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157. Cash Accounts. In keeping a cash account it is customary to write each item of the receipts on the left side (called the debit side), and each item of the expenditures on the right side (called the credit side), thus :

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6|90|| 9

1915

1915 Mar. 4 Cash on hand || $125 | 50 || Mar. 5 Groceries $17 22||$ 6 P. F. Roberts 30

6 Meat bill 7 R. S. Ball

72 25

7 Balance 203 63|h 227 75

227 75 i Mar. 7 Balance

203 63

с

ů

e

Here on the left side a shows the balance on hand when this page of the account is begun; b and c are receipts from Messrs. Roberts and Ball ;

d is the sum of these three items on the day that the account is added, or balanced. On the right side s and g are bills paid. To find how much is now on hand we subtract the sum of $17.22 and $6.90, or $24.12, from $227.75, and we find that the remainder (in cash accounts called the balance) is $203.63, which is written on the right at h, and again on the left at e. To check the work, f, g, and h are added, and the sums at d and i must agree.

EXERCISE 92

Make out cash accounts and balance them as above :

1. Receipts: May 1, cash on hand, $36.50; May 2, R. S. Jacobs, $20; May 4, M. R. Randall, $32.60. Expenses: May 3, groceries, $7.86; meat, $3.50. Balanced on May 5.

2. Receipts: April 3, cash on hand, $25.30; April 4, J. B. Fuller, $30; April 7, R. H. Bates, $4.30. Expenses : April 4, groceries, $9.32. Balanced on April 8.

3. Receipts : Feb. 6, cash on hand, $135.60; Feb. 6, R. S. Roberts, $75.50; Feb. 7, M. L. Richards, $87.90; Feb. 8, R. P. Jasper, $42.25. Expenses : Feb. 6, rent, $75; Feb. 7, salaries, $60; Feb. 8, coal, $15.30; Feb. 8, account book, $2.25; Feb. 8, gas bill, $3.75. Balanced on Feb. 9.

Insert dates and items as in Exs. 1-3, and balance the following accounts:

4. Receipts : $125, $32.60, $28.90, $50; expenses : $35, $15.30, $28.40.

5. Receipts: $16.30, $15.50, $10.10, $3.50; expenses : $4.80, $3.45, $20, $4.75.

6. Receipts : $10.30, $5.25, $6.32, $7.20; expenses : $5.30, $2.40, $3.80, $1.50.

7. Receipts : $34.30, $15.30, $10.75, $6.32; expenses : $32.50, $8.20, $4.30, $3.

8. Receipts: $42.60, $18.50, $13.60, $2.80, $4; expenses : $15.40, $15, $32.75, $4.60.

9. Receipts: $75.50, $62.30, $4.72, $16, $25.30; expenses : $3.25, $80, $14.20, $15, $3.25.

10. Receipts: $62.30, $15.40, $14.75, $21.32, $5; expenses : $35.75, $10.42, $29.60, $28.40.

11. Receipts : $1250.50, $620, $300, $175, $16.25, $120.50, $32.75, $68.50; expenses : $600, $360, $166.67, $33.33, $240.

12. Receipts : $625.75, $130.50, $200, $75, $50, $15.20, $14.60,$33.80; expenses : $430, $250, $100, $32.75, $28.50.

13. Receipts : $128.50, $32.75, $68.75, $43.50, $28.90; expenses : $62.30, $28.50, $75.50, $38.40, $25.25, $20.30.

14. Receipts : $875.80, $260.50, $350, $400, $80, $25, $380, $125; expenses : $250, $375, $480.70, $200, $75.

15. Receipts: $1025.30, $535.40, $287.50, $126.75, $25, $324.80, $125.45, $135.42, $12.87; expenses : $10, $225, $430.75, $223.50, $121.60, $123.75, $2.35, $6.27, $4.68.

16. Receipts: $287.60, $821.75, $327.42, $196.80, $427, $236.90, $481.73, $87.96, $52.80; expenses : $327.50, $427.39, $179.86, $321.42, $83.96, $75, $1.24, $3.50.

