How to Subtract Fractions with Unlike Denominators

To subtract fractions with unlike denominators, follow these steps:

1. Find the least common multiple of the denominators of the fractions.
2. Write equivalent fractions that have the least common multiple as the denominator.
3. Keep this least common multiple as the denominator of the answer.
4. Subtract the numerators in the question to get the numerator of the answer.

The most important rule when subtracting fractions is to first make a common denominator. The denominators of the fractions must be the same before subtracting them.

For example, here is   ⁴/₆   -   ³/₈  .

Denominators are the numbers on the bottom of the fraction. The denominators are 6 and 8, which are different. To subtract fractions, we need the denominators to be the same.

A common denominator is a number that is a multiple of all of the other denominators. It is usually chosen as the first number that appears in all of the times tables of the denominators. For example, with   ⁴/₆   -   ³/₈  , the common denominator is 24 because 24 is the first number in the 6 and 8 times tables.

To find the least common denominator, list the multiples of each denominator and write down the first number to appear in every list. Alternatively, a common denominator can be found by multiplying the denominators together.

The multiples of 6 are 6, 12, 18, 24 and the multiples of 8 are 8, 16, 24. 24 is the first number to appear in each list and so, it is the least common denominator of 6 and 8. The least common denominator is also commonly known as the lowest common denominator. It is the smallest common denominator that can be found.

The next step is to find equivalent fractions that have the least common denominator.

The first fraction denominator has been multiplied by 4. Therefore we need to multiply the numerator by 4 as well.

The denominator calculation is 6 × 4 = 24. The numerator calculation is 4 × 4 = 16. Both the numerator and denominator are multiplied by 4.

The second fraction denominator has been multiplied by 3. Therefore we need to multiply the numerator by 3 as well.

The denominator calculation is 8 × 3 = 24. The numerator calculation is 3 × 3 = 9. Both the numerator and denominator are multiplied by 3.

Now that the fractions have common denominators, the subtraction can be done. The denominator of the answer is the same as the common denominator.

The lowest common denominator is 24 and so, the denominator of the answer is also 24.

To find the numerator of the answer, simply subtract the numerators in the question.

16 - 9 = 7 and so, the numerator of the answer is 7.

⁴/₆   -   ³/₈   =   ⁷/₂₄  .

Here is another example of subtracting unlike fractions step by step.

We have   ¹/₂   -   ¹/₅  .

The denominators are different and so, we need to find equivalent fractions with a common denominator.

The multiples of 2 are 2, 4, 6, 8, 10 and the multiples of 5 are 5 and 10.

We can see that 10 is the first number in both lists and so, 10 is the least common denominator of 2 and 5.

We write   ¹/₂   as   ⁵/₁₀  .

We write   ¹/₅   as   ²/₁₀  .

Now that we have a common denominator, we can subtract the fractions   ⁵/₁₀   -   ²/₁₀   =   ³/₁₀  .

If both denominators are prime, the least common denominator is found by multiplying the denominators together. For example in   ¹/₂   -   ¹/₅  , the least common denominator is 10 because 2 × 5 = 10.

Subtracting Fractions with the Butterfly Method

The butterfly method is a short method that can be used for adding or subtracting 2 fractions. It involves multiplying the numerator of one fraction by the denominator of the other with the bubbles around each multiplication drawn to make an image of a butterfly.

To subtract fractions using the butterfly method, follow these steps:

1. Multiply the two denominators together to find the denominator of the answer.
2. Multiply the first numerator by the second denominator.
3. Multiply the second numerator by the first denominator.
4. Write both of these two answers on the numerator, separated by a subtraction sign.
5. Work out the subtraction to get one number as the numerator.
6. Simplify the fraction if possible.

For example, we have   ⁴/₅   -   ²/₃  .

The diagram below shows how the butterfly method works.

We first multiply the denominators of 5 and 3.

5 × 3 = 15 and so the denominator of the answer is 15.

Next we multiply the numerator of the first fraction by the denominator of the second fraction.

4 × 3 = 12, so we write 12 on the numerator of the fraction.

