios is a:b = a/b

For example, the ratio of a and b is 3:5.

You know that a = 86 and you need to find b.

To calculate the ratio you would take the following steps:

a:b = 3:5
a/b = 3/5
86/b = 3/5
b = (5/3) x 86
b = 143.3

Depending on the information you have, the easiest way to calculate a ratio is:

Scenario A: What is 3:5 of $30? 1. Find the total number of parts – if the ratio is 3:2, the total is 5 2. Divide the figure by the number of parts to find the sum of one part –$30 divided by 5 = 6. One part is 6
3. Multiply each number in the ratio by the value of one part – 3 x 6 and 2 x 6. If you are finding 3:2 of $30 your answer is 18:12 Scenario B: What is the ratio of apples to lemons in a field of 100 apples and 80 lemons? 1. Find your two starting figures. For example, if you were looking for the ratio of apples to lemons in a field that has 100 orchids and 80 tulips. 100 and 80 are your starting figures. 2. In this scenario you are trying to find the simplest ratio. You do this by finding the highest number that both figures divide into. In this case, 20 is the highest. 3. You then divide each figure by this number: 100/20 = 5 and 80/20 = 4 4. The answers give you your ratio of 5:4 Ratio analysis is an analytical technique that combines several financial ratios to assess a company’s financial position. Depending on the figures you are asked to find, you might use one, some, or all of these ratios: Liquidity • Current Ratio = Current Assets / Current Liabilities • Cash Ratio = Cash & Cash Equivalents / Current Liabilities • Quick Ratio = (Cash & Cash Equivalents + Accounts Receivables) / Current Liabilities Solvency • Debt-To-Equity Ratio = Total Debt / Total Equity • Debt Ratio = Total Debt / Total Assets • Interest Coverage Ratio = EBITDA / Interest Expense Efficiency • Receivables Turnover Ratio = Sales / Accounts Receivable • Inventory Turnover Ratio = COGS / Inventories • Payable Turnover Ratio = COGS / Accounts Payable • Asset Turnover Ratio = Sales / Total Assets • Net Fixed Asset Turnover Ratio = Sales / Net Fixed Assets • Equity Turnover Ratio = Sales / Total Equity Profit • Gross Margin = (Sales – COGS) / Sales • Operating Profit Margin = EBIT / Sales • Net Margin = Net Income / Sales • Return on Total Asset (ROA) = EBIT / Total Assets • Return on Total Equity (ROE) = Net Income / Total Equity To calculate these ratios, you simply need to enter the correct figures or enter these formulas into a program such as Microsoft Excel. You can find a ratio’s simplest form by finding a number both sides of the ratio have in common and dividing them. For example, a ratio of 20:60. Both sides are multiples of 10. 20/10 = 2 60/10 = 6 The ratio then becomes 2:6 Or if you wanted to make it simpler both 2 and 6 are multiples of 2. 2/2 = 1 6/2= 3 The final ratio is 1:3. To calculate ratio analysis there are several programs and apps you can use. These include: • Ready Ratios • Microsoft Excel • Google Sheets • Financial Ratio Calculator app If you want to find the ratio of two numbers online you would use a ratio calculator such as the Calculator Soup. There are specific online calculators for ratios, but is it also possible to use a physical calculator to calculate your ratios. The method you use to find ratios on a calculator differs depending on the information you have. However, you will follow the same easy steps you would use if you were to mentally calculate: • Find your two starting figures. For example, if you were looking for the ratio of orchids to tulips in a garden that has 150 orchids and 70 tulips. 150 and 70 are your starting figures. • In this scenario you are trying to find the simplest ratio. You do this by finding the highest number that both figures divide into. In this case, 10 is the highest. • Using your calculator, enter the first number and divide by the number you found: 150/10 = 15 and 70/10 = 7 • The answer to both is your ratio: 15:7 Alternatively, if you wanted to know the ratio of a figure, say 6:2 of$70, you would:

1. Determine the total number of parts: if the ratio is 6:2, the total is 8
2. Divide the figure by the number of parts to find the sum of one part: $70 divided by 8 = 8.75. So one part is 8.75. 3. Multiply each number in the ratio by the value of one part: 6 x 8.75 and 2 x 8.75 Therefore 6:2 of$70 is 52.5:17.5

## Summary

Ratios are a mathematical expression to compare units.

They can be used as equivalent ratios to help you scale up numbers – for example, quantities of ingredients for baking a cake.

In mathematical terms, they can be used to work out problems relating to direct proportion, where the increase or decrease in units occurs in the same ratio.

Ratios can be simplified and, in most cases, it is preferable to give a simplified ratio as an answer. Like fractions, you can simplify a ratio by dividing it by the highest common factor.

When using scales on drawings or models, ratios help to describe the relationship between the real-life item and the created one – allowing for accurate measurements as well as an idea of proportion.

When trying to understand ratios, it is easiest to work with the same units.

Remember, to fully explore a ratio, you need to use a whole number, so try to avoid creating any decimals when you are transforming units to match.

Practicing ratio problems will make them much easier to understand.

It is likely you will use ratios throughout your life and might be tested on math skills like these when applying for jobs in technical industries.