Dividing one number x, by another, y, means to find how many times y can be multiplied before the result is equal to x. The only problem is to be able to multiply easily in your head. To help with this section I've included the multiplication table from 2 to 12 below. I was required know this when I was in school.
Examples
27 / 9 -> Let's start off with an easy example just to show that division just means to multiply the divisor a certain
number of times.
In other words the problem is: 9 * x <= 27 ( '<=' means less than or equal to )
Since 9 * 3 = 27 the answer is 3.
38 / 7 -> How many times can 7 be multiplied before the result is greater than 38?
7 * x <= 38
7 *10 = 70 (too high)
7 * 4 = 28 (too low)
7 *5 = 35 (too low)
7 * 6 = 42 (too high)
The dividend(38) falls between 7 * 6 and 7 * 5. However because 7 * 6 is greater than 38 we must take the
other one. In other words we want to get as close to 38 or equal to, but not more than 38.
In this case 7 * 5 = 35. However we're dividing 38 not 35. This means that there is a remainder. To get the
remainder subtract the result(35) from the dividend(38)
38 - 35 = 3
Therefore 38 / 7 = 5 and 3 remainder or 5 and 3/7 (5 and 3 over 7)
72 / 7 -> How many times can 7 be multiplied before the result is greater than 72?
In other words: 7 * x <= 72
7 * 8 = 56 (too low)
7 * 9 = 63 (too low)
7 * 10 = 70 (too low)
7 * 11 = 77 (too high)
72 falls between 7 * 10 and 7 * 11 so as always we take the lower one (7 * 10)
Therefore x = 10 and a remainder because the result of 7 * 10 did not equal 72.
To get the remainder we do:
72 - (7 * 10)
72 - 70 = 2
Therefore 72 / 7 = 10 and 2 over 7 or 10 and 2/7
86 / 4 -> How many times can 4 be multiplied before the result is greater than 86?
In other words: 4 * x <= 86
4 * 12 = 48
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4 * 20 = 80
4 * 21 = 84
4 * 22 = 88
x = 21 because 4 * 22 is greater than the dividend(86). Remember we alsways go with the lower of the two.
86 - 84 = 2
86 / 4 = 21 and 2/4. However 2 / 4 can be broken down to 1 /2 by dividing each number by 2. Divide each
number by two. Therefore our result is: 21 and 1/2
Multiplication Table from 2 to 12
2 * 1 = 2 3 * 1 = 3 4 * 1 = 4 5 * 1 = 5 6 * 1 = 6 7 * 1 = 7
2 * 2 = 4 3 * 2 = 6 4 * 2 = 8 5 * 2 = 10 6 * 2 = 12 7 * 2 = 14
2 * 3 = 6 3 * 3 = 9 4 * 3 = 12 5 * 3 = 15 6 * 3 = 18 7 * 3 = 21
2 * 4 = 8 3 * 4 = 12 4 * 4 = 16 5 * 4 = 20 6 * 4 = 24 7 * 4 = 28
2 * 5 = 10 3 * 5 = 15 4 * 5 = 20 5 * 5 = 25 6 * 5 = 30 7 * 5 = 35
2 * 6 = 12 3 * 6 = 18 4 * 6 = 24 5 * 6 = 30 6 * 6 = 36 7 * 6 = 42
2 * 7 = 14 3 * 7 = 21 4 * 7 = 28 5 * 7 = 35 6 * 7 = 42 7 * 7 = 49
2 * 8 = 16 3 * 8 = 24 4 * 8 = 32 5 * 8 = 40 6 * 8 = 48 7 * 8 = 56
2 * 9 = 18 3 * 9 = 27 4 * 9 = 36 5 * 9 = 45 6 * 9 = 54 7 * 9 = 63
2 * 10 = 20 3 * 10 = 30 4 * 10 = 40 5 * 10 = 50 6 * 10 = 60 7 * 10 = 70
2 * 11 = 22 3 * 11 = 33 4 * 11 = 44 5 * 11 = 55 6 * 11 = 66 7 * 11 = 77
2 * 12 = 24 3 * 12 = 36 4 * 12 = 48 5 * 12 = 60 6 * 12 = 72 7 * 12 = 84
8 * 1 = 8 9 * 1 = 9 10 * 1 = 10 11 * 1 = 11 12 * 1 = 12
8 * 2 = 16 9 * 2 = 18 10 * 2 = 20 11 * 2 = 22 12 * 2 = 24
8 * 3 = 24 9 * 3 = 27 10 * 3 = 30 11 * 3 = 33 12 * 3 = 36
8 * 4 = 32 9 * 4 = 36 10 * 4 = 40 11 * 4 = 44 12 * 4 = 48
8 * 5 = 40 9 * 5 = 45 10 * 5 = 50 11 * 5 = 55 12 * 5 = 60
8 * 6 = 48 9 * 5 = 54 10 * 6 = 60 11 * 6 = 66 12 * 6 = 72
8 * 7 = 56 9 * 7 = 63 10 * 7 = 70 11 * 7 = 77 12 * 7 = 84
8 * 8 = 64 9 * 8 = 72 10 * 8 = 80 11 * 8 = 88 12 * 8 = 96
8 * 9 = 72 9 * 9 = 81 10 * 9 = 90 11 * 9 = 99 12 * 9 = 108
8 * 10 = 80 9 * 10 = 90 10 * 10 = 100 11 * 10 = 110 12 * 10 = 120
8 * 11 = 88 9 * 11 = 99 10 * 11 = 110 11 * 11 = 121 12 * 11 = 132
8 * 12 = 96 9 * 12 = 108 10 * 12 = 120 11 * 12 = 132 12 * 12 = 144