EXERCISE 93

PROBLEMS WITHOUT NUMBERS

1. If you know the cost per dozen of certain articles, how do you find the cost of a given number of dozen ? of each article ?

2. How do you make the extensions in a bill ? foot the bill ? receipt the bill ?

3. If you know the items representing purchases, and those representing payments on an account, how do you balance the account?

4. If you know the amount of indebtedness on an account, and the balance, how will you find the sum of the payments ?

5. How do you keep a cash account? How do you balance it?

6. If you know the cost of each of several things, how do you

find the cost of all of them ? 7. If you know the sum of two numbers and one of them, how do you find the other ?

8. If you know the cost of one thing, how do you find the cost of several things of the same kind ?

9. If you know the cost of several things of the same kind, how do you find the cost of one ?

10. Name some things that are sold by the dry quart; by the peck; by the bushel.

11. Name some things that are weighed by the ounce; by the pound; by the ton.

12. If you know the cost of an ounce of anything, how do you find the cost per pound ?

13. If you know the cost of a pound of anything, how do you find the cost per ounce ?

CHAPTER IX

FACTORS, MEASURES, MULTIPLES

158. Factors. Integral numbers whose product is a given number are called factors of that number.

Thus, since 2 x 3 x 5 x 7 = 210, some of the factors of 210 are 2, 3, 5, and 7. We also see that 210 has other factors, like 6, 10, 14, and so on. Although every number has as factors itself and 1, we do not usually speak of these as factors.

159. Prime Number. A number that has no factors is called a prime number.

As stated in § 158, this means that the number itself and 1 are excluded. Thus 2, 3, 5, and 7 are prime numbers.

160. Prime Factor. A factor that is a prime number is called a prime factor.

Thus 2, 3, and 5 are the prime factors of 30. Although 6 is a factor of 30, it is not a prime factor.

161. Composite Number. A number that is not a prime number is called a composite number.

Thus 4, 15, 100, and 250 are composite numbers.

162. Exact Divisor. A number that divides another without a remainder is called an exact divisor of that number.

163. Exact Division. When we have an exact divisor, the case is said to be one of exact division.

Thus 15 is exactly divisible by 5. Usually we speak of an exact divisor simply as a divisor of a number. Then again we often speak of an exact divisor as a measure of a number, because with it we may exactly measure the number, just as with a yardstick we may measure the length of a carpet that is 10 yd. long.

164. Divisible Numbers. When we speak of one number as being divisible by another we mean exactly divisible, that is, divisible without a remainder.

165. Even Number. A number that is divisible by 2 is called an even number.

166. Odd Number. A number that is not divisible by 2 is called an odd number.

167. Divisibility by 2. A number is divisible by 2 if it ends in 0, 2, 4, 6, or 8.

Thus 36 must be divisible by 2 if 6 is; because 30, or any other number of tens, is divisible by 2, ten being 2 x 5.

Thus we may tell without dividing that 1,023,578 is divisible by 2.

168. Divisibility by 3. A number is divisible by 8 if the sum of the digits is divisible by 3.

We often use the word digits to mean the value of the symbols 0, 1, 2, and so on to 9, as well as the characters from 1 to 9.

Thus 54 is divisible by 3 since 5 + 4 is divisible by 3.

Likewise, 534 is divisible by 3 because 5 + 3 + 4, or 12, is divisible by 3.

169. Divisibility by 5. A number is divisible by 5 if it ends in 0 or 5.

For if a number ends in 0, it is tens, and 10 is divisible by 5. If it ends in 5, it is tens plus 5, and both are divisible by 5.

There is no easy test for divisibility by 7. 170. Finding Prime Factors. Find the prime factors of 420.

By $ 167, 2 is a factor of 420 and of 210; by $ 168, 3 is a factor of 105; by $ 169, 5 is a factor of 35, the other factor

2)420 being 7. Hence the prime factors of 420 are 2, 2, 3, 5, 7.

2) 210

3) 105 That is, divide as often as possible by the small

5)35 est prime factor, and then by the next larger, and

7 so on until a prime quotient is reached. The several divisors and the last quotient are the prime factors.

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