Elementary arithmetic, with brief notices of its history... by Robert Potts.

33

16. 18^9 17. 5, O. 18. 1. 19. 251k. 20. -.. 21 1-17 22. 10631.
23. 43 -.
Note.-The four fractions in example 18 may be more readily added together by
resolving the denominators of the fractions into their prime factors.
7 29 1 7 29_ 626
Here 7 -2431 2717-11X13 t 17 19) 11X13X17X19
And 589 3446 1 589 1 3146 45563
3553 4199 17 X19 ~ 11 13X 17X19
46189 46189
Sum of the four fractions = 61 461 1
1. ~i. 2. 2kl. 3. 12-. 4. 102-3. 5. 12k. 6. 122. 7. o. 8. 238-. 9.
l8o.10. 7T 11. 42T '. 12. 3459. 13. 211. 14. 234-1. 15. 19597s.
VI.
1.. 2. -. 3.. 4. -. 5. -. 6. 3-. 7. 252. 8. 9. 17133792-7 10.
11. —.3 —. 12. 4 13. 4A7. 14. 1. 15. 4}7. 16. 193xv. 17. 3460*. 18.
1154-,. 19. - 20. 4. 21. 17831. 22. 15603 - 23. 100002 ---L-. 24.
80 2.C 8-0' 21. 178.
90909090-0.
VII.
1..' 2. 3. 3. A. 4. 11. 5. 6. 1.4. 7. 2-. 8. 81. 9.1. 10. 2-.
VIII.
2. 2W, 26,. 3. 182th part.
4. Their relative magnitudes will be obvious when the fractions are reduced U
the same denoirminator. 5. Art. 7. 6. Art. 12, note.
7. If 3 be added to the numerator and denominator of the proper fraction -
'43 0 4 74' +3 10
It becomes or - or -,
And 12 is greater or less than -.
Bu4. t re is obviously greater than.are reduced
It follows that 7+3 is greater than 7
12+3 12
or that the proper fraction -7 is increased by adding the same number 3 to its.
numerator and denominator.
In a similar way it may be shewn that the proper fraction -7c is diminished bysubtracting the same number 3 from its numerator and denominator.
The remaining examples 8, 9, 10, 11, 12, offer no difficulties.
With respect to Ex. 12 see Art. 7.
IX.
1. Reduce to single fractions and find the sum. 2. The result is 484-91,_. 3.
jun. 4.:. 5. The sum of the fractions is —: and the lowest fraction required
with denominator 1000, will be next greater than -x, which will be found to be ~1,0.
7. -. 8. 6l^. 9. 1 excess, s of 7. 10. 300. 11.ro can be subtracted 11 times,
from 2, and leaves a remainder — o. 12. 3+5+7 =15, and 3 + 5+ 7.