17. Twenty-five trillion two hundred seven million thirtyseven thousand three hundred one. 18. Four trillion seventeen million five hundred one. 19. One hundred billion thirty-five thousand nine hundred. 20. Six quadrillion ten trillion one million twenty-three thousand five hundred sixty-three. Notation and Numeration of United States Money. 20. The dollar sign is $. It is written before the number. Thus, $45 is read forty-five dollars. 21. A period, called the decimal point, is used in connection with $ in expressing cents and mills. The first two places at the right of the decimal point express cents, and the third expresses mills. Thus, $.124 is read twelve cents and four mills. Dollars and cents are written as one number by placing the decimal point between them, and writing $ before the number of dollars. Thus, $3.25 is three dollars and twenty-five cents. When the number of cents is less than ten, a cipher must be written in the first place at the right of the decimal point. Thus, four dollars three cents five mills is written $4.035. 23. Express by signs and figures: 1. Sixteen dollars; five dollars, twenty-two cents, one mill; twelve dollars, nine cents. 2. Sixty-five cents; forty-seven dollars, five cents, two mills ; one hundred dollars, two cents. 3. One cent, one mill; three hundred twenty-one dollars. 4. Seventy-four cents; ninety-seven cents, four mills. 5. Thirty-one dollars; two hundred dollars, seven mills. 6. Six thousand seven hundred four dollars, five cents. 7. Forty-three thousand seventy-one dollars, nine mills. 8. Two hundred sixty-two dollars, six cents, one mill. 9. 85 dollars, 70 cents, 8 mills. 10. 721 dollars, 4 cents, 3 mills. Definitions. 24. A scale in Arithmetic is the relation between the successive orders of units. In the decimal system the scale is ten, because the value of the unit of any order is ten times as great as the unit of the next lower order. 25. In the decimal system of notation each figure has a simple and a local value. Its local value is the value which its place gives it. Thus, in 527 the simple value of 5 is five, and its local value is five hundred; the simple value of 2 is two, and its local value is two tens. 26. When numbers are used without reference to any particular units, they are called abstract or pure num bers. Three, seven, 13, 25, are abstract numbers. 27. When numbers are associated with particular units, they are called concrete numbers. Three bushels, 5 days, 10 pints, are concrete numbers. 28. Like numbers are those which have the same unit. Five feet and 9 feet are like numbers; 5 feet and 9 days are not like numbers. ADDITION. Definitions and Principles. 29. How many beads are 5 beads, 4 beads, and 6 beads? |||||, | |||, ||||||, 15 Solution: (1) I may make as many marks as there are beads, count them, and thus find that there are 15 beads in all. This is uniting integers by counting. (2) I may say 6 beads and 4 beads are 10 beads, and 10 beads and 5 beads are 15 beads. This is uniting integers by addition. 5 4 6 15 30. Addition is a short method of counting the units in two or more numbers. 31. The numbers to be added are called parts, and the result is called the sum of the parts. 32. The sign of addition is +, which is called plus, meaning more. When stands between two numbers, it indicates that they are to be added. 33. The sign of equality is =, which is read equals, or is equal to. Thus, 7 + 4 = 11 is read: 7 plus 4 equals 11. It may also be read : 7 and 4 are 11. 34. An equation is an expression containing the sign of equality (=). 35. PRINCIPLES.-1. Only like numbers can be added. 2. The sum is the same in whatever order the parts may be added. Fundamental Combinations. 36. To perform addition one must know the sums of the following forty-five combinations : The sums of these combinations should be studied until they can be given instantly. They are embraced in the fol Each combination should be read forwards and backwards. Thus, 7 and 4 are 11, 4 and 7 are 11. EXERCISES (Drill). 37. 1. Add 2 to 29, to 59, 19, 89, 69, 49, 79, 39, 99. 2. Add 3 to 57, to 27, 67, 17, 87, 37, 77, 97, 47. 3. Add 4 to 68, to 88, 18, 58, 28, 78, 38, 48, 98. 4. Add 5 to 96, to 36, 76, 46, 66, 86, 16, 56, 26. 5. Add 6 to 27, to 57, 17, 87, 67, 47, 77, 37, 97. |