1. Find the product of $34.50 and 53.4. OPERATION $34.50 53.4 13.800 103.50 1725.0 $1842.300 EXPLANATION To multiply by 53.4, means to take 53 times the multiplicand plus 4 tenths of the multiplicand. One tenth of $34.50 is $3.45. Four tenths of $34.50 is $13.80. Three times $34.50 is $103.50. The sum of these three partial products is $1842.30. Practical application of the foregoing. If one acre of land costs $34.50, how much will 53.4 acres cost? One tenth of an acre costs $3.45. Four tenths of an acre cost $13.80. Three acres cost $103.50. Fifty acres cost $1725. 53.4 acres cost $1842.30. a. Complete the following bill, and find the amount To the Teacher. This page is for drill. If pupils have not had such problems in the grades below, the page may be omitted until the book is reviewed. Whenever the work is done, require pupils to give an approximate answer to each problem on the page before attempting its solution with the aid of a pencil. Find the cost of: a. 26420 lb. hard coal at $7.75 per ton. d. 8250 ft. lumber at $24.50 per thousand. i. 7250 lb. beef at $8.75 per cwt. Find the cost of: m. 175 bu. corn at 34.5 cents a bushel. 56 bu. potatoes at 46 cents a bushel. r. 24 hogs (4360 lb.) at $5.75 per cwt. 8. 15 cattle (13640 lb.) at $4.35 per cwt. The usual method of testing the work in multiplication is to divide the product by the multiplier; the quotient should be like the multiplicand. CASTING OUT THE 9's This proof is based on the fact that if the excess of 9's in the multiplicand is multiplied by the excess of 9's in the multiplier, the excess of 9's in this new product equals the excess of 9's in the original product. Solve the following multiplication problems, and prove by casting out the 9's. a. Multiply 2275.23 by 12 b. Multiply 8427 by 125 e. Multiply .2036 by 51 f. Find the sum of the five products, a to e, and prove by casting out the 9's. *Observe that this method of proof is no check on the use of the decimal point; neither would an error made by a transposition of figures be detected. The careful accountant often tests his work by solving a second time in another way. Some of these tests are given below. a. Multiply 5286 by 9, and prove by subtracting 5286 from 10 times 5286. 6. Multiply 8437 by 15, and prove by taking 10 times 8437 and adding to the product half of 10 times 8437. c. Multiply 5836 by 16, and prove by finding the sum of 10 times 5836 and 5 times 5836 (half of 10 times 5836) and 5836. d. Multiply 4378 by 25, and prove by taking 1 fourth of a hundred times 4378. e. Multiply 2750 by 75, and prove by taking 3 fourths of a hundred times 2750. f. Multiply 5462 by 19, and prove by subtracting 5462 from 20 times 5462. g. Multiply 7140 by 48, and prove by subtracting twice 7140 from 50 times 7140. h. Multiply 6175 by 35, and prove by finding the sum of 10 times 6175 and 10 times 6175 and 10 times 6175 and 1 half of 10 times 6175. i. Multiply 4352 by 12, and prove by adding 10 times 4352 and once 4352 and once 4352. j. Multiply 3246 by 99, and prove by subtracting 3246 from 100 times 3246. . Multiply 6372 by 21, and prove by adding 6372 to 1 fifth of 100 times 6372. 7. Multiply 1357 by 24, and prove by subtracting 1357 from 1 fourth of 100 times 1357. DIVISION NOTE. For definitions of terms see page 342. 1. Tell which is the dividend, which the divisor, and which the quotient in each of the above examples. Observe that in written problems in division the divisor is usually written to the left of the dividend. The quotient in short division is written under the dividend; in long division (see next page) it may be written either over, or to the right of, the dividend. The dividend may always be thought of as concrete; that is, as standing for a number of things. If the divisor is concrete, it must be like the dividend, and the quotient will show how many times the divisor is Contained in the dividend. If the divisor is abstract, the quotient will be like the dividend will be a part of the dividend. There are 64 primary facts of division. These are the converse of the 64 facts of multiplication given on pages 341, 342. The primary facts of division should be learned while learning the 64 multiplication facts. These facts should be observed in their double aspect. The pupil must know that since 3 times 5 are 15, 5 is contained in 15 three times, and 1 third of 15 is 5. |