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

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Division

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

Division is the contrary of multiplication in mathematics.

Division is often thought about the most an overwhelming of the 4 main arithmetic functions. This page defines how to perform division calculations. Once we have a good understanding the the technique and rules, we can use a calculator for much more tricky calculations without making mistakes.

Division permits us to divide or "share" numbers to discover an answer. For example, let’s think about how we would uncover the answer to 10 ÷ 2 (ten divided by two). This is the very same as ‘sharing’ 10 sweets in between 2 children. Both children must end up v the same variety of sweets. In this example the answer is 5.


Some fast Rules around Division:

When you divide 0 by an additional number the price is constantly 0. Because that example: 0 ÷ 2 = 0. That is 0 sweets mutual equally among 2 children - each boy gets 0 sweets.

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

When you division by 1, the answer is the same as the number you were dividing. 2 ÷ 1 = 2. 2 sweets split by one child.

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

Any number divided by the exact same number is 1. 20 ÷ 20 = 1. Twenty sweets divided by twenty youngsters - each son gets one sweet.

Numbers have to be separated in the exactly order. 10 ÷ 2 = 5 whereas 2 ÷ 10 = 0.2. Ten sweets divided by two youngsters is really different to 2 sweets split by 10 children.


Multiple Subtractions

Just as multiplication is a quick means of calculating many additions, division is a quick method of performing lot of subtractions.

For example:

If John has 10 gallons the fuel in his car and also uses 2 gallons a day how many days prior to he runs out?

We deserve to work this difficulty out by law a series of subtractions, or by counting backwards in procedures of 2.

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

John runs out of fuel on job 5.

A quicker method of performing this calculation would certainly be to division 10 through 2. That is, how numerous times walk 2 go into 10, or how countless lots of 2 gallons are there in ten gallons? 10 ÷ 2 = 5.

The multiplication table (see multiplication) can be provided to assist us find the answer come simple department calculations.

In the example over we needed to calculation 10 ÷ 2. To do this, making use of the multiplication table situate the obelisk for 2 (the red shaded heading). Work-related down the tower until you find the number you are looking for, 10. Move across the row to the left to check out the price (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 have the right to work out other simple division calculations making use of the very same method. 56 ÷ 8 = 7 because that example. Discover 7 on the optimal row, look under the tower until you discover 56, then discover the corresponding row number, 8.

If possible, you should shot to memorise the multiplication table over because it renders solving basic multiplication and department calculations much quicker.

Dividing bigger Numbers


You can use a calculator come perform department calculations, specifically when girlfriend are splitting larger numbers that are more difficult to work out in her head. However, that is necessary to understand exactly how to perform division calculations manually. This is valuable when you don’t have actually a calculator to hand, but is likewise essential for making certain that you use the calculator correctly and also don’t do mistakes. Division can look an overwhelming but in fact, similar to most arithmetic, it is logical.

As through all mathematics, that is most basic to understand if we occupational through one example:

Dave’s vehicle needs new tyres. He demands to replace all four tyres on the car, add to the spare.

Dave has had a quote native a local garage because that £480 to include the tyres, fitting and also disposal of the old tyres. Just how much walk each tire cost?

The difficulty we must calculate here is 480 ÷ 5. This is the same as saying how countless times will 5 get in 480?

Conventionally, we compose this as:

5 4 8 0

We work from left to ideal in a reasonable system.

We start by splitting 4 by 5 and immediately struggle a problem. 4 does not divide through 5 to leave a totality number, together 5 is higher than 4.


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

We understand that 2 goes into 4 double (4 ÷ 2 = 2) and we recognize that 1 goes right into 4 four times (4 ÷ 1 = 4), but 5 does not enter 4 because 5 is bigger than 4.

The number we are splitting by (in this instance 5) needs to enter the number we are separating into (in this situation 4) a whole number of times. It doesn’t need to be specific whole number, as you will see.


