(8.) (+)×6, (†+3 — — }) × 4, (13· ×9, (3+1+1 — §) × 9. (9.) (+)×6+(+5) × 5 (ans. 3), (1+1)×5(+)×9. (10.) (-) 2 + ( + ) × 3 − ( − ) × 4, (+3) × 3— (82)×4+ (+1)×6. (11.) George bought 22 lbs. of nuts, and he found that after giving lb. of them to each of his companions, he had just 16. left to himself. How many companions has he? (12.) A man walks 3 miles to his work every day, and the same distance home again. How many fifths of a mile does he walk in a week of 6 days? DIVISION. Sign, as 62; or = 3. Terms to be explained :Division, dividend, divisor, quotient, complete quotient, remainder. 9 12 MENTAL EXERCISES. 10 12 9 8 11 12. &c. a. 3, 5, 1, 1; 3, V ; ;, ; ; V, V ; &, & ; 7, 9; 7, 3, c. Multiply the half of 12 by the third part of 18; the fourth part of 20 by the fifth part of 30, &c. d. To divide any number by 25-Multiply by 4, and divide the result by 100. Divide 896 by 25. e. To divide any number the result by 1000. by 125-Multiply by 8, and divide Divide 968 by 125. f. What is the square root of 9, 16, 25, &c.? g. √36, √ 49, √ 64, † 8, † 125, &c. Note.-Sums like the above should be put down on the black board step by step, the pupils meanwhile calculating mentally. In the following find the (1.) 69845164 ÷ 2, 3, 4. Answers, 34922582. 23281721}. 17461291. (2.) 87638495 ÷ 2, 3, 4. XIX. complete quotient :- In the following find the quotient and remainder :(13) 419019087 ÷ 6, 7, 8. (14) 305070901 ÷ 9, 11, 12. (15.) 416283658 ÷ 5, 7, 9. In the following find the complete quotient: (16) 845832146 ÷ 10, 100, 1000. VULGAR FRACTIONS-continued. (2.), 7999 12. 1680 1971 (3.) 1142 1372 (4.) ×5 (ans. 23), 4×8 (ans. 69), 5×4, × 6. (5.) 5×7, 9×4, 4×8, 7×9. (6.) 63×9 (ans. 60), 7×5 (ans. 39), 62 × 8, 919 × 11. (7.) ÷÷5 (ans. †), &÷8 (ans. §%), § ÷ 4, ÷ ÷ 6. (8.)÷7, ÷ 4, ÷ 8, 7 ÷ 9. (9.) 639 (ans. 29), 74÷5 (ans. 114), 6o÷8, 919 ÷ 11. (10.) 85, 67, 95, 8÷7. (11.) 103, 1136, 911, 113 ÷ 12. (12.) 45, 91÷10, 63÷7, 82÷9. XXI. In the following find the complete quotient :- 61028685 (2.) 865347853 ÷ 18, 21, 22. In the following find the quotient and remainder :- In the following find the complete quotient :(13.) 864596006÷ 490, 560, 9600. (14) 678009608 ÷ 81000,990000, 1080000. (15.) 430201967 ÷121000, 1320000, XXII. 1440000. In the following find the complete quotient :(1.) 896752105 ÷ 13, 17, 19, 23. Answers. 68980931 527501231 47197479-10 38989221 (2.) 32587460129, 31, 37, 41. (10) 9871236540 ÷ 157, 211, 269. In the following find the quotient and remainder XXIII. (1.) Divide eight thousand nine hundred and sixtyfive by 11. If we were first to multiply the dividend by 5, would the quotient be increased or diminished ?—and how many times? (2.) Divide eighty-six thousand four hundred and fiftysix by 12. If we were first to multiply the divisor by 6, would the quotient be increased or diminished ?—and how many times? If we were first to multiply both the dividend and divisor by 6, would the quotient be increased or diminished? What effect would it have on the remainder? (3.) Divide two hundred and seventy-two thousand eight hundred and sixty-six millions ten thousand and eighty-eight by forty-two. (4.) Divide six thousand three hundred and twentytwo millions nine hundred and eighty-eight thousand six hundred and seventy two by ninety thousand six hundred and eight. (5.) Divide four hundred and fifty-nine millions six hundred and fifty-four thousand eight hundred and nineteen by two thousand eight hundred. (6) If twenty-four millions seven hundred and forty thousand four hundred and nine be the quotient, thirty-two the remainder, and thirty-nine the divisor, what is the dividend? (7.) If six billions four hundred and sixty-nine thousand eight hundred and nine millions five hundred and forty-two thousand six hundred and nineteen be the dividend, and ninety-nine the divisor, what is the remainder? (8.) If fourteen millions fifty-five thousand and seventy be the product, and two thousand three hundred and six the multiplier, what is the multiplicand? (9.) If six billion nine hundred and eight thousand and seventeen millions nine thousand six hundred and one be the dividend, thirty-two the remainder, and one hundred and seventy-seven thousand one hundred and twentyeight millions six hundred and forty-one thousand two hundred and seventy-one the quotient, what is the divisor? (10.) Divide 16 by 4; sixteen thousand by four thousand; sixteen billions by four billions. XXIV. (1.) If £9648 were divided equally among 36 persons, how much would each receive? (2.) What is the twenty-seventh part of £11853? (3.) How often will a wheel which measures 16 feet in circumference turn in 6 miles, each mile containing 5280 feet? (4.) How long will it take a person to read a work of 9 volumes, each containing 464 pages, if he read 116 pages daily? (5.) If a cistern can be filled in 39 minutes by a pipe discharging 42 gallons a minute, in how many minutes may it be emptied by one discharging 18 gallons a minute? If both were opened when the cistern contained 1182 gallons, in what time would it be filled? (6.) If 16 yards cost 48 shillings, what is the price of 19 yards? |