Next we multiply the numerator of the second fraction by the denominator of the first fraction.

2 × 5 = 10 and so we write a 10 alongside the 12 with a subtraction sign in between.

For each multiplication in the butterfly method, draw a bubble around the numbers. This makes the overall calculation look like a butterfly and can help make the method easier to remember and learn.

Finally, we work out the subtraction on the numerator.

12 - 10 = 2 and so, 2 is the numerator.

The result of the butterfly method calculation is   ²/₁₅  

The butterfly method is an easy way to routinely solve the addition and subtraction of 2 fractions. The benefits of the butterfly method are that it reduces working out and the method is easier to remember due to the symmetrical butterfly pattern. It is a useful method to teach when the initial understanding of how to add and subtract fractions has been learnt.

The main problem with the butterfly method is that it only allows for the addition and subtraction of two fractions. It is not recommended to introduce adding and subtracting fractions with the butterfly method because it does not allow for a strong understanding of why the method works and it is limited to use on specific types of question.

Subtracing Unlike Fractions Easy Examples

Here are some easier examples to practise with. When teaching subtracting fractions with unlike denominations, it is helpful to start with examples where only one fraction needs changing.

These examples only require one fraction to change in order to find a common denominator. If one fraction denominator is a multiple of the other, only one fraction needs to be changed.

The first easy example is   ¹/₂   -   ¹/₄  .

We can see that the denominator of 4 is a multiple of the denominator of 2.

This means that we can simply double the values in the fraction   ¹/₂   to get a common denominator of 4.   ¹/₂   =   ²/₄  .

We rewrite   ¹/₂   -   ¹/₄   as   ²/₄   -   ¹/₄  .

2 - 1 = 1 and so, the numerator of the answer is 1. The denominator remains as 4.

The answer is   ¹/₄  .

Here is another easy example of subtracting fractions with different denominators.

We have   ¹¹/₁₂   -   ³/₄  .

We can see that 12 is a multiple of 4 and so, only one fraction needs changing. The 4 needs to be multiplied by 3 to make 12.

We rewrite the fraction   ³/₄   as   ⁹/₁₂  .

  ¹¹/₁₂   -   ⁹/₁₂   =   ²/₁₂  .

It is possible to simplify this answer by halving both the numerator and denominator.

²/₁₂   simplifies to   ¹/₆  .

How to Subtract Mixed Numbers with Unlike Denominators

To subtract mixed numbers with unlike denominators, follow these steps:

1. Write the mixed numbers as improper fractions.
2. Find the least common denominator.
3. Write the improper fractions as equivalent fractions that have the least common denominator.
4. The denominator of the answer is the same as this least common denominator.
5. Subtract the numerators to find the numerator of the answer.

For example, here is 5   ¹/₄   - 2   ²/₃  .

The first step is to convert the mixed numbers into improper fractions.

To convert a mixed number to an improper fraction, multiply the whole number by the denominator and add the numerator. This result is the new numerator and the denominator is the same as the denominator of the mixed number.

5 × 4 = 20 and then 20 + 1 = 21.

The mixed number of 5   ¹/₄   can be rewritten as an improper fraction as   ²¹/₄  .

2 × 3 = 6 and then 6 + 2 = 8.

The mixed number of 2   ²/₃   can be rewritten as an improper fraction as   ⁸/₃  .

Now that the mixed numbers have been written as improper fractions, the next step in the subtraction is to find the lowest common denominator.

The first number in both the 4 and 3 times table is 12. The least common denominator is 12.

We multiply the denominator and numerator of the first fraction by 3 and the second fraction by 4.

²¹/₄   is rewritten as   ⁶³/₁₂  .

⁸/₃   is rewritten as   ³²/₁₂  .

Now that the mixed numbers have been converted into improper fractions and the improper fractions now have common denominators, we can finally perform the subtraction.

The denominator remains the same and we subtract the numerators.

⁶³/₁₂   -   ³²/₁₂   =   ³¹/₁₂  .

The final step is to write the improper fraction as a mixed number if necessary.

