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Reduce to fractions having a common denominator :— (3.,,, ; 4, 7, 1, 4; 6, 4 b b ; 5 1 b b ft.

49

(4.) + (ans. 11), + (ans. 2), 1+}, }+1.
(5.) ++, }+&+z+1, 3+}+8.

(6.) 3+2 (ans. 52), 52+41, 63+†, 4}+17.
(7.) 2+1+5, 6+5%+7%, 85 +91.
(8.)-(ans. 1), 3-1, 1-1, 1-8.

(9.) 4-2 (ans. 1), 5-43, 48-1%, 64-1.
(10.) 88-7%, 94 — 6, 11-8, 13-57.

9

[blocks in formation]

(6.) 8 ÷ 10, 84 ÷ 11, 6 ÷ 12, 74 ÷ 12.

(7.) ×

(8.)

(ans. 1), 4×21 (ans. 2), 4ק×5.

××, of, of .

(9.) of, of 4 of 8 × 8, 9 of 1x of 7.

(10.) 2×3 (ans. 10), 43×6 (ans. 30), 7×43.

(11.) 8 × 7, 94 of 68, 87 of 78.

X

(12.) of of of of 15, of 9×3×3

18

(13.)x13x18x, 21 of 1 x 5.

(14.) (6+4-58)×6, (59-4×8.

of 15.

(15.) (6-4+51-21)×6, (72 +82-63-419)×9.

(16.)

22

[ocr errors]

(ans. 112), & ÷ (ans. 111), ? ÷÷÷1.

5 69

(17.) 음흉, 숲, 우승, 송은

(18.) 67 (ans. 28), 83÷47 (ans. 17), 947.

(19.) 21, 99÷4, 12÷2

(20.) (3×41)÷(82×42) (ans. 7). (24×62) ÷ (71⁄2 of 4}).

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(1.) What fraction is 5 of 10 (ans. )? 3 of 9 (ans. })? 7 of 28? 18 of 16?

(2.) Reduce 72 to the fraction of 84, 96 to the fraction of 176, 189 to the fraction of 210, 297 to the fraction of 324.

(3.) What fraction of 112 is 252? what fraction of 432 is 576?

(4.) Reduce to the fraction of (ans. ), to the fraction of (ans. 3), 51⁄2 to the fraction of 43.

(5.) Reduce to the fraction of 12, 43 to the fraction

of, of to the fraction of of §.

(6.) If 9 be of a certain number, what is the whole number? Ans. 117.

[ocr errors]

of No.

.. The number required of 93= of 1995=11}.

(7.) If 11 be of a number, what is the whole number? (8.) If 5 be of a number, what is of the whole number?

(9.) A workman during a three month's engagement saved, the first month £23, the second £33, the third £23. For how many weeks during the winter will this money keep him at the rate of £3 per week?

(10.) A said that he would give of whatever sum B gave towards a certain charity. B gave of £50. How much would A require to give?

(11.) What is the half of one-fourteenth? the sixth of one-third? the twelfth of one-half ?

XXIX.

Multiplication when the Multiplier contains a Fraction. (1.) Find the half of 6984, 9833. Answers, 3492, 49163. (2.) Find the third of 6743, 9648.

(3.) Find the seventh of 87641, 11409.

(4.) of 45968, of 96483. Answers, 394017, 826995. (5.) of 839645, of 897681.

[ocr errors]

(6.) of 1149683, 1 of 1468971.

(7.) 678954 X 3,

3691614.

(8.) 975003 × 61,

(9.) 761142 × 71,

851911 × 4. Answers, 2376339,

857643 × 51.

610109 × 84.

(10.) 839764 × 89, 1149683 × 11. Answers, 74379095. 131574833.

(11.) 4896456 × 91, 7412968 × 24.

(12.) 8967432 × 29‡, 7643281 × 7421%.

(13.) 9784564 × 9001, 7645983 × 760011.

Division when the Divisor contains a Fraction.

In the following sums find the quotient and remainder :

(14) 54132131, 694130 ÷ 51. Answers, 154663+ r., 132215+ r. 14.

(15) 8976016, 674289 ÷ 7.

(16.) 87643 ÷ 83, 96459 ÷ 7%.

In the following sums find the complete quotient :-
(17.) 64983111, 846134 ÷ 213. Answers, 5507035,
39870.

(18.) 6897658 ÷ 2311, 4964581 ÷ 41714.
(19.) 6814870901, 8764589 ÷ 100011.

Multiplication when the Multiplicand contains a Fraction. (20.) 648976 × 6, 729894 x 8. Answers, 3893860, 5839157.

(21.) 8740967 × 9, 60590811 × 11.

(22.) 67098457 × 24, 906807611 × 27. (23.) 4974651 X 32, 7610919 x 64.

17

(24) 4729643 x 23, 7642050 x 37. (25.) 8745961 × 43, 965387511 × 51.

Division when the Dividend contains a Fraction.

In the following remainder :

sums find the quotient and

(26.) 6428497÷7, 961072 ÷ 9. r. 43, 106785 + r. 7.

(27.) 77496111, 874072 ÷ 12.

(28.) 654291825, 9754827 ÷ 32.

Answers, 91835+

In the following sums find the complete quotient :— (29.) 6497832 ÷ 56, 7641891 ÷ 84. Answers, 11603245, 909741.

(30.) 9621843§ ÷ 23, 79617764 ÷ 31.
(31) 98700191 ÷ 69, 689174211 ÷ 73.

Miscellaneous Exercises

XXX.

(1.) Find the sum of 968, 47, 8745, 19, 2847, 6894, 5897, 765, 849, and 74.

(2.) Add together four billions six hundred and ninetytwo thousand eight hundred and nine millions five hundred and forty-one thousand six hundred and seven, six hundred and eighty-four thousand seven hundred and ninety-two millions eight hundred and ninety-six thousand five hundred and eleven, ninety-six thousand eight hundred and forty-nine millions nine thousand and thirteen, eighty-seven thousand six hundred and eight millions nine hundred and ten thousand seven hundred and nine,

eight hundred and ninety-seven millions six hundred and forty-three thousand nine hundred and forty-two, and seven hundred and sixty-five millions eight hundred and ninty-six thousand seven hundred and sixty-five.

(3.) Express 1596 in Roman numerals.

(4.) Find the square of 249.

(5.) Five boys set out to gather nuts. Andrew gathered nine hundred and eight; Robert, seven hundred and eleven; David, one thousand and nineteen; Charles, ninety-seven; and Frank, seven hundred and forty-nine. How many did they gather among them?

(6.) From 6549862709804 take 2958974811915.

(7.) From nine billions six hundred and four thousand and ninety millions six hundred and eighty-two thousand five hundred and forty-nine subtract nine hundred and sixty-five thousand eight hundred and ninety-two millions seven hundred and ninety-three thousand six hundred and fifty-nine.

(8.) What is the difference in population between two towns, the one having eighteen thousand four hundred and fifty-three inhabitants, and the other fifteen thousand eight hundred and ninety-six ?

(9.) Express the following number in words :897068643009.

(10.) How many years elapsed between the year MDCCLXIX and the year MDCCCLXX?

(11.) From six apple-trees there were gathered respectively three hundred and sixty-five, nine hundred and seventy-nine, four hundred and one, eight hundred and eleven, seven hundred and three, and four hundred and nineteen apples. Of these one thousand nine hundred were sold to one customer, and five hundred and nine to another. How many were left unsold.

(12.) Express the following number in words :8976001901893.

(13.) John got six times as many apples for his money as the number of pence which he spent on them. He spent fivepence. How many apples did he receive?

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