LESSON IX.

PRACTICE EXERCISES.

This lesson should be studied as follows: Use first the sign+, as 11+2=13, etc.; then the sign as 11-2-9, etc.; afterwards both signs, as 11+2=13 or 9.

21. 136 ? 23+6=? 33+6=? 43+6=? etc. 22. 13±7=? 23±7=? 33±7=? 43±7=? etc. 23. 13+8=? 23+8=? 33+8=? 43+8=? etc. 24. 139 ? 23+9=? 33+9=? 439=? etc.

44+6=? etc.

29. 14+6=? 24+6=? 34+6=?

30. 14+7=? 24+7=? 34+7=? 447? etc.

31. 148 ? 24+8=? 34+8=?

44+8=? etc.

37. 156 ? 25+6=? 35+6=? 45+6=? etc.

38. 15+7=? 25±7=? 35±7=? 39. 158 ? 25+8=? 35+8=? 40. 159 ? 25±9=?

45+7=? etc.

45+8=? etc.

35+9=? 45+9=? etc.

41. 16+2=? 26+2=? 36+2=? 42. 163 ? 26+3=? 36+3=?

46+2=? etc.

46±3=? etc.

36±4=? 46±4=? etc. 36+5=? 46±5=? etc.

43. 164 ? 26±4=? 44. 165 ? 26+5=? 45. 166 ? 26±6=? 36+6=? 46±6 ? etc. 46. 167? 26+7=? 36+7=? 46+7=? etc. 47. 1618 ? 26+8=? 36+8=? 46±8=? etc. 48. 169 ? 26+9=?

36+9=?

46+9=? etc.

SECTION I.

DEFINITIONS.

Article 1. A Unit is a single thing, or one of any

kind.

Thus, one, one hat, one gallon, one year.

One denotes a single thing; one and one more is called Two; two and one more is called Three; and thus, by the successive additions of one, are obtained the several numbers one, two, three, four, five, six, seven, eight, nine.

2. A Number is an expression of one or more units. Thus, one, four, six miles, fifty dollars, one hundred, are numbers. 3. Arithmetic is that branch of mathematics which treats of numbers and their applications.

Hence, all forms of counting and business operations involving the use of numbers belong to Arithmetic.

4. A Denominate Number is a number whose kind of unit is named.

Thus, 2 apples, 5 bushels, 30 yards, are denominate numbers.

5. An Abstract Number is a number whose kind of unit is not named.

Thus, 4, 7, 40, 100, are abstract numbers.

6. The Unit or Unit Value of a number is one of that number.

Thus, 1 foot is the unit value of 5 feet or 10 feet; 1 is the unit value of 5, 10 or 50.

7. Like Numbers are numbers that have equal unit values.

Thus, 2 miles and 8 miles are like numbers, because they have equal unit values, 1 mile, 1 mile.

8. Unlike Numbers are numbers that have different unit values.

Thus, 5 boys, 10 apples, 20, 30 dollars, are unlike numbers, because their unit values, 1 boy, 1 apple, 1, 1 dollar, are not alike.

9. Units are of the same kind, when they are either abstract or of the same denomination.

Thus, 2, 4, 10, 50, express units of the same kind.

So, 2 feet, 4 feet, 10 feet, 50 feet.

10. Units are of different kinds when they are of different denominations.

Thus, 3 dollars, 4 gallons, 2 quarts, express units of different kinds. 11. Simple Numbers are numbers that express units of the same kind.

Thus, 4, 6, 12, 25, 48, are simple numbers.

So, 3 years, 40 years, 100 years. Hence,

Simple numbers are either abstract or denominate. 12. Compound Numbers are numbers that, regarded as one quantity, express units of different kinds. Thus, 12 feet 4 inches, 8 pounds 6 ounces, are compound numbers. Hence,

Compound numbers are always denominate.

13. An Integer or Integral Number is a number that expresses one or more whole units.

Thus, 7, 16 pears, 100, are integers.

14. Figures are characters used to represent num

bers.