31 ÷ 12 = 2 remainder 7. We write the whole number down and the remainder as the numerator of the fraction.

The improper fraction of   ³¹/₁₂   is written as the mixed number of 2   ⁷/₁₂  .

This is the final answer.

Subtracting mixed numbers with unlike denominators has several steps. In simple terms, to subtract mixed unlike fractions, first convert them to improper fractions and then convert these to equivalent fractions with a common denominator before subtracting.

The numerator of a fraction is the number on the top of a fraction, above the dividing line.

The denominator of a fraction is the number on the bottom of a fraction, below the dividing line.

Like fractions are two or more fractions that have the same denominator.

Unlike fractions are fractions that do not have the same denominator. The denominators are different numbers.

In this lesson we look at the steps required to add fractions with unlike denominators by converting the fractions into like fractions.

The steps to add fractions with unlike denominators are:

1. Find the lowest common denominator, which is the first number to appear in both times tables of the given denominators.
2. Rewrite each fraction as an equivalent fraction containing this common denominator by multiplying its numerator and denominator by the same value.
3. The fractions are now like fractions and can be added by keeping the denominator the same and adding the numerators.

In order to better understand these steps, we will look at some examples.

We will start by looking at examples where only one fraction will change.

In the following example, we are asked to add the fractions

¹ ⁄ ₂   +   ¹ ⁄ ₄ .

However, this is not easy to calculate because the fractions are divided into different sizes. Therefore the two fractions are unlike fractions.

This is because the denominators are different and the denominator tells us how many equal parts to divide the shape into.

The shapes have been divided into a different number of parts. To be able to add these two fractions, the parts need to be the same size so we can count them.

The denominators need to be the same. When fractions have the same denominator we say that they have a common denominator.

Here we have divided the first shape so that it also has four equal parts. The same proportion of the shape is still shaded in. However, the total number of parts has changed.

Now that the parts are the same size, we can add the fractions.

We can see that if we combine the two-quarters with the one-quarter that we have a total of three-quarters.

² ⁄ ₄   +    ¹ ⁄ ₄    =    ³ ⁄ ₄.

Therefore,

¹ ⁄ ₂    +    ¹ ⁄ ₄    =     ³ ⁄ ₄.

Once two fractions have the same denominator, we can simply add the numerators and keep the denominator the same. To change a fraction so that it has the same denominator as another fraction, we need to find their lowest common multiple.

This means, the smallest number that both denominators divide into.

We will use our previous example:

We are looking for the smallest number that both 2 and 4 divide into. We can start by looking at the largest denominator and seeing if both numbers divide into it. The largest denominator out of the two fractions is the 4.

Both 2 and 4 divide into 4 since 2 x 2 = 4. So, the smallest number that both denominators divide into is 4.

We will change one fraction so that they are both quarters i.e. both have a denominator of 4.

To find a fraction that is the same size, but has a different numerator and denominator, we are finding an equivalent fraction.

We must change both the numerator and the denominator by the same proportion. To do this, we must multiply

One-quarter already has a denominator of 4, so we don’t need to change it. We can keep this fraction the same.

However, one-half has a different denominator of 2.

To work out what the numerator will be, we must find out what we multiply the denominator by to get to 4. To get from 2 to 4, we multiply by 2.

Because we multiplied the denominator by 2, we must also multiply the numerator by 2.

1 x 2 = 2

The numerator is therefore 2.

We now have

² ⁄ ₄   +   ¹ ⁄ ₄.

We now have two like fractions which have the same denominator.

To add like fractions, we keep the denominator the same and we add the numerators.

2 + 1 = 3

Therefore,

² ⁄ ₄   +   ¹ ⁄ ₄    =    ³ ⁄ ₄

and so,

¹ ⁄ ₂   +    ¹ ⁄ ₄     =   ³ ⁄ ₄.

In the example above it was only necessary to change one fraction before adding them.

This was because one fraction’s denominator was a factor of the other denominator. This means that the smaller denominator could be multiplied by a number to make the larger denominator.

Now we will look at examples in which this is not the case. We will be changing both fractions in order to obtain a common denominator and make them like fractions.