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

Hundreds Tens Units
0
5 4 8 0

Next, we relocate to the right to include the 10s column. Now we can see how many times 5 goes right into 48.

5 does get in 48 as 48 is greater than 5. However, we need to find out how many times that goes.

If we describe our multiplication table, we deserve to see that 9 × 5 = 45 and also 10 × 5 = 50.

48, the number we’re looking for, falls between these two values. Remember, we room interested in the whole variety of times that 5 goes into 48. Ten times is also many.

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

9 × 5 = 45 48 – 45 = 3

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

So 5 × 9 = 45, + 3 to gain 48.

We can get in 9 in the tens column as our answer because that the second part of the calculation and also bring ours remainder in front of our critical number in the devices 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 have the right to see the price is exactly 6, v no remainder. 5 × 6 = 30. We write 6 in the units tower of ours answer.

Hundreds Tens Units
0 9 6
5 4 8 30

As there space no remainders, we have finished the calculation and also have the price 96.

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

Recipe Division

Our final example of division is based on a recipe. Regularly when cooking, recipes will tell you just how much food they space going come make, enough to feed 6 people, for example.

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

The an initial thing we need to develop is how countless 8"s there are in 24 – use the multiplication table above or her memory. 3 × 8 = 24 – if we divide 24 through 8 we acquire 3. Therefore we need to divide every ingredient below by 3 in order to have to right lot of mixture to make 8 fairy cakes.

ingredients 120g butter, softened at room temperature 120g caster street 3 free-rangeeggs, easy beaten 1 tspvanilla extract 120gself-raising flour 1-2 tbspmilk

The quantity of butter, sugar and also flour are all the same, 120g. The is because of this only important to job-related out 120 ÷ 3 once, together the answer will be the same for those three ingredients.

3 1 2 0

As before we start in the left (hundreds) column and also divide 1 by 3. But 3 ÷ 1 doesn’t go together 3 is better than 1.Next, we look in ~ how countless times 3 goes right into 12.Using the multiplication table if required we can see the 3 goes into 12exactly 4 timeswith no remainder.

0 4 0
3 1 2 0

120g ÷ 3 is therefore 40g. we now know that we’ll need 40g that butter, sugar and flour.

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

Next the recipe calls for 1tsp (teaspoon) that vanilla extract. We need to divide one teaspoon by 3. We understand that division can be created as a fraction, for this reason 1 ÷ 3 is the exact same as ⅓ (one third). You’ll need ⅓ of a teaspoon of vanilla extract – although in truth it may be challenging to accurately measure up ⅓ of a teaspoon!


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

We deserve to look at this another way, if we recognize that one teaspoon is the exact same as 5ml or 5 millilitres. (If you need some aid with units, check out our page on Systems that Measurement.) If we want to be much more accurate, we can try dividing 5ml by 3. 3 goes right into 5 as soon as (3) through 2 left over. 2 ÷ 3 is the same as ⅔, so 5ml separated 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 separated by 3 is a small bit more than one and also a half ml. If you have some the those small measuring spoons in your kitchen, you have the right to be super-accurate!

We can estimate the answer, to inspect that we are correct. Three many 1.5 ml offers us 4.5 ml. For this reason three numerous ‘a tiny bit much more than 1.5 ml’, offers us roughly 5ml. Recipes are rarely an accurate science, therefore a little bit of estimating have the right to be fun and great practice because that our mental arithmetic.


Next the recipe calls because that 1–2 tbsp of milk. The is in between 1 and 2 tablespoons of milk. We have actually no definitive amount and how lot milk you include will it is in dependent on your mixture consistency.

We already know the 1 ÷ 3 is ⅓ and also 2 ÷ 3 is ⅔. We will thus need ⅓–⅔ that a tablespoon the milk to make eight fairy cakes. Stop look at this another way. One tablespoon is the same as 15ml. 15 ÷ 3 = 5, so ⅓–⅔ the a tablespoon is the very same as 5–10ml, which is the very same as 1–2 teaspoons!


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