1. If all these ships were formed in a single unbroken line, how many feet long would the line be? 2. How many miles long would it be? 3. What is the average tonnage? 4. How many guns do they all carry? 5. How many men are there on all the ships? 6. How many knots greater is the average speed of the cruisers than of the battleships? 7. What is the average number of men on a ship? (See tables on page 171.) 8. A knot, or nautical mile, is used in measuring the speed of vessels. It is equal to about 1.15 common or statute miles. 9. The California's speed is how many common miles per hour? 10. The North Dakota's speed per hour is how many common miles greater than the Tennessee's? 11. How many common miles farther can the cruiser Washington sail in an hour than the battleship New York? 12. If the Pennsylvania is 9.9 knots ahead of the Delaware, and both ships are moving at their highest speed, in how many hours can the Delaware overtake the Pennsylvania? 13. How many common miles can the Utah go in 24 hours, if she goes 21.4 knots per hour all the time? 14. How many feet can the Arkansas go in 1 minute? Make other problems about these warships, using the numbers given in the table. FACTORS AND PRODUCT In the greater part of the computation work of arithmetic, the relation of factors and product appears. For example, when we know the cost of one article and the number of articles purchased, we find the cost of all by multiplication. That is to say, the number of articles and the cost of one are factors and the cost of all is their product. If the cost of all and the cost of one are given, the product and one factor are given, and the other factor is found by division. When the cost of all and the number of articles are known, the cost of one article may be found by division. In every case, then, involving the relation of product and factors, the only thing needful, in order to decide upon the process, is to determine which terms are given and which one is to be found; thus, 1. At 30¢ apiece, 10 arithmetics will cost 10 × 30¢ (factors), or $3.00 (product). 2. When 10 (factor) baseball suits cost $47.50 (product), one suit will cost $47.50 ÷ 10, or $4.75 (factor). 3. When of Paul's earnings are $1.50, how much does he earn? STATEMENT OF THE PROBLEM: of (Paul's earnings) are $1.50 SOLUTION: 1.50 (product) ÷ (given factor) = $2.50 (other factor). 4. .35 of the cost of a piano is $70. What does the piano cost? STATEMENT OF THE PROBLEM: .35 of (cost of piano) is $70 or, .35 X SOLUTION: 70.35 200. $200 Ans. ? = $70 5. When $1200 is of the value of a house, what is the house worth? STATEMENT OF THE PROBLEM: $1200 is of (value of house) or, $1200X (value of house) SOLUTION: 1200 (product) ÷ (one factor) = $3200 (other factor). COMPUTING IN HUNDREDTHS Decimals in hundredths are used very generally in business calculations. The merchant computes his gain or loss as a certain number of hundredths of the cost or selling price of the goods. Banks compute interest in hundredths. The relations of numbers are expressed generally in hundredths. Problems involving computation in hundredths usually present one of the two questions of relation between product and factors, namely: a. Two factors given, to find the product, or, b. The product and one factor given, to find the other factor; e.g. 1. .25 of $30 is how much money? The question may be stated, .25 × $30 =? .25 X $30 2. .35 of Frank's money is $7.00. = $7.50 How much has he? STATEMENT OF THE PROBLEM: .35 of (Frank's money) is $7.00 Observe that we use the X sign, which means "of," and we use the sign =, which means is. Observe also that 7.00 is a product and .35 one of its factors. How may the other factor be found? 3. Leona had $1.80 and spent $.36 for a box of paper. How many hundredths of her money did she spend? STATEMENT OF THE PROBLEM: (How many hundredths) of $1.80 is $.36, or, X $1.80 36. SOLUTION: .36 ÷ 1.80 = .20. Ans. ? Which number is a product? Which are factors? 4. Give the solution for each of the following: = a. STATEMENT OF THE PROBLEM: .85 of $5.00 is (cost of Fred's shoes). b. STATEMENT OF THE PROBLEM: .75 of (cost of John's skates) is $2.25. C. STATEMENT OF THE PROBLEM: How many times 2.16 is .54? In the following problems give the Statement of the Problem and the Solution as on page 174. Observe that the Statement can be found right in the problem as printed in the book. 1. 7 days are how many hundredths of the month of June? = STATEMENT OF THE PROBLEM: 7 days are (how many hundredths) of 30 da., or, 71 ? X 30. (The product may be at the left as well as at the right of the (=) sign.) 2. .90 of the pupils in a class were promoted. If 36 pupils were promoted, how many were there in the class? 3. It cost $24 to decorate a room. The labor cost $18. How many hundredths of the $24 were for labor? 4. A farmer's crop of apples amounted to 960 bushels; 864 bushels were fit for market. How many hundredths of the crop were fit for market? 5. A speculator sold some property for $78,000 and invested .33 of the money in grain. a. How much did he invest in grain? b. (How many hundredths) of his money were left? 7. 24 quarts are how many hundredths of six bushels? 8. A grocer bought 8 bushels of potatoes for $6 and sold them for $7.80. He gained how many hundredths of the cost? (First think how much he gained.) 9. .85 of (a certain number) is 595. What is the number? 10. A boy paid .24 of his money for books, .07 of his money for stationery, and .22 of his money for a football. If he then had $3.76 left, how much had he at first? (First find how many hundredths he spent, then how many hundredths he had left; then give the Statement of the Problem.) |
