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Read from left to right as a series of numbers that are always divided by four (or by two if you alternate between the top and bottom rows). 96 ÷ 4 = 24; 24 ÷ 4 = 6 (or 06); 48 ÷ 4 = 12 ...
Next, the 1 is multiplied by the divisor 4, to obtain the largest whole number that is a multiple of the divisor 4 without exceeding the 5 (4 in this case). This 4 is then placed under and subtracted from the 5 to get the remainder, 1, which is placed under the 4 under the 5.
This is denoted as 20 / 5 = 4, or 20 / 5 = 4. [2] In the example, 20 is the dividend, 5 is the divisor, and 4 is the quotient. Unlike the other basic operations, when dividing natural numbers there is sometimes a remainder that will not go evenly into the dividend; for example, 10 / 3 leaves a remainder of 1, as 10 is not a multiple of 3.
In fact any multiple of five plus one is a solution, so a possible general formula is 5 · k – 4, since a multiple of 5 plus 1 is also a multiple of 5 minus 4. So 11, 16, etc also work for one division. [17] If two divisions are done, a multiple of 5 · 5=25 rather than 5 must be used, because 25 can be divided by 5 twice. So the number of ...
Long division is the standard algorithm used for pen-and-paper division of multi-digit numbers expressed in decimal notation. It shifts gradually from the left to the right end of the dividend, subtracting the largest possible multiple of the divisor (at the digit level) at each stage; the multiples then become the digits of the quotient, and the final difference is then the remainder.
By employing an inductive proof, one can arrive at a formula for f(n) in terms of f(n − 1). Proof. In the figure the dark lines are connecting points 1 through 4 dividing the circle into 8 total regions (i.e., f(4) = 8). This figure illustrates the inductive step from n = 4 to n = 5 with the dashed lines.
The solution = is in fact a valid solution to the original equation; but the other solution, =, has disappeared. The problem is that we divided both sides by x {\displaystyle x} , which involves the indeterminate operation of dividing by zero when x = 0. {\displaystyle x=0.}
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