Divisibility by sum and difference by a number.
The operations addition and multiplication are always possible, but operations subtraction and division without remainder are possible at certain conditions. In subtraction we can easily see if it is possible or not: it is enough the minuend to be higher or equal to the subtrahend. In division it is not always so simple to see if a number is divisible without remainder. There are certain cases of division in which by some indications of the numbers, we can see in advance if the division can be done without remainder or not.
Divisor and dividend
If a number can be divided by another without remainder, we say that the first number is dividend or it is divisible on the second and the second is divisor of the first number.
For example: Number 8 is dividend to 4 and 4 is divisor to 8.But 8 is not dividend to 3 and 3 is not a divisor to 8
15 is dividend to 1, 3, 5, 15 and
every one of these numbers is divisor to 15
Every number is dividend to itself. 1 is dividend to all numbers. For example: 4/4 = 1; 7/7 = 1; 9/1 = 1; 12/1 = 12
Divisibility by sum with number
Numbers 6 and 14 are divisible by 2; Their sum 20 is also divisible by 2
Numbers 12, 18, 30 are divisible by 6; Their sum 60 is also divisible by 6
If the addends are divisible individually by a number. their sum is divisible by that number too.
We can use this property of the sum to see if a number is divisible by another, without doing the division
Divisibility by difference with number
40 and 12 are divisible by 4. Their difference 28 is also divisible by 4
If the minuend and the subtrahend are divisible individually by a number. their difference is divisible by that number too.
We use this property to determine if a number is divisible by another one, without making the division