In this article you will find different **Tasks** to the rule of three. The tasks deal with the **proportional** and the **antiproportional rule of three**. In addition, there are also some tasks for the **compound rule of three**. For each problem you will find the **Solution** at the end of the post.

You would like to be explained again step by step how to proceed when solving problems of the rule of three? No problem, then first look at our **Video** before you start yourself!

- Rule of three: short repetition
- Proportional, antiproportional and composite rule of three
- Proportional rule of three exercises
- Tasks Antiproportional rule of three
- Mixed tasks: Proportional and Antiproportional
- Tasks compound rule of three
- Solutions proportional rule of three exercises
- Solutions Tasks for the antiproportional rule of three
- Solutions Mixed Tasks
- Solutions Compound rule of three
- More about the rule of three

## Rule of three: short repetition

The rule of three is a method by which you **Tasks** about the **ratio between different sizes** you can solve. Here you know what the ratio between the quantities is for a given unit of measure and you have to calculate it for another unit of measure. For example, you know that 3 kg of flour costs 2 € and you have to calculate how expensive 8 kg of flour are in the episode.

- Write down all the information you already know
- Calculate the ratio between the sizes for a single unit of one size
- Determine the ratio for the given unit of measure

## Proportional, antiproportional and compound rule of three

There are two different types of the rule of three: The **proportional and the antiproportional rule of three**. The principle of the proportional rule of three is **"the more the more"**. In the case of the antiproportional rule of three, on the other hand **"the more the less"**. Depending on the type of rule of three you have to calculate differently.

The **Compound sentence of three** is an extension of the simple rule of three. Here we look at the ratio between three or more quantities. To solve tasks with the compound rule of three, you have to calculate several rule of three in a row.

If you want to have another look at the different kinds of the rule of three, check out our **Articles for the rule of three ** or our contribution to the **Compound rule of three** to. There you will also find detailed **Examples**, how to calculate the rule of three. Afterwards, feel free to come back to this article to do some of your own **Tasks** to solve.

## Tasks Proportional rule of three

The **Solutions** to the following tasks you will find further down on this page.

**Task 1:**

6 pieces of butter weigh 300 grams together. How many grams do 4 pieces weigh?

**Task 2:**

In 5 attics live 40 mice. How many mice live in 13 attics?

**Task 3:**

An employee earns 2800 €. From this amount he saves 350 €. Assume that the employee always saves the same proportion of his wages. How much would the employee have to earn to save €420?

**Task 4:**

You return old bottles to the collection point in the supermarket. For 12 bottles you get 1,80 €. How much money would you get if you brought back 87 bottles?

**Task 5:**

To solve 7 math problems you need 56 minutes. How many tasks can you calculate completely in 20 minutes at the most??

**Task 6:**

A car drives a distance of 68 km. On this distance it consumes 2.72 liters of gasoline. How much gasoline does the car need to travel 13 km??

## Tasks Antiproportional rule of three

**Task 7:**4 excavators need 6 hours to dig a pit. How long does it take 10 excavators to dig the same pit??

**Task 8:**

It takes 6 people 3 hours and 15 minutes to clean up after a party. How many people would have to help clean up to complete the task in only half an hour?

**Task 9:**

For a party you have to bring chairs to a hall. A total of 420 chairs have to be transported. 20 people need 1 hour to bring all the chairs into the hall. One person can always carry 4 chairs at the same time. How many minutes would it take a group of 24 people to complete the task?

**Task 10:**

There is candy to snack on at a birthday party. If 14 guests come, each one gets 4 sweets. How many guests may appear at most, so that everyone gets at least 8 sweets?

## Mixed tasks: Proportional and Antiproportional

**Task 11: **New sneakers are produced in a shoe factory. 20 pairs of shoes consist of a total of 620 individual parts. How many parts make up 37 pairs of shoes?

**Task 12:**

You want to sow tulips in a bed. If you put the flowers 15 cm apart, you need 225 tulips. How many tulips do you need if you want to reduce the distance to 5 cm?

**Task 13**:

You distribute some of your old toys to your 4 little cousins. Each of your cousins will receive 6 toys. How many toys would each person get if you distributed them not only among your 4 cousins, but also among your 8 cousins??

**Task 14:**

In the school library there are 5 shelves with 7 shelves each. There are a total of 56 books on 4 shelves. How many books are there in total on 4 shelves?

## Tasks composite rule of three

**Task 15:**

5 tilers lay 60 square meters of tiles in 4 hours. How long does it take 7 tilers to cover 30 square meters??

**Task 16:**

12 moles dig 15 holes in 6 hours. How many holes do 9 moles dig in 8 hours? ?

**Task 17:**

A gift that is 12 cm high, 8 cm wide, and 24 cm deep weighs 5.8 kg. How high is a gift that is 6 cm wide, 18 cm deep and weighs 3.4 kg?

## Solutions proportional rule of three problems

**Solution to task 1:**

4 pieces of butter therefore weigh 200 grams.

**Solution to task 2:**

A total of 104 mice live in 13 attics.

**Solution to task 3:**

The employee would have to earn 3360 € to save 420 €.

**Solution to Task 4:**

If you returned 87 bottles, you would receive 13,05€.

**Solution to task 5:**

In 20 minutes you can complete at most 2 tasks (the third task you will not be able to complete within the time limit).

**Solution to Task 6:**

On a distance of 13 km the car consumes 0.52 liters of gasoline.

## Solutions Tasks for the antiproportional rule of three

**Solution to task 7:**

10 excavators would need 2.4 hours for the same pit.

**Solution to task 8:**

To complete the task in only half an hour, 39 people are needed.

**Solution to Task 9:**

If 24 people help, 50 minutes are needed to bring all chairs into the hall.

**Solution to Task 10:**

In order for each person to receive at least 8 sweets, a maximum of 7 guests may appear.

## Solutions mixed tasks

**Solution to task 11:Proportional rule of three:** The more pairs of shoes, the more individual parts

37 pairs of shoes consist of 1147 individual parts.

**Solution to task 12:** **Antiproportional rule of three:** The less distance you leave between the tulips, the more tulips you can plant in your bed.

If you want to reduce the distance between the flowers to 5 cm, then you need 675 tulips.

**Solution to Task 13:** **Antiproportional rule of three:** The more people you distribute your stuff to, the less toys each person gets.

If you were to distribute your old toys among both your cousins, each person would receive 2 toys.

**Solution to Task 14:** **Proportional rule of three:** The more shelves, the more books

There are a total of 392 books on 4 shelves.

## Solutions Compound rule of three

**Solution to Task 15:**

7 tilers need 1.44 hours for 30 tiles .

**Solution to Exercise 16:**

9 moles dig 15 holes in 8 hours.

**Solution to Task 17:**

A gift that is 6 cm wide, 18 cm deep and weighs 3.4 kg is then 12.51 cm high.

## More about the rule of three

You would like to have it explained again how the rule of three actually works? Then watch our video on the rule of three now!