We want to find the smallest denominator to keep the fractions as simple as possible. This is known as the lowest common denominator.

To find the lowest common denominator use the following steps:

• List the multiples (times tables) of each of the given denominators.
• The lowest common denominator is the first number to appear in both lists.
• If the denominators cannot both be divided by the same number then the lowest common denominator is equal to the denominators multiplied together.

Here is an example of adding fractions with unlike denominators.

¹ ⁄ ₂   +   ¹⁄₅ .

To be able to add these two unlike fractions, the denominators must first be the same. We begin by finding the lowest common denominator.

This is the smallest number that both denominators: 2 and 5 divide into.

To find the lowest common denominator, we list the first few numbers in each times table, and continue until we find a number in both lists.

The smallest number in both the 2 and 5 times tables is 10. So, 10 will be our lowest common denominator.

Note that it would have been possible to multiply the denominators of 2 and 5 to make the common denominator of 10 in this example.

This is because there is not a whole number that can divide into both 2 and 5 exactly.

Because we have changed the denominators of both fractions, we must also change their numerators. We must change the numerator and denominator of each fraction in proportion, so we multiply.

We follow the rule for finding equivalent fractions: whatever we multiply the denominator by, we must multiply the numerator by.

So, we begin by finding out what we multiplied each denominator by to get to 10.

To get from 2 to our new denominator of 10, we multiplied by 5.

So we must also multiply the numerator by 5.

1 x 5 = 5

The numerator is therefore 5.

To get from 5 to 10, we multiplied by 2.

So we must also multiply the numerator by 2.

1 x 2 = 2

The numerator is therefore 2.

Both denominators are now the same, so we have two like fractions and we can add them.

To add like fractions, we add the numerators but keep the denominator the same as the common denominator.

We can now add the numerators.

5 + 2 = 7

The numerator is therefore 7. And so,

⁵ ⁄ ₁₀   +   ² ⁄ ₁₀   =   ⁷ ⁄ ₁₀

Therefore,

¹ ⁄ ₂   +   ¹ ⁄ ₅   =   ⁷ ⁄ ₁₀

When teaching adding fractions with unlike denominators, the most common error is to add both the numerators and the denominators together without finding a common denominator.

To avoid this very common mistake, refer back to visual models such as the bar models shown above and keep reminding them that we must find a common denominator before adding.

It is also common for some students to always multiply the two given denominators together when finding the lowest common denominator.

Whilst this will always find a common denominator, it will not give the lowest common denominator in some circumstances where the denominators share common factor.

This may result in them obtaining a larger answer through larger multiplications that needs simplifying at the end.

How to Add Unlike Fractions using the ‘Butterfly Method’

A methodical procedure known as the ‘Butterfly Method’ for adding fractions is shown below. I would not recommend introducing the topic of adding fractions with the method below but it can provide an easier structure to some people and help with mental addition of the fractions.

In this example, we are adding ² ⁄ ₅   +   ³ ⁄ ₇.

These fractions have unlike denominators and both 5 and 7 do not have a shared factor. This means that there is not a whole number (apart from 1) that can divide exactly into 5 and 7.

The denominator of the answer will be the two denominators multiplied together.

5 x 7 = 35

We can multiply across the diagonals and then add these answers together to obtain the numerator.

2 x 7 = 14

and

3 x 5 = 15

14 + 15 = 29

and so, 29 is the numerator of our answer.

² ⁄ ₅   +   ³ ⁄ ₇   =   ²⁹ ⁄ ₃₅  .

What are Like Fractions?

Like fractions are fractions that have the same denominator on the bottom of the fraction. For example, the fractions   ⁴/₅   and   ²/₅   are like fractions because they both have a denominator of 5.

When adding and subtracting fractions, they must have like denominators. Finding like denominators is an important part of adding and subtracting fractions because the denominator tells us how many parts we have in total. If the number of parts in each fraction is the same, then adding and subtracting the fractions is possible just by looking at the numerators of the fractions.

