📖Definition
Dividing a number by another splits it into parts or groups.
Method
You should be familiar with the various techniques (chunking, written method, long division)
Dividing a Decimal
First, count how many digits are after the decimal point. Then remove the decimal point. Do the division. Then, replace the decimal point in the answer putting the same number of digits after the decimal point as there were originally.
For example, to calculate 3.64 ÷ 4
First count the number of digits after the point - there are 2.
Now do the division 364 ÷ 4 = 91.
Now replace the decimal point leaving 2 digits after it.
The answer is 0.91
Dividing by a Decimal
Find a multiple of 10 (10, 100, 1000) that we can multiply the number we're dividing by to remove the decimal point.
Multiply the other number by this too.
Now do the division as normal.
This works because we multiplied both parts of the sum by the same amount.
For example, calculate 7.5 ÷ 0.5
Multiply both sides by 10 to remove the decimal point from 0.5
The sum then becomes 75 ÷ 5 = 15. That's the answer.
Dividing by 10, 100 or 1000
It the number to be divided doesn't have a decimal point, add one at the right hand side.
To divide by 10, 100 or 1000, just move the decimal point in the number being divided to the left by the same number of places as there are 0s after the 1 in the number dividing.
For example, to divide 35.889 by 100, there are two 0s after the 1 in 100 so move the decimal point two places to the left to get .35889 ie. 0.35889
Ratios
A Ratio tells you the relative size of the portions into which a quantity is to be divided.
The sign used to denote a ratio is :
For example, a large bag of apples is divided into two smaller bags in the ratio 5 : 3.
That means, for every 5 apples in one of the smaller bags, there'll be 3 in the other.
With a question about ratios, always find out what one part represents. Usually you'll need to work out the Total number of parts the quantity is to be divided into and then divide the quantity by that total. Then, once you know the size of one part, you can work out the size of each portion.
💡Tips/hints
Ratios can be cancelled down like fractions.
That means, if something is divided in the ratio 2 : 4, we can divide through by 2 and say it's divided in the ratio of 1 : 2
✏️Example
Normally, a certain packet of crisps costs 40p but if you buy 8 packets, you only pay £2.75. To the nearest penny, what is the cost per packet if you buy 8?
✅Solution
We need to divide 8 into £2.75
This works out at £0.34 remainder 3
We're asked to give the answer to the nearest penny.
In this type of question, when there's a remainder, if it's half or greater of the number you're dividing by, round up, otherwise, round down.
In this instance, 3 is less than half of 8 so we round down to 34p per packet.
✏️Example
Ben and Bob's auntie gives them £20 for Christmas but tells them to share in the ratio of their ages. If Ben is 6 and Bob is 2, how much does each one receive?
✅Solution
The ratio they're dividing it up into is 6 : 2 which cancels down to 3 : 1.
Now find the total number of parts which is 3 + 1 = 4.
So, the size of one part is £20/4 = £5 and the size of three parts is £15
So, Ben gets £15 and Bob gets £5.
You can do a final check - add up the portions and see if it equals the original total.
£15 + £5 = £20