See our various other arithmetic pages for discussion and also examples of: addition (+), subtraction (-) and Multiplication (×).

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Division

The usual written symbol for department is (÷). In spreadsheets and also other computer applications the ‘/’ (forward slash) price is used.

Division is the opposite of multiplication in mathematics.

Division is often thought about the most difficult of the 4 main arithmetic functions. This page defines how come perform division calculations. Once we have actually a good understanding that the an approach and rules, we deserve to use a calculator for more tricky calculations there is no making mistakes.

Division allows us to division or "share" numbers to discover an answer. For example, let’s take into consideration how us would find the answer come 10 ÷ 2 (ten divided by two). This is the very same as ‘sharing’ 10 sweets in between 2 children. Both children must end up with the same variety of sweets. In this instance the answer is 5.


Some fast Rules around Division:

When you division 0 by one more number the answer is always 0. Because that example: 0 ÷ 2 = 0. That is 0 sweets mutual equally amongst 2 kids - each kid gets 0 sweets.

When you divide a number by 0 you are not splitting at all (this is quite a trouble in mathematics). 2 ÷ 0 is not possible. You have actually 2 sweets but no kids to divide them among. Friend cannot divide by 0.

When you division by 1, the prize is the very same as the number you to be dividing. 2 ÷ 1 = 2. 2 sweets split by one child.

When you divide by 2 you room halving the number. 2 ÷ 2 = 1.

Any number separated by the very same number is 1. 20 ÷ 20 = 1. Twenty sweets split by twenty kids - each boy gets one sweet.

Numbers must be split in the exactly order. 10 ÷ 2 = 5 whereas 2 ÷ 10 = 0.2. Ten sweets split by two kids is really different come 2 sweets split by 10 children.


Multiple Subtractions

Just together multiplication is a quick way of calculating multiple additions, division is a quick way of performing many subtractions.

For example:

If John has 10 gallons the fuel in his car and uses 2 gallons a day how countless days before he operation out?

We have the right to work this problem out by act a series of subtractions, or by counting backwards in procedures of 2.

On work 1 man starts through 10 gallons and also ends v 8 gallons. 10 - 2 = 8 On work 2 man starts v 8 gallons and also ends v 6 gallons. 8 - 2 = 6 On work 3 man starts v 6 gallons and also ends with 4 gallons. 6 - 2 = 4 On day 4 man starts v 4 gallons and ends through 2 gallons. 4 - 2 = 2 On day 5 john starts with 2 gallons and ends with 0 gallons. 2 - 2 = 0

John runs the end of fuel on day 5.

A quicker way of performing this calculation would be to division 10 by 2. That is, how plenty of times walk 2 enter 10, or how plenty of lots of 2 gallons are there in ten gallons? 10 ÷ 2 = 5.

The multiplication table (see multiplication) deserve to be used to help us find the answer to simple department calculations.

In the example over we necessary to calculate 10 ÷ 2. To perform this, utilizing the multiplication table situate the pillar for 2 (the red shaded heading). Occupational down the pillar until you uncover the number you are looking for, 10. Move throughout the row to the left to check out the prize (the red shaded heading) 5.


Multiplication Table

× 1 2 3 4 5 6 7 8 9 10
1 1 2 3 4 5 6 7 8 9 10
2 2 4 6 8 10 12 14 16 18 20
3 3 6 9 12 15 18 21 24 27 30
4 4 8 12 16 20 24 28 32 36 40
5 5 10 15 20 25 30 35 40 45 50
6 6 12 18 24 30 36 42 48 54 60
7 7 14 21 28 35 42 49 56 63 70
8 8 16 24 32 40 48 56 64 72 80
9 9 18 27 36 45 54 63 72 81 90
10 10 20 30 40 50 60 70 80 90 100

We can work out other simple department calculations using the same method. 56 ÷ 8 = 7 for example. Find 7 ~ above the top row, look down the pillar until you uncover 56, then find the matching row number, 8.

If possible, you should shot to memorise the multiplication table above because it makes solving simple multiplication and department calculations much quicker.

Dividing bigger Numbers


You can use a calculator to perform department calculations, particularly when girlfriend are splitting larger number that room more difficult to job-related out in your head. However, the is necessary to understand just how to perform department calculations manually. This is helpful when friend don’t have actually a calculator to hand, yet is also essential for making certain that you usage the calculator correctly and don’t make mistakes. Division can look daunting but in fact, just like most arithmetic, it is logical.

As through all mathematics, that is simplest to understand if we occupational through an example:

Dave’s auto needs brand-new tyres. He needs to change all 4 tyres on the car, plus the spare.

Dave has had actually a quote indigenous a local garage because that £480 to include the tyres, fitting and also disposal the the old tyres. Exactly how much does each tire cost?

The difficulty we need to calculate below is 480 ÷ 5. This is the very same as speak how countless times will 5 get in 480?

Conventionally, we compose this as:

5 4 8 0

We work from left to best in a reasonable system.

We start by splitting 4 through 5 and also immediately fight a problem. 4 does no divide by 5 to leaving a whole number, together 5 is greater than 4.


The language we usage in maths can be confusing. Another method of looking at this is to say, ‘how many times walk 5 get in 4?’.

We recognize that 2 goes right into 4 twice (4 ÷ 2 = 2) and we recognize that 1 goes right into 4 four times (4 ÷ 1 = 4), however 5 does not get in 4 since 5 is larger than 4.

The number we are splitting by (in this case 5) needs to get in the number us are dividing into (in this instance 4) a whole number of times. It doesn’t have to be an accurate whole number, as you will certainly see.


