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(55.) The sum of two numbers is four millions four thousand and four, and the greater is three millions forty thousand and forty. Find the less.

(56.) How many times is six hundred and eighty-nine thousand five hundred and forty-seven contained in four millions one hundred and thirty-seven thousand two hundred and eighty-two?

(57.) What is the remainder when eighty-four millions five hundred and sixty-nine thousand four hundred and fifty-three is subtracted as often as possible from three hundred and thirty-eight millions three hundred and seventy-seven thousand eight hundred and thirteen ? (58.) Subtract 4 hundred from 13 hundred. (59.) Subtract 649 thousand from 960 thousand. (60.) Take 999 billions from 1000 billions.

(61.) If the difference between two numbers be 13 and 500 be added to each number, what will their difference be then?

IX.

(1.) From 3 gross, 5 dozen, 2 score and nine, subtract 2 gross, 6 dozen, 3 score and 11.

(2.) How many years elapsed between the accession of George I. in 1713 and that of Queen Victoria in 1837 ?

(3.) Two travellers set out on a journey at the same time from the same place. The first day A travelled 106 miles by rail and walked 16; the second day he rode 29 miles and sailed 9. The first day B drove 31 miles, and the second day travelled 99 miles by rail. How many miles were they apart at the end of the second day?

(4.) Kepler was born in 1571 and Galileo was 7 years older than he. In what year was Galileo born?

(5.) A merchant commenced business with a capital of £2500. The first year his losses amounted to £695 and his gross gains to £749. The second year he gained £947 and lost £348. The third year he lost £219 and gained £875. His average expenses were £250 per aunum. What was his capital at the end of the third year, and how much had he gained after deducting losses and expenses?

(6.) A carriage and two horses cost £165; each horse cost £49. What was the price of the carriage?

(7.) In one box there are 976 oranges, and in another 842. If 436 be sold out the first box and 349 out of the second, and then 98 be put out of the first into the second, and 69 out of the second into the first, how many oranges will then be in each box, and how many more in the one than in the other?

(8.) John had just as many nuts more than James as James had more than Robert. Now Robert had 2 score and 9, and James had 5 dozen and 8. How many had John? (9.) If 5 yds. of cloth cost 85s., and 4 yds. cost 68s., what is the price of 3 yds. ?

(10.) Three merchants possess among them £1748. A and B have £13896, B and C have £8974. much has each of them?

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(3.) 96 (ans. 34), 114 — 93, 165 — 13'T

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(4.) 84-65 (ans. 18), 6-4, 11-61
(5.) 107, 133-113, 243-19.
(6.) 136-12811, 645-637, 721-69§.
(7.) 971—311, 101-991, 204-10811.
(8.) 469-3721, 56911-32118, 41117-918.

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How

(9.) 561-56011, 61019 - 50915, 91813 - 81718. (10.) ++—4—4 (ans. 4), 8—3 +1-8. (11.)+2+12-12, 67 +44-54+ (ans. 53). & (12.) 23-18-28, 24+ 3-1-3.

(13) John received of a sovereign from his uncle and spent of a sovereign. He then received of a sovereign from his aunt and spent of a sovereign. What part of

a sovereign has he left?

(14.) of a pole was in the sand, in the water. How much of it was above the water?

(15.) John ate of his nuts, gave away of them, and of them. What part of the whole number had he

lost

left?

Sign X.

MULTIPLICATION.

Terms to be explained :-Multiplication, multiplicand, multiplier, factors, product.

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b 13 × 20, 24 × 30, 19 ×
c 15 x 14, 16 x 15, 17 x
d (6 + 3 8 + 4) × 6, (7 3+ 4
e (8- 4) x (6 + 3), (3 + 9) × (7
ƒ To multiply any number
divide the result by 4.

g To multiply any number
divide the result by 8.

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1) × 8, &c.

