The Psychology of Arithmetic

by Edward L. Thorndike

1. Let it be required to divide 34531 by 15.

Operation

Divisor	Divided 15 ) 34531 ( 30 45 45 31 30 1	23021⁄15 Quotient
	Remainder

For convenience we write the divisor at the left and the quotient at the right of the dividend, and begin to divide as in Short Division.

15 is contained in 3 ten-thousands 0 ten-thousands times; therefore, there will be 0 ten-thousands in the quotient. Take 34 thousands; 15 is contained in 34 thousands 2 thousands times; we write the 2 thousands in the quotient. 15 × 2 thousands = 30 thousands, which, subtracted from 34 thousands, leaves 4 thousands = 40 hundreds. Adding the 5 hundreds, we have 45 hundreds.

15 in 45 hundreds 3 hundreds times; we write the 3 hundreds in the quotient. 15 × 3 hundreds = 45 hundreds, which subtracted from 45 hundreds, leaves nothing. Adding the 3 tens, we have 3 tens.

15 in 3 tens 0 tens times; we write 0 tens in the quotient. Adding to the three tens, which equal 30 units, the 1 unit, we have 31 units.

15 in 31 units 2 units times; we write the 2 units in the quotient. 15 × 2 units = 30 units, which, subtracted from 31 units, leaves 1 unit as a remainder. Indicating the division of the 1 unit, we annex the fractional expression, ¹⁄₁₅ unit, to the integral part of the quotient.

Therefore, 34531 divided by 15 is equal to 2302¹⁄₁₅.

[B. Greenleaf, Practical Arithmetic, '73, p. 49.]