Since 5 does not get in 4 we placed a 0 in the an initial (hundreds) column. For aid with the hundreds, tens and also units columns see our web page on numbers.

Hundreds Tens Units
0
5 4 8 0

Next, we move to the best to encompass the tens column. Now we can see how numerous times 5 goes into 48.

5 does go into 48 as 48 is greater than 5. However, we require to discover out how countless times it goes.

If we refer to our multiplication table, we have the right to see that 9 × 5 = 45 and 10 × 5 = 50.

48, the number we’re feather for, falls in between these two values. Remember, we space interested in the whole number of times that 5 goes right into 48. Ten time is as well many.

We deserve to see the 5 goes right into 48 a entirety number (9) times, but not exactly, v 3 left over.

9 × 5 = 45 48 – 45 = 3

We have the right to now say that 5 goes right into 48 nine times, but with a remainder that 3. The remainder is what is left as soon as we subtract the number we have discovered from the number us are splitting into: 48 - 45 = 3.

So 5 × 9 = 45, + 3 to get 48.

We can go into 9 in the tens obelisk as ours answer for the second component of the calculation and bring our remainder in front of our critical number in the units column. Our last number becomes 30.

Hundreds Tens Units
0 9
5 4 8 30

We currently divide 30 by 5 (or find out how plenty of times 5 goes into 30). Utilizing our multiplication table we can see the answer is specifically 6, through no remainder. 5 × 6 = 30. We write 6 in the units column of our answer.

Hundreds Tens Units
0 9 6
5 4 8 30

As there are no remainders, we have finished the calculation and also have the answer 96.

Dave’s new tyres room going to expense £96 each. 480 ÷ 5 = 96 and 96 × 5 = 480.

Recipe Division

Our final instance of division is based upon a recipe. Frequently when cooking, recipes will tell you exactly how much food they are going to make, sufficient to feed 6 people, for example.

The ingredients below are required to do 24 fairy cakes, however, we just want to make 8 fairy cakes. We have modified the ingredients slightly for the benefit of this example (original cooking recipes at: BBC Food).

The an initial thing we need to develop is how many 8"s there space in 24 – use the multiplication table over or your memory. 3 × 8 = 24 – if we division 24 through 8 we acquire 3. Therefore we have to divide each ingredient listed below by 3 in bespeak to need to right amount of mixture to make 8 fairy cakes.

ingredient 120g butter, softened at room temperature 120g caster sugar 3 free-rangeeggs, lightly beaten 1 tspvanilla extract 120gself-raising flour 1-2 tbspmilk

The amount of butter, sugar and flour space all the same, 120g. The is thus only necessary to occupational out 120 ÷ 3 once, as the answer will certainly be the same for those 3 ingredients.

3 1 2 0

As prior to we start in the left (hundreds) column and divide 1 through 3. Yet 3 ÷ 1 doesn’t go together 3 is higher than 1.Next, we look in ~ how many times 3 goes into 12.Using the multiplication table if needed we have the right to see the 3 goes right into 12exactly 4 timeswith no remainder.

0 4 0
3 1 2 0

120g ÷ 3 is because of this 40g. we now understand that we’ll need 40g of butter, sugar and also flour.

The initial recipe calls for 3 eggs and we again divide by 3. Therefore 3 ÷ 3 = 1, thus one egg is needed.

Next the cooking recipes calls for 1tsp (teaspoon) of vanilla extract. We must divide one teaspoon by 3. We know that division can be created as a fraction, for this reason 1 ÷ 3 is the very same as ⅓ (one third). You’ll need ⅓ of a tespoon of vanilla extract – back in fact it may be an overwhelming to accurately measure up ⅓ that a teaspoon!


Estimating deserve to be useful, and also units can be changed!

We deserve to look at this an additional way, if we recognize that one teaspoon is the exact same as 5ml or 5 millilitres. (If you need some aid with units, view our web page on Systems of Measurement.) If we desire to be more accurate, us can try dividing 5ml by 3. 3 goes into 5 once (3) through 2 left over. 2 ÷ 3 is the very same as ⅔, so 5ml divided by 3 gives us 1⅔ml, i m sorry in decimal is 1.666ml. We have the right to use ours estimating an abilities and say that one teaspoon split by three is a tiny bit much more than one and also a half ml. If you have actually some of those tiny measuring spoons in your kitchen, you have the right to be super-accurate!

We have the right to estimate the answer, to examine that we space correct. Three many 1.5 ml provides us 4.5 ml. So three numerous ‘a tiny bit much more than 1.5 ml’, gives us roughly 5ml. Recipes are rarely an accurate science, so a little bit the estimating can be funny and an excellent practice for our psychological arithmetic.


Next the cooking recipes calls for 1–2 tbsp that milk. The is in between 1 and 2 tablespoons the milk. We have no critical amount and how much milk you include will it is in dependent on your mixture consistency.

We currently know the 1 ÷ 3 is ⅓ and also 2 ÷ 3 is ⅔. Us will as such need ⅓–⅔ the a tablespoon that milk to make eight fairy cakes. Stop look at this one more way. One tablespoon is the exact same as 15ml. 15 ÷ 3 = 5, for this reason ⅓–⅔ that a tablespoon is the same as 5–10ml, which is the same as 1–2 teaspoons!


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Further reading from an abilities You Need

Fundamentals that Numeracy component of The skills You Need guide to Numeracy

This eBook provides operated examples and also easy-to-understand explanations to show you just how to use an easy mathematical operations and also start come manipulate numbers. It also includes real-world examples to do clear just how these concepts are useful in actual life.

See more: What Are The Figures With The Same Size And Shape Are Called

Whether you want to brush increase on your basics, or assist your youngsters with your learning, this is the publication for you.