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GEOMETRY.

184. QUADRILATERALS.-REVIEW.

Square. 1. All the geometrical figures on this page are quadrilaterals; that is, each has four sides.

1

a

b

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185. MISCELLANEOUS REVIEW.

1. The difference of two numbers is 37416; the smaller number is 24317. What is the larger number ? *

2. The difference of two numbers is a; the smaller number is b. What is the larger number?

3. James had a certain number of dollars and John had three times as many; together they had 196 dollars. How many had each ? (x + 3 x = 196) †

4. William had a certain number of marbles; Henry had twice as many as William, and George had twice as many as Henry; together they had 161. How many had each ? (x + 2 x + 4 x = 161)

5. Divide 140 dollars between two men, giving to one man 30 dollars more than to the other. (x + x + 30 = 140)*

6. By what integral numbers is 30, (2 x 3 x 5), exactly divisible besides itself and 1 ?

7. By what is abc, (a x b x c), exactly divisible besides itself and 1 ?

(1) How many times is a contained in abc ?
(2) How many times is b contained in abc ?
(3) How many times is c contained in abc ?
(4) How many times is ab contained in abc ?
(5) How many times is ac contained in abc ?
(6) How many times is bc contained in abc ?

Observe that a number composed of three different prime factors has

exact integral divisors.

8. Change to 60ths. Is žmore or less than 7 ? 9. Change š to 100ths. Change { to 100ths. 10. Change 1 to 100ths. Change to 100ths.

* The difference of two numbers is 5; the smaller number is 4. What is the larger number?

+ See page 78.

FRACTIONS.

Art. 179, continued from page 86. Find the sum of-1. and go

6. 11, 1, and 13 2. and 18

7. 1}, }, and 18 3. U and a

8. 21, 1, and is 4. i's and 13

9. 15, }, and is 5. 1 and 16

10. 1, 1, and 16 (a) Find the sum of the ten sums.

5 28

186. TO SUBTRACT COMMON FRACTIONS. RULE.-Reduce the fractions if necessary to equivalent fractions having a common denominator, find the difference of their numerators, and write it over the common denominator.

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5 18

Find the difference of -
1. and

3. and
2. and is 4. land
(b) Find the sum of the six differences.

5. -
6. 4-5

Fractions.

187. To subtract one mixed number from another when the fraction in the subtrahend is greater than the fraction in the minuend.

EXAMPLE.

From 58% take 32.
Operation.

Explanation.
58% = 58 14 is greater than , therefore we take 1 unit
323 = 3241

from the 8 units, change it to 24ths, and add it

to the 9 24ths. Difference 2531

31 += 3.37 - 19= 11. 2 units from 7, (8 — 1), units = 5 units. 3 tens from 5 tens = 2 tens.

I. Find the difference of-1. 244 and 16%

6. 354 and 263 2. 29% and 151

7. 28 and 14% 3. 46 and 18,0 8. 36, and 81% 4. 525 and 313

9. 654 and 223 5. 473 and 187

10. 341 and 271 (a) Find the sum of the ten differences.

II. Reduce to simplest form

1. 5+ 33 - 54
2. 63 – 3+ 47
3. 2 - 11 + 3%
4. 73 + 33 - 13
5. 63 – 31 + 5}
6. 34 + 43 – 38 – 23 + 13
7. 63 - 24 - 13 - 131 + 24

8. 52 +43 + 2 + 3 + 31
(b) Find the sum of the eight results.

Fractions.
188. To multiply a fraction by an integer.

Multiply z by 6.
Operation No. 1.

Operation No. 2.
6 times of are di = 1

6 times I = 1 = 11 1. Observe that by the first operation we obtain 1}; that in 11 there are 6 times as many parts as there are in and that the parts are of the same size as those in 14.

2. Observe that by the second operation we obtain ; that in there are the same number of parts as there are in 71, and that the parts are 6 times as great as those in 14.

Note 1.—The 7 of ja may be regarded as a dividend; the 24, as a divisor, and a itself, as a quotient. In jy, we have a dividend 6 times as great as that in js, the divisor remaining unchanged. In 1, we have a divisor 1 sixth as great as that in is, the dividend remaining unchanged. Multiplying the dividend or dividing the divisor by any number, multiplies the quotient by the same number.

Note 2.—The 7 of a may be regarded as the antecedent of a couplet ; the 24, as the consequent, and is itself as the ratio. Multiplying the antecedent or dividing the consequent of any couplet multiplies the ratio by the same number.

RULE.— To multiply a fraction by an integer, multiply its numerator or divide its denominator by the integer. I. Find the product. 1. x4 5. o 8

4
2. 1 x 6 6. x 9

7
10. x 6

15

9 3. li x 5 7. X8

x 5 4. 17 x 7 8. * * 9 12. 13 x 7 (a) Find the sum of the twelve products.

9. 12

II. Find the product.
1. 37 x 7 5. 43 x 5

9. 6.3 x 5
2. 53 x 6 6. 17 x 4 10. 213 x 4
3. 72 4 7. 53 x 5

11. 4g

x 6 4. 3.7 x 5 8. 85 x 4

12. 61

x 7 (b) Find the sum of the twelve products.

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