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Reduction teaches to find how many of one name are equivalent to a certain number of another name.

EXERCISES.

Reduction descending. Reduction ascending.

Reduce

350246 far. to £s.

734082 far. to £s.

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355087 far. to £s.

12165 far. to £s.

1. £364, 16s. 94d. to far. 2. £764, 13s. 4 d. to far. 3. £369, 17s. 7 d. to far. 4. £12, 13s. 51d. to far. 5. £17, 16s. 9 d. to far. 6. £1, 2s. 6d. to far. 7.33 gs. 9s. 24d. to far. 8. 74 gs. 15s. 34d. to far. 9. £73, 16s. 4 d. to hfp. 10. £61, 38. 54d. to halfp. 29363 halfp. to £s.

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- 17127 far. to £s.
- 1081 far. to £s.
33706 far. to guins.
75325 far. to guins.
35433 halfp. to £s.

-

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Reduction descending.

Reduction ascending.

Reduce

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11. £42, 5s. 3 d. to halfp.
12. £756, 13s. 4d. to pen.
13. £312, 16s. 9d. to pen.
14. £400, 19s. 11d. to pen.
15. £71, 13s. 6d. to sixp.
16. £1, 10s. 6d. to sixp.
17. £761, 15s. to shillings
18. £841, 13s. to shillings
19. £38,12s. 6d. to hf.-crs.
20. £7, 158. to half-crs.
21. £71, 7s. 6d. to hf.-crs.
22. £61, 15s. to crowns
23. £73, 10s. to crowns
24. £64, 5s. to crowns
25. 700 guineas to £s.
26. 76412 gs. 3s. to £s.
27. 84000 guineas to £s.
28. 62cwt.3qr. 16lb. todr.
29. 34 cwt. 1 qr. 171b.todr.-
30.253 cwt.2qr. 14 lb.tolb.—
31. 11 tons 1 cwt. to lb.
32. 17 lb. 6 oz. to dr.

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20287 halfp. to £s. 181600 pen. to £s. 75081 pence to £s. 96239 pence to £s. 2867 sixpen. to £s. 61 sixpences to £s. 15235 shill. to £s. 16833 shill. to £s. 309 half-crs. to £s. 62 half-crs. to £s. 571 half-crs to £s. - 247 crowns to £s. 294 crowns to £s. 257 crowns to £s. £735 to guineas £80,232, 15 sh. to gs. £88200 to guineas. 1803264 dr. to cwt. 986368 dr. to cwt. 28406 lb. to cwt. 24752 lb. to tons. 4448 dr. to lb.

33. 27 lb. 13 oz. 10 dr. to dr.-7130 dr. to lb.

34. 41 lb. 13 oz. 9 dr. to dr.

35. 18 lb. 6 oz. to gr.
36. 59 lb. 13 dwt. to gr.
37. 37 lb. 3 dwt. to gr.
38. 7912 miles to inches
39. 24856 miles to inches
40. 76 yd. 1qr. 3 nl. to nl.
41. 34 yd. 2 qr. 1 nl. to nl.
42. 12 yd. 2 qr. 2 nl. to nl.
43. 15 ac. 21 po. to po.

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10713 dr. to lb.

106560 gr. to lb.

340152 gr. to lb.

213192 gr. to lb.

501304320 in. to m.
1574876160 in. to m.
1223 nl. to yd.
553 nl. to yd.
202 nl. to yd.
2421 po. to ac.

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SIMPLE PROPORTION.

Proportion teaches to find a fourth proportional

to three given numbers.

1st Term. 2d Term. 3d Term. 4th Term

The terms are thus arranged; 2 : 8: : 5:

20

and thus read, as two is to eight so is five to twenty.

To find the fourth term.

RULE.-Make that number which is of the same kind as the number sought, the third term; then, if the answer ought to be greater than this term, make the greater of the two remaining numbers the second term, and the less the first; but if the answer ought to be less, make the less the second, and the greater the first term. Multiply the second and third terms together, and divide the product by the first, the quotient is the fourth term in the same name as the third. If any of the terms are compound reduce the first two to the same name, and the third to its lowest before multiplying.

EXERCISES.

1. If 8 yd. cost £3, what cost 56 yd.? Ans. £21. 2. If 6 yd. cost £2, what cost 78 yd.? Ans. £26.

3. If 9 cwt. cost £13, what cost 27 cwt.? Ans. £39.

4. If 4 cwt. cost £6, what cost 28 cwt.? Ans. £42.

5. If 11 cwt. cost £5, what cost 99 cwt.? Ans. £45.

6. If 7 cwt. cost £19, what cost 126 cwt.? Ans. £342.

7. If 3 qr. cost £2, what cost 111 qr.? £74.

Ans.

8. If 12 qr. cost £17, what cost 156 qr.? Ans. £221.

9. If 14 bush. cost £4, what cost 728 bush.? Ans. £208.

10. If 18 bush. cost £11, what cost 558 bush.? Ans. £341.

11. If 38 gal. cost £29, what cost 1596 gal.? Ans. £1218.

12. If 46 gal. cost £57, what cost 506 gal.? Ans. £627.

13. If 13 ac. cost £670, what cost 169 ac.? Ans. £8710.

14. If 49 yd. cost £7, 6s. 82d., what cost 147 yd.? Ans. 22, 0s. 21d.

15. If 37 oz. cost £31, 38.54d., what cost 185 oz.? Ans. £155, 17s. 21d.

16. If 41 oz. cost £11, 16s. 44d., what cost 123 oz.? Ans. £35, 9s. 11⁄2d.

17. If 21 lb. cost £7, 11s. 64d., what cost 3 lb. ? Ans. £1, 1s. 7 d.

18. If 97 lb. cost £3, 2s. 7 d., what cost 35 lb.? Ans. £1, 2s. 7 d.

19. If 365 lb. cost £15, 11s. 91d., what cost 25 lb.? Ans. £1, 1s. 41d.

20. If 1000 oz. cost £11, 9s. 2d., what cost 7 oz.? Ans. 18. 7 d.

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