Like denominators are used to compare two fractions. If fractions have the same denominator, then they can be compared simply by looking at their numerators. The larger the numerator of like fractions, the larger the fraction.

If fractions do not have the same denominator, then equivalent fractions are used to make them like fractions as part of the method to add, subtract or compare them.

How to Subtract Fractions with Like Denominators

To subtract fractions with like denominators, follow these steps:

1. Keep the denominator of the answer the same as the like denominators.
2. Subtract the numerators to get the numerator of the answer.
3. Simplify the fraction if necessary.

For example,   ³/₄   -   ¹/₄   =   ²/₄  .

Step 1 is to keep the denominator of the answer the same as the like denominators in the question.

Step 2 is to subtract the numerators in the question to find the numerator of the answer.

3 - 2 = 1 and so, 1 is the numerator of the answer.

Step 3 is to simplify the fraction if possible.

²/₄   =   ¹/₂  .

To simplify a fraction, divide the numerator and denominator by the same number.

To simplify   ²/₄   to   ¹/₂  , we divided the numerator and denominator both by 2.

2 is half of 4 and so   ²/₄   =   ¹/₂  .

Here is another example of subtracting like fractions. We have   ⁸/₉   -   ³/₉   =   ⁵/₉  .

Step 1 is to keep the denominator of the answer the same as the denominator of the like fractions in the question.

Step 2 is to subtract the numerators. 8 - 3 = 5.

  ⁸/₉   -   ³/₉   =   ⁵/₉  .

Step 3 is to simplify the fraction, however it is not possible to simplify   ⁵/₉  . There is no number that divides exactly into both 5 and 9.

Here are some more examples of subtracting fractions with the same denominator.

In this question we are asked to work out   ⁶/₆   -   /₆  .

The denominator of the fractions is 6 and so, the denominator of the answer is 6.

6 - 2 = 4 and so, the numerator of the answer is 4.

⁶/₆   -   ²/₆   =   ⁴/₆  .

The final step is to simplify the fraction. We can simplify the fraction by halving both the numerator and the denominator since they are both divisible by 2.

  ⁴/₆   =   ²/₃  .

In this next example we are asked to work out   ⁷/₈   -   ³/₈  .

The first step is to keep the denominator the same. The denominator is 8.

The next step is to subtract the numerators. 7 - 3 = 4, so the numerator is 4.

  ⁷/₈   -   ³/₈   =   ⁴/₈  .

The fraction   ⁴/₈   can be simplified to   ¹/₂   by dividing the numerator and the denominator by 4.

  ⁷/₈   -   ³/₈   =   ¹/₂  .

How to Subtract Improper Fractions with Like Denominators

To subtract improper fractions with like denominators, follow these steps:

1. Keept the denominator of the answer the same as the denominator of the like fractions.
2. Subtract the numerators to get the numerator of the answer.

Subtracting improper fractions uses the same rules as subtracting proper fractions.

An improper fraction is a fraction that has a larger numerator than its denominator.

For example,   ¹³/₅   -   ⁶/₅   =   ⁷/₅  .

The first step is to keep the denominator of the answer the same as the denominator of the question. The denominator is still 5.

The next step is to subtract the numerators. 13 - 6 = 7 and so, the numerator of the answer is 7.

How to Subtract Mixed Numbers with Like Denominators

To subtract mixed numbers with like denominators, follow these steps:

1. Write the fractions as improper fractions.
2. Keep the denominator of the answer the same as the denominator of the like fractions.
4. Subtract the numerators to find the numerator of the answer.
5. Write the fraction as a mixed number again if necessary.

For example, here is 3   ¹/₃   - 1   ²/₃  .

To convert mixed numbers to improper fractions, multiply the whole number part with the denominator and then add the numerator. This gives the numerator of the improper fraction. The denominator of the improper fraction is the same as the denominator of the mixed number.

3 × 3 = 9 and 9 + 1 = 10. Therefore 3   ¹/₃   =   ¹⁰/₃  .

1 × 3 = 3 and 3 + 2 = 5. Therefore 1   ²/₃   =   ⁵/₃  .

We then subtract the improper fractions like usual.

