Maths

Division (3)

Before we look at remainders lets review the last session. In the last session we finished off looking at simple division. I took you through a few simple division sums just to get you used to the method and self-checking your work. Here's two to remind you (with the answers).

a,                           b,

4 X 197 = 197                         3 X 286 = 858

Everything we have looked at so far does not have a remainder. There is no decimal part to this number. Now we are going to look at division that does have a remainder/decimal at the end.

Look at this example.

Step 1     How many 3's in 4 (answer = 1) but there is 1 more left.

Put the one after the 4 next to the nine and then go to step 2

Step 2     How many 3's in 19? (answer = 6)

This time we have a 1 left over and no more numbers to go
What do we have to do to this 1?
We have to divide it by 3.

We could put for our answer 16(we say sixteen and one third) This is leaving our answer in fraction form.

(IF YOU FIND FRACTIONS HARD TO DO, GO TO OUR FRACTIONS PAGE)

If we want to change this fraction part to a decimal we have to go one step further.

We put a decimal point after the 6 and then put a nought next to the 1 to make it 10.
Now we carry on has before
10 divide by 3 = 3 remainder 1

We still have 1 left and so we bring down another nought

(WE DO NOT PUT IN ANOTHER DECIMAL POINT. IT IS ONLY DONE ONCE)!

You can see that we are going to have 1 remainder every time. This means that our .333333333 could go on forever.
We normally stop after two places after the decimal point..

Remember the rules are the same as any other division.
Try and follow the next example.

Step 1     Fours into 7 = 1 remainder 3 Put the answer (1) above the 7and the remainder (3) in front of the 4

Step 2     Fours into 34= 8 remainder 2. Put the eight above the 4 and the 2 next to the 4

So our answer is 18 or 18 and a half
But we want to turn our remainder into a decimal. We have to divide 2 by 4.
Do you know what the decimal equivalent of 2/4 is?

Go to answer

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Answer = 0.5

Let us see if this works for our division.
Remember we put in the decimal point and put a nought after the remainder (2)

Now how many 4's in 20?                     5

Now we have no remainders at all.

So the final answer is

Now check

4 X 18.5 = (4 X 18) = 72 and (4 X .5) = 2                            So 72 and 2 = 74.

Our answer is correct.

How was that? It will take some time to practise it but you will get quicker.

Here are a few to try out. I will just put the answers and you should check your answers before to click on my check.

Questions

 a,                 b,                 c,                 d,                 e,

Don' forget to self-check before you have look at the answers!

Go to answers

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Answers

Here are the answers as fractions

 a        b                   c                   d.                  e.

Now we have converted the fraction part to a decimal.

a,             b,         c,        d,         e,

 Self checks:

a, 4 X 14.5= 58     b,3 X 27.33 = 81.99     c, 6 X 14.33=85.98      d, 4 X 24.75 = 99     e,3 X 27.66=88.98

Notice that the self-checks for decimals that are recurring never equal the answer but are very close.

Well how did you do? I hope you are getting used to this kind of method now.

What happens if we have a bigger number to break up (divide)

You may want to have a calculator ready to help you.

Look at the following example.

 
Here we use the same method

Step 1 42's into 48 answer 1 remainder 6

 

42's into 68 = 1 remainder 26 put the 1 above the 8 and the remainder 26

 

Our answer could now be put in fraction form which =  . But we want to divide 26 by 42 we must carry on.

 

Put in the decimal point after the 11 and a nought after the 26.

Now we have 260 divide by 42 which = 6 remainder 8

Bring down another nought 80 divide by 42

 

80 divide by 42 = 1 remainder 38.

Finally bring down a nought

380 divide by 42 = 9 remainder 2.

 

Now we only need to go to 2 decimal places (2 numbers after the decimal point) So we look at the final digit. It is a nine

This is bigger than 5 so we round up the 1.

After all that our final answer is 11.62

Self check this 42 X 11.62 = 488.04

This is very close but just over (because we rounded the number up)

Phew!

Well if you managed to follow all that through then you really can do division.

Now you see why calculators are useful things.

Review.

Today we looked at dealing with the remainders in division.

We can either leave them as whole numbers and fractions or change the fraction part to a decimal.

To change the remainder to a decimal, put in a decimal point and bring down a nought.

Then continue to divide as normal. Donít go past 2 decimal points (three numbers after the decimal point), then round the last number up or down. (if the last number = 5 or greater round up. If the last number less than 5 round down)

ALWAYS check your answers.

The only way to improve you ability on division is to practise (a lot).

Well that is enough for today. How did you find that?
Tomorrow we will look at real problems involving division.
Good luck!

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