American Elementary Arithmetic by Middlesex Alfred Bailey

Author:Middlesex Alfred Bailey
Language: eng
Format: epub, pdf
Publisher: American Book Co.
Published: 1898-03-25T05:00:00+00:00

231. Find the least common multiple of 2, 3, 4, 6, and 8.

S =z2 X 2 X 2 '^^^ least common multiple must

^ __ 9 v^ ® contain 8, or 2 x 2 x 2, and we

. _ gj ^ retain these factors.

■* """ ^ ^ The least common multiple must

2x2x2x3 = 24, L, CM. contain 6, or 2 x 3. We have the

2 and retain the 3. The least common multiple must contain 4, or 2 x 2. We have the two 2's. The least common multiple is 2 x 2 x 2 x 3, or 24.

Find the L. (7. M. of:

232. 8, 10 236. 6, 9, 10

233. 9, 12 237. 2, 3, 4

234. 8, 14 238. 8, 9, 12

235. 8, 12 239. 10, 12, 18

COMMOK FRACTIONS

A common fraction is one or more of the equal parts of a unit.

The number showing into how many parts the unit is divided is the denominator; it is written below a horizontal line.

The number showing how many parts are taken is the numerator; it is written above the horizontal line.

Illustiiation. —3 quarters of an inch = j of an inch. J b a common fraction; 3, the iiumei'ator; 4, the denominator. It means that an iiic)i has been divided into 4 equal parts, and that 3 of those parts have been taken.

Reduction to Lower Terms

Dividing both numerator and denominator hy the same number does not change the value of a fraction,

1. Draw a square, divide into parts, and letter as on the preceding page.

2. What part of the whole is ^ ? Bl CI B?

3. Prove that ^ = |.

Ans, ^=4D = t\; A = 2B = i. Therefore A = f

4. Prove that f = :f.

Arts. A =2B = i', i4=J. Therefore } = J.

5. Draw a line § inch long; draw another ^ inch long. Compare the two lines.

6. Prove, by drawing and dividing a rectangle, that

7. In the same way, prove that ^ = 1^-

8. In the same way, prove that ^| = ^.

9. Reduce r^ to lowest terms.

72 __ 8 _2 We divide both terms of ^ by 9; both terms

108^12^3 of A by 4.

Note. — A fraction is in its lowest terms when both numerator and denominator are prime to each other. Thus: J is in its lowest terms because 2 and 3 are prime to each other. See p. 151.

Reduce to lowest terms:

10. ^j; jf 13. H; n 16- Bl5 IM

11. ij; ji 14. H; n "• Ml; m

12. If; If 15. ^^ H 18- m-> M

Reduction to Higher Tenns

Multiplying both numerator and denominator by the same number does not change the value of a fraction.

19. Draw a re^ctangle as on p. 154, and prove that ^ = ^q. Ans. B = i; J5 = 2D; D = ^. Therefore J = A-

20. In the same way, prove that ^ = ^.

21. Draw a rectangle; divide it into 12 equal parts; prove that J = ^.

22. Change ^ to 12ths.

2 _ 8 To make the denominator 12, we must multiply 3 by

3^ 12 45 multiplying both terms by 4, § = ^.

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