The denominator is kept the same, so the denominator of the answer is still 3.

Subtract the numerators. 10 - 5 = 5 and so, 5 is the numerator of the answer.

⁵/₃   can be written as a mixed number again if necessary.

5 ÷ 3 = 1 remainder 2. The whole number part of the answer is 1 and the remainder of 2 is the numerator of the fraction.

⁵/₃   = 1   ²/₃  .

3   ¹/₃   - 1   ²/₃   = 1   ²/₃  .

To find the perimeter of an irregular shape you simply add up the outer side lengths of the shape.

In this lesson we will look at some examples of irregular shapes and learn how to calculate their perimeters.

A regular shape is a shape in which every side is the same length. All of its angles will also be the same size.

An irregular shape is simply any shape where not all of the side lengths and angles are the same. An irregular shape is any shape that is not regular.

We name irregular shapes based on how many sides they have. Since the number of corners a shape has is the same as the number of its sides, we can also name a shape by how many corners it has.

Below are some common examples of irregular shapes arranged in a list with their properties shown.

When teaching irregular shapes it is important to be aware of a common mistake. People sometimes think that for a shape to be irregular, all of its sides have to be different to each other. However, a shape is irregular if it has at least one side that is of a different length to any of the other sides.

For example, a triangle can have two sides that are the same, but just one side that is different to the other two sides and it is an irregular shape.

Below are some examples of irregular shapes.

The perimeter of a shape is the total distance around its outside edges.

To calculate the perimeter of a shape, we add the lengths of each side.

Here is an example of finding the perimeter of an irregular triangle:

To find the perimeter of this irregular triangle, we add up the three side lengths.

A tip for teaching perimeter of irregular shapes is to cross off each side length as you have added it.

A common mistake for children calculating perimeter is that they miss a side out completely or count a side more than once.

I recommend that to avoid this mistake, you could teach the child to pick a corner to start at. Move around the outside of the shape and cross off the sides as you add them if they are simple enough for your child to add. You could draw around the original shape as you go, or highlight each side, until you are back where you started.

However for some questions with larger numbers, this could result in calculations that are not always the easiest to do first. You could instead look for sides that add up to easier numbers, such as using number bonds and then just cross these sides off as you add them.

In this example, we only have three sides so we will just cross the sides off as we add them.

8 + 10 = 18

18 + 5 = 23

The perimeter of this triangle is 23 mm.

Remember that perimeter is a measure of the total outside length of the shape and the answer that we get is a measurement of length.

Therefore our units of measurement are going to be length units. Since in our example we have measured each side in millimetres (mm), we have added up a total length in millimetres also.

We write an ‘mm’ after 23 to show that we have 23 millimetres. ‘mm’ is a short way of writing millimetres.

In the same way that we put a space between ’23’ and the word ‘millimetres’, we put a space in between ’23’ and ‘mm’. We wouldn’t write ’23millimetres’ we would write ’23 millimetres’ and in the same way we write ’23 mm’ not ’23mm’. This rule of leaving a space applies to all units of measurement.

Here’s another example of finding the perimeter of an irregular pentagon:

As we said previously, this shape will be irregular because not all of its sides are the same.

Even though it has two sides that are the both 13 metres, it has three others sides that are all different to this. It is not regular, it is irregular.

To find the perimeter of this pentagon, we add the lengths of each side together.

To make sure that we don’t add a side more than once, we will cross out the sides when we add them.

We will also make sure that we write down our calculations to avoid making mistakes.

The side lengths are in metres. Instead of writing the word ‘metres’ next to every number, it is quicker and easier to write ‘m’. ‘m’ is the abbreviation of ‘metres’ and we write our number, then a space and then ‘m’.

We can start with the two largest sides, since these will not be particularly nice to add later to an already large number.

The two largest sides are both 13 metres long and because we have two of them, it means that we can double 13 to get our answer.

Doubling is generally an easier strategy to use than addition and it is another tip to look out for when approaching these perimeter calculations. We can look for any sides that are the same and multiply the length by how many sides have this length.

