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7. £56 4s. 104d. to farthings.
8. £+ as. + d. to pence.
9. £3. 5s. 720. to farthings.
10. Zs. to farthing.
11. £j to pence.
12. £to farthings.
13. £; to integers of lower denominations.
14. £; to integers of lower denominations.
15. £4 to integers of lower denominations.
16. $150 to mills.
17. $17.28 to cents.
18. 10 eagles to mills.
19. 19 francs to decimes.
20. 19 francs 8 decimes to centimes.

REDUCTION ASCENDING.

INDUCTIVE STEPS. 1. How many pence in 8 farthings? In 12 farthings? In

24 far.? 2. How many shillings in 12d.? In 36d. ? In 108d. ? 3. 40 shillings equal how many pounds ? 60 shillings? 4. If you take £2 out of 45s., how many shillings remain ? 5. If you reduce 45s. to pounds, what is your result?

Reduction ascending changes a denominate number from a lower to a higher denomination without changing its value.

EXERCISES. 1. How many pounds are there in 8365 pence? Process.

Explanation. 12) 8365d.

Since 12d. 1s., of the number 20) 697s. + 1d. pence the number of shillings. Since

20s. = £l, zo of the number of shillings £34 + 17s.

the number of pounds. Hence, 8365d. 8365d. = £34 17s. 1d. : £34 17s. 1d.

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2. Reduce d. to the fraction of a pound.

Process. şd. ģ of 125. Toss.

láss. = Tās of £2b = £216 = £132• Or,

. x

08

5

5

2

Ed. X

1 = £

432

9

12

RULE.

Divide by the numbers of the scale, beginning with the number of the given denomination that makes one of the next higher, and continuing until the required denomination is reached.

3. Reduce s. to a fraction of a pound. 4. Reduce 4 far. to a fraction of a shilling. 5. Change 495d. to units of higher denominations. 6. Change 4257 shillings to pounds. 7. Reduce 4697d. to pounds. 8. Reduce 5967s. to pounds. 9. Reduce 6969 far. to pounds. 10. Reduce 4995d. to pounds. 11. Reduce 5796 far. to shillings. 12. Reduce 59,678 far. to pounds. 13. Reduce £4 15s. 6d. to far. 14. Reduce 59,607 far. to pounds. 15. Reduce 25,392 far. to £, s., d. 16. Reduce £26 to dollars. 17. Reduce $567 to pounds. 18. Reduce $394.45 to pounds. 19. Reduce $48.60 to pounds. 20. Reduce £36 to dollars. 21. Reduce 25,488 far. to £, s. and d. 22. Reduce $973.30 to pounds.

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23. Reduce $1,216,625 to pounds.
24. Reduce $1084.40 to cents.
25. Reduce 3596 cents to dollars.
26. Reduce 48,567 mills to dollars.
27. Reduce 1930 francs to dollars.
28. Reduce 3846 francs to dollars.
29. Reduce 4856 dollars to francs.
30. Reduce 5968 centimes to francs.
31. Reduce centime to the fraction of a franc.
32. Reduce £1 to integers of lower denominations.

MEASURES. 1. Extension has three dimensions,-length, breadth, and thickness.

2. These dimensions are the origin of three different kinds of Measures,-Linear Measures, Surface Measures, and Measures of Volume or Capacity.

LINEAR MEASURES. Linear Measures are used in determining lengths and distances.

Common Linear Measure.

12 Inches (in.) 1 Foot (ft.). 3 Feet

1 Yard (yd.). 5} Yards

1 Rod (rd.). 161 Feet Ś 320 Rods = 1 Mile (mi.). 40 Rods

1 Furlong (fur.). 8 Furlongs

1 Mile. mi. rd. yd. ft. in. 1 - 320 1760 5280 63,360.

Scale : 12, 3, 51, 320.

=

}

Surveyors' Linear Measure.
7.92 Inches

1 Link (l.).
25 Links

1 Rod (rd.). 4 Rods

1 Chain (ch.). 100 Links

80 Chains 1 Mile (m.).
mi. ch. rd. 1.

in.
1 : 80 320 8000 - 63,360.

Scale : 7.92, 25, 4, 80.
The following have special uses :
3 Barleycorns

1 Inch. Shoe-length measure. 4 Inches

1 Hand. Horse-height measure. 6 Feet

1 Fathom. Sea-depth measure. 3 Feet

1 Pace. 5 Paces

1 Rod.

Pacing measure. 1.15 Statute Miles = 1 Geographical, or Nautical Mile.

3 Geographical Miles 1 League. 60 Geographical Miles

of Latitude, or S9.16 Statute Miles

of Longitude at the Equatoi

ر

1 Degree {

EXERCISES.

1. In 12 rd. 3 yd. 2 ft. how many feet ? 2. In 5 mi. 18 rd. 4 yd. how many yards? 3. Change 7 rd. 5 ft. 6 in. to inches. 4. Reduce 5 miles to inches. 5. In 5 mi. 2 fur. 4 yd. how many feet ? 6. In 51 yd. of ribbon how many inches ? 7. How many inches in one mile? 8. Reduce 3 mi. 4 yd. 2 ft. to feet. 9. Reduce 13,769 ft. to mi., fur., rd., etc. 10. In 15,347 in. how many yd., ft., etc. ? 11. Change 250,497 ft. to miles, etc. 12. Reduce 77,565 in. to miles, etc. 13. Reduce 5 miles to links. 14. Reduce 9 miles 54 ch, to links.

15. Reduce 11 mi. 68 fathoms to fathoms. 16. Reduce 43,000 1. to miles. 17. Reduce 79,400 1. to miles. 18. Reduce 9968 fathoms to miles. 19. In 481,401,716 in. how many degrees? 20. If a horse is 151 hands high, find his height in feet. 21. Change 29,763 1. to higher denominations. 22. How many inches in 2 degrees at the equator ? 23. Reduce 677,653 in. to higher denominations. 24. Reduce 7912 mi. (the diameter of the earth) to inches

and to paces.

25. A ship was sailing in 121 fathoms of water. How deep was the water ?

SURFACE MEASURES.

1. An angle is formed by two straight lines drawn from the same point.

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2. When a line is drawn from a point between the ends of another line, making the two angles equal, the angles are called right angles.

3. A Rectangle is a figure having four sides and four right angles.

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4. A Square is a rectangle with four equal sides.

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