To Find The Year Of The Cycle, We Have Therefore The Following Rule: Add Nine To The Date, Divide The Sum By Twenty Eight; The Quotient Is The Number Of Cycles Elapsed, And The Remainder Is The Year Of The Cycle.

Treating x as the unknown quotient corresponding to the original dividend, we obtain successive dividends corresponding to quotients x-200, x- 230 and x-231.

In incomplete partition the quotient is 3, and the remainders 11 and 17 are in effect disregarded; if, after finding the quotient 3, we want to know what remainder would be produced by'a direct division, the simplest method is to multiply 3 by 2 4 0 and subtract the result from 935.

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Nevertheless, it has been found in practice, when syrups with low quotient of purity and high quotient of impurity are being treated, injecting the feed at a number of different points in the pan does reduce the time required to boil the pan, though of no practical advantage with syrups of high quotient of purity and free from the viscosity which impedes circulation and therefore quick boiling.

Division by a Mixed Number.-To divide by a mixed number, when the quotient is seen to be large, it usually saves time to express the divisor as either a simple fraction or a decimal of a unit of one of the denominations.

In short division the divisor and the quotient are placed respectively on the left of and below the dividend, and the partial products and remainders are not shown at all.

To Find If A Year Is Intercalary Or Common, Divide It By 30; The Quotient Will Be The Number Of Completed Cycles And The Remainder Will Be The Year Of The Current Cycle; If This Last Be One Of The Numbers 2, 5, 7, 10, 13, 16, 18, 21, 24, 26, 29, The Year Is Intercalary And Consists Of 355 Days; If It Be Any Other Number, The Year Is Ordinary.

From the purely geometrical point of view, a quaternion may be regarded as the quotient of two directed lines in space - or, what comes to the same thing, as the factor, or operator, which changes one directed line into another.

In long division the divisor is put on the left of the dividend, and the quotient on the right; and each partial product, with the remainder after its subtraction, is shown in full.

B,, Y the numerator (or denominator) of the last preceding term by the corresponding quotient and adding the numerator (or denominator) of the term before that.