13 + 13 = 26   (or 13 x 2 = 26)

Next we can see that we have a number bond to 10. We have 2 m and 8 m.

We can add these two sides together first.

8 + 2 = 10

Ten is an easier number to work with and to add. Adding ten simply involves adding one more to our tens column. We try and look for pairs of sides that will add to make ten if we can.

Now we add our final side, 9 m.

26 + 10 + 9 = 45

An easy way to do this calculation is that 10 + 9 is 19 and that adding 19 is the same as adding 20 and then subtracting 1.

This method is known as the addition by compensation strategy. To learn more about this, see our lesson: Addition using the Compensation Strategy.

26 + 10 + 9 is the same as 26 + 19, which is the same as 26 + 20 then subtract 1.

26 + 20 = 46 and then we subtract one to compensate and we get 45 as we got before.

The perimeter of this irregular pentagon is 45 m.

The method for finding the perimeter is generally the same for all of our irregular shapes. We move around the outside of our shape and add up the outside edges, crossing them off as we add them.

Remember if there are multiple sides that are the same length, a strategy can be to use multiplication instead of adding them. We can also look for multiples of ten and number bonds to help with our addition, along with the strategy of adding with compensation if we have to add a number like 9 or 19.

To find the perimeter of a regular shape, we multiply the length of one side by the total number of sides.

In this lesson we will use some examples of common regular shapes to explain why.

The definition of a regular shape is a shape in which every side is the same length and every angle is the same size.

Below are some examples of common regular shapes.

A regular triangle has the special name of equilateral triangle. We only call triangles that have three equal sides ‘equilateral triangles’.

A regular quadrilateral has the special name of square. We only call quadrilaterals that have four equal sides ‘squares’.

The perimeter of a shape is the total distance around its edge.

Here is an example of finding the perimeter of a regular triangle:

Remember that we might just be told that it is an equilateral triangle.

If a triangle is equilateral it is always regular and its sides are always the same.

Remember that ‘regular’ means that all of the sides are the same length.

One side is 6 cm long.

Because we are told that our shape is regular, this means that all of the other sides are also 6 cm long.

We have 3 lots of 6 cm.

6 x 3 = 18 The perimeter of the equilateral triangle is therefore 18 cm.

The method was to multiply one side length by the total number of sides.

Remember that perimeter is measuring the total length around the outside and because it is a length, our

will be the same as the lengths that we have added up.

We where measuring side lengths in centimetres and so our perimeter units are in centimetres.

Here is another example of finding the perimeter of a regular hexagon:

Above, is a regular hexagon.

Because it is a hexagon we know it has six sides.

We just have to remember the names. When teaching regular shape names, it can help us to think that hexagon contains a letter ‘x’ and six is the only number up to ten that also contains a letter ‘x’.

We are told that the hexagon is regular, which means that each of its 6 sides are the same length.

Remember that to find the perimeter of a regular shape, we multiply one side length by the total number of sides.

Each side is 9 cm long. We have 6 lots of 9 cm.

9 x 6 = 54

The perimeter of this hexagon is therefore 54 cm.

Next, we will look at a worded problem of finding the perimeter of a regular shape.

A hexagon has 6 sides.

It is a regular hexagon, which means that each side is the same length.

Therefore, each side is 6 cm long. We have 6 lots of 6 cm.

The method to find the perimeter of a regular shape is just to multiply one side length by the total number of sides.

6 x 6 = 36

The perimeter of the regular hexagon is 36 cm.

Here’s another worded problem example involving a regular pentagon:

A pentagon has 5 sides. It is a regular pentagon, which means that each side is the same length.

The total perimeter of the shape is 45 cm and each of the 5 sides must be the same length.

So, we need to share the total perimeter of 45 cm over the 5 sides.

The mathematical word for sharing is dividing.

We therefore divide 45 by 5.

45 ÷ 5 = 9

Each side of the regular pentagon is 9 cm in length.

When teaching this lesson on perimeter of regular shapes, it can be a disadvantage to not know the names of the common regular shapes first of all.

Print our regular shapes list found in the top of the page summary to have handy when going through our lesson video.