8 = .... 4s 12 = .... 6s 9 = .... 9s 8 = .... 2s 12 = .... 4s 9 = .... 3s 8 = .... 1s 12 = .... 3s 9 = .... 1s 8 = .... 1/2s 12 = .... 2s 9 = .... 1/3s 8 = .... 1/4s 12 = .... 1s 9 = .... 1/9s 8 = .... 1/8s 12 = .... 1/2s 12 = .... 1/3s 12 = .... 1/4s 16 ÷ 16 = 9 ÷ 9 = 10 ÷ 10 = 12 ÷ 6 = 16 ÷ 8 = 9 ÷ 3 = 10 ÷ 5 = 12 ÷ 4 = 16 ÷ 4 = 9 ÷ 1 = 10 ÷ 1 = 12 ÷ 3 = 16 ÷ 2 = 9 ÷ 1/3 = 10 ÷ 1/5 = 12 ÷ 2 = 16 ÷ 1 = 9 ÷ 1/9 = 10 ÷ 1/10 = 12 ÷ 1 = 16 ÷ 1/2 = 12 ÷ 1/2 = 16 ÷ 1/4 = 12 ÷ 1/3 = 16 ÷ 1/8 = 12 ÷ 1/4 = 12 ÷ 1/6 = (8) _'% of' means 'hundredths times'._--In the case of percentage a series of bonds like the following should be formed:-- 5 percent of = .05 times 20 " " " = .20 " 6 " " " = .06 " 25% " = .25 × 12% " = .12 × 3% " = .03 × Four five-minute drills on such connections between '_x_ percent of' and 'its decimal equivalent times' are worth an hour's study of verbal definitions of the meaning of percent as per hundred or the like. The only use of the study of such definitions is to facilitate the later formation of the bonds, and, with all save the brighter pupils, the bonds are more needed for an understanding of the definitions than the definitions are needed for the formation of the bonds. (9) _Habits of verifying results._--Bonds should early be formed between certain manipulations of numbers and certain means of checking, or verifying the correctness of, the manipulation in question. The additions to 9 + 9 and the subtractions to 18 - 9 should be verified by objective addition and subtraction and counting until the pupil has sure command; the multiplications to 9 × 9 should be verified by objective multiplication and counting of the result (in piles of tens and a pile of ones) eight or ten times,[4] and by addition eight or ten times;[4] the divisions to 81 ÷ 9 should be verified by multiplication and occasionally objectively until the pupil has sure command; column addition should be checked by adding the columns separately and adding the sums so obtained, and by making two shorter tasks of the given task and adding the two sums; 'short' multiplication should be verified eight or ten times by addition; 'long' multiplication should be checked by reversing multiplier and multiplicand and in other ways; 'short' and 'long' division should be verified by multiplication. [4] Eight or ten times _in all_, not eight or ten times for each fact of the tables.