MULTIPLICATION LESSON 13 Cross Multiplication "Cross Multiplication" is a method of multiplication in which it is unnecessary to write any partial products, as the final product is obtained at once. In multiplying numbers of two orders as 23 × 21, it 23 will be noticed that the units' figure of the product 21 is obtained by multiplying the units' figures of the 23 multiplier and of the multiplicand; thus, 3 × 1=3. 46 The tens' figure of the product is the sum of the 483 tens' figure of the multiplicand multiplied by the units' figure of the multiplier, plus the units' figure of the multiplicand multiplied by the tens' figure of the multiplier; thus, (2 × 1) +(3 × 2) = 8. The hundreds' figure of the product is obtained by multiplying the tens' figures of the multiplicand and of the multiplier; thus, 2 X 2 = 4. Now, if we had added 2 and 6 in tens' place without writing them, we would have had 483 for the answer just as before, but we would have written no partial products; thus: 483 3 X 1 = 3; write 3; 2 X 1 = 2; 3 X 2 = 6; 2 + 6 = 8; write 8; 2 X 2 = 4; write 4. Remember, we multiply in this order: First: Units X Units. 23 21 3 Second: (Units > Tens) plus (Tens × Units). Third: 4 × 3 = 12; 12 + 4 (carried) = 16; write 16. If there is a carrying figure from any product or sum, carry to the next place as usual. Exercise 27-Oral. 1. In the multiplication here shown, how is the 14 21 14 28 3. Tell us where the hundreds' figure of the 294 product comes from. 4. Begin the multiplication. No writing of partial products. 43 X21 5. Show where you get the tens' figure of the product. 6. Show where you get the hundreds' figure of the product. 7. What is done with the carrying figures in cross multiplication? Do not copy the following to multiply; write nothing 21. Find the cost of the following merchandise, without writing partial products: 45# Rice.... @14¢ per lb. . . .$?.?? 24 Cans Peaches. @ 17¢ per can.. 14# Cocoa.......@ 38¢ per lb.. (Practice this till you can do the last nine in 5 minutes or less.) 31. In plowing 45 A. of land by tractor, a farmer used 91 gal. gasoline at 31¢, 52 hr. labor at 55¢, and other items amounting to $3.18; what was the cost per acre? 32. A farmer bought a horse one morning for $75. and sold it the afternoon of the same day at a profit of 24%; what amount did he gain? 33. If a farmer sells eggs for 44¢ per dozen, what does he receive for 78 doz.? 34. A farmer sold 35% of 80 bbl. apples @ $4.25 per bbl., and the remainder @ $4.75 per bbl.; what did he receive in all? 35. If spraying a crop of grapes costs $4. per acre, and the sprayed crop yields $60. per acre more than an unsprayed crop would yield, what is gained by spraying the grapes on 18 acres? 36. A farmer had a herd of cows which produced an average of 40 gal. of milk per day; though he could have sold this milk at 7¢ per quart, the farmer thought it would be more profitable to convert it into butter which he sold at 50¢ per pound. If 1 qt. of milk makes 20 lb. of butter, what did the farmer gain by converting the 40 gal.? TIME AND WAGES LESSON 14 How Wages Are Figured Most tradesmen are paid by the hour (or fraction of an hour) for their labor, based on a certain sum, as $25.00, $30.00, etc., for a week's work consisting of a certain number of hours, as 42, 45, 48, etc.; thus, if a man is working on a 48-hr. basis at $25.00 per week, he receives of $25.00, or 5211⁄2¢ for every hour he works, and his wages for 46 hr. would be 48 of $25.00, or $23.96. EXAMPLE: 12 hr. @$24.00 per week on a 48-hr. basis 1; of $24.00 = $6.00, Ans. = EXAMPLE: 9 hr. @ $30.00 per week on a 48-hr. basis = = ? When the number of hours worked is an aliquot part of a week plus or minus a fraction of such aliquot part, find the amount corresponding to the aliquot part and add or subtract the amount corresponding to the fraction of the aliquot part. |