2), &c.

by 25: affix two ciphers and Multiply 19, 21, 39, &c., by 25. by 125: affix three ciphers and Multiply 29, 37, &c., by 125.

h To multiply any number of two figures by 11: between the figures place the sum of the figures-thus, 63 × 11

=

693, 74 x 11

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(16) 8945675 × 10, 100.
(17) 9056786 × 100, 1000.
(18.) 3467890 × 30, 50, 70.
(19.) 8978609 x 800, 900, 7000.

(20) 6745901 × 1100, 12000.

Terms to be explained :-Composite numbers, prime

numbers.

MENTAL EXERCISE.-What are the factors of 14, 16, 18, 22, 24, 15, 21, 27, 33, 36, 28, 32, 44, 48, 25, 35, 45, 55, 42, 54, 66, 72, 49, 56, 63, 77, 84, 64, 88, 96, 81, 99, 108, 121, 132, 144?

XII.

(1.) 3412765 × 14, 16, 18.

(2.) 9806574 × 15, 21, 24.
(3.) 2301654 × 22, 27, 33.
(4.) 8715463 x 28, 32, 36.
(5.) 4523876 × 25, 44, 48.

(10.) 6542107 x
(11) 96458307 ×
(12.) 87367218 x
(13) 78276309 ×

Ans. 47778710.
54604240.
61429770.

(6.) 8917685 × 35, 45, 55.
(7.) 5634987 × 42, 54, 66.
(8.) 9028796 x 49, 56, 72.
(9.) 8764329 × 96, 99, 108.
121, 132, 144.
630, 770, 840.
6400, 8800, 96000.
81000, 990, 12100.

XIII.

(1.) 647983 × 13, 19, 23. (5.) 865376 ×

Ans.

8423779.

(6.) 678987 ×

65, 71, 83. 67, 79, 87.

(7.) 567876 ×

89, 101, 103.

(8.) 789098 x (9) 432678 x (10.) 608934 ×

91, 109, 113.

97, 107, 119. 127, 139, 143.

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(15.) 453987 × 942, 385.
(16) 842109 × 2345, 6789.
(17) 953210 × 3087, 8009.
(18.) 731098 × 6503, 7092.
(19) 382907 × 6007, 1671.
(20.) 289765 × 4576, 3908.

(26) 8170983 × 890067. (27.) 908963 × 769005. (28) 6475328 × 680007. (29.) 5364217 × 900008. (30.) 7586439 × 456789.

C

XIV.

(1.) Multiply six hundred and forty-nine millions eight hundred and sixty-five thousand three hundred and nine, by ninety-six.

(2.) Multiply eighty thousand nine hundred and seventy millions sixty-seven thousand and eight, by nine thousand and seven.

(3.) What is the product of six thousand seven hundred and sixty-five, multiplied by three thousand eight hundred and seven?

(4.) What number is equal to seven hundred and nine times eighty-nine millions four hundred and seventy-four thousand?

(5.) What number is equal to six millions four hundred and seventy-five thousand six hundred and eighty-nine times eighty-nine?

(6.) How much greater is the product of seventy-five thousand six hundred and forty-nine and twenty thousand eight hundred and forty-two, than the product of seventy-four thousand nine hundred and eighty-nine, and nineteen thousand eight hundred and seventy-two?

(7.) From the sum of eight hundred and seventy-four, ninety-seven, six thousand five hundred, subtract the sum of seven hundred and sixty-nine, eighty-four, nine hundred and forty-nine, five hundred and seventy-nine, and multiply the remainder by six hundred and forty-five.

(8.) Find by how many nine hundred and seventy-eight multiplied by eight hundred and seventy-nine is greater than eight hundred and seventy-six multiplied by six hundred and seventy-eight.

(9.) Multiply nine hundred and eighty-five billions by seventy-four.

(10.) Multiply six hundred and seven millions by fortynine thousand.

XV.

Terms to be explained :-Square, or second power; cube, or third power; fourth power, &c.; indices; continued product.

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