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DIVISION FACTS

Most people find dividing things a daunting task: It is the same Maths. However, division problem can be solved simply by thinking about multiplication, instead.

What then is division? It is the ‘splitting’ of items into equal parts or groups. In other words, division is the act of ‘grouping’ or ‘sharing’.

You probably use division in a lot of your day to day life, without realising it.

Imagine you have 12 muffins and you need to share among 4 people. How many muffins should each person equally get? To get the answer, you must share (divide) the muffins among the four people. With this, each person gets 3 muffins.

This implies that 12 divided by or grouped into 4 is 3.

The symbol ‘➗’ is used to divide. It is used to divide. It is derived from a greek word ‘Obelus’ which is a sharpened stick used for splitting and cooking. So in Maths, the statement 12 divided by 4 is written as

12 ➗ 4 = 3.

Each of the three numbers in a division statement has a special name.

The number being divided as in 12 for the problem above is called the dividend; the number dividing, as in 4 is the divisor and the result of (the answer to) the division is called the quotient.

Shall we learn some division facts at this stage:

The fact that the quotient can have a remainder leads us to the question:

“Is there any way to tell whether a division problem is going to work out to give a whole number?” It is yes. There is a set of divisibility rules that show this without having to work out the full division.

DIVISIBILITY RULES

Dividing by 1: If you divide any whole number by 1, you always get a whole number.

Dividing by 2: Even numbers “evenly” divide into 2. Odd numbers divide into 2 with a remainder (odd one out). For e.g 49 is an odd number and dividing it by 2 leaves a remainder.

Dividing by 3: Add up the digits (twice if necessary); if the sum is divisible by 3, then the the number is too. Let’s say you need to divide 4,932: 4 + 9 + 3 + 2 = 18, which is divisible by 3, so 4,932 is divisible by 3. Another example 625: 6 + 2 + 5 = 13; 13 is not divisible by 3 and so will be 625.

Dividing by 4: Look at the last two digits. If they are divisible by 4, the number is as well. For example, the last two digits of 17,924 are 24 which is divisible by 4. Therefore 17,924 is divisible by 4. Meanwhile, the last two digits in 322 is not 24, so it is not divisible by 4.

Dividing by 5: If the last two digits is a 5 or a 0, then the number is divisible by 5. For example, 925 is divisible by 5 because the last digit is a 5; 8,340 is also divisible because it ends in 0;

8,347 is however not divisible by 5.

Dividing by 6: If the number is divisible by both 3 and 2, it is divisible by 6 as well. For example, 924 is divisible by six because it is even (divisible by 2) and the digits add up to 15, which is divisible by 3. However, 154 is divisible by 2 but not divisible by 3. It is therefore not divisible by 6.

Dividing by 7: To find out if a number is divisible by 7, take the last digit, double it and subtract it from the rest of the number without the last digit if you get an answer divisible by 7 (including 0) then the original number is divisible by 7. For example,161 is divisible by 7 because 2 x 1 (the last digit) = 2 and 16 - 2 = 14 which is divisible by 7. 312 is not divisible; 2 x 2 (the last digit) = 4 and

31 - 4 = 27 which is not divisible by 7.

Dividing by 8: If the last three digits of a number are divisible by 8, then so is the whole number. To check that, if the digit in the hundreds is even and the last two digits are divisible by 8, then the whole number is. For e.g 2448 has the last three digits as 448. With this 4 is even and 48 is divisible by 8 so is 2448.

If the digit in the hundreds is odd, subtract 4 from the last two digits and if the answer is divisible by 8, then the whole number is as well.

For e.g 192 has the number 1 in the hundreds. 1 is an odd number so you need to subtract 4 from the last two digits: 92 - 4 = 88; 88 is divisible by 8, so is 192 as well. With the number 323, 3 in the hundreds is odd so we subtract 4 from last two digits: 23 - 4 = 19; this is not divisible by 8 and so is 323.

Dividing by 9: Add the digits. If the sum is divisible by 9, then the number is as well. For example: 7,866 is divisible by 9 because 7 + 8 + 6 + 6 = 27 and 27 is divisible by 9. 523 is not divisible

because 5 + 2 + 3 = 10 and this is not divisible by 9.

Dividing by 10: If the number ends in 0, it is divisible by 10. 216 is not divisible since the last digit is not 0.

Dividing by 11: Keep subtracting the last digit from the rest of the number until you can tell if the resulting number is divisible by 11. For example, 6479 is divisible by 11 because 6479; 647 - 9 = 638; 63 - 8 = 55, and 55 is divisible by 11. 512 is not divisible since 51 - 2 = 49 which is not a multiple of 11.

Dividing by 12: Check for divisibility by 3 and 4. For example, 300 is divisible by 12 because 3 + 0 + 0 = 3 which is divisible by 3 and the last two digits for the are 00 and 4 x 0 = 0 which makes it divisible by 4. However, 256 is not divisible by twelve: the last two digits (56) are divisible by 4; 256, being 2 + 5 + 6 = 13 and 13 is not divisible by 3.

Having knowledge in these divisibility rules will help to make calculating division problems easier and quicker.