Multiplication 27. Multiplication is the process of taking one number or amount, called the multiplicand, additively as many times as there are units in another number, called the multiplier. The result of multiplication is called the product. 28. The sign of multiplication (x) is read times when the multiplier is written before it, and multiplied by when the multiplier is written after it. Thus, 4 × 7 days is read 4 times 7 days, 7 days × 4 is read 7 days multiplied by 4. 29. The multiplier is always a number, and if the multiplicand is an amount, the product must be a similar amount. REMARK. It is evident from Sec. 29 that such expressions as "2 ft. x 3 ft. = 6 sq. ft.," "2 ft. x 5 sq. ft. = = 10 cu. ft.," and "15° x 2 hr. = 30°," cannot be justified and should not be employed. Exercise 12 Read the following; name the multiplicand, the multiplier, and give at sight the product : I. 7x6 pk. 7. 6x9 ft. 9. 10 x $12 2. 7 bu. x 8 4. 9 sq. ft. x 8 6. 10 × 7 da. 8. 12 doz. x 12 10. 8×8 qt. Special Multipliers 30. 1. Multiply 48 by 10. 10 x 8 units = 80 units, or 8 tens. 10 x 4 tens 40 tens, or 4 hundreds. The product is 4 hundreds + 8 tens, or 480. Annexing one cipher to a number multiplies it by 10. 2. Multiply 48 by 100. Annexing two ciphers to a number multiplies it by 100. 3. Multiply 48 by 1000. 1000 x 4810 × 100 × 48 = 10 × 4800 = 48000 Annexing three ciphers to a number multiplies it by 1000. In the form, what figure is omitted from the 2d partial product? In the form, what figures are omitted from the 3d partial product? Multiply across; add upward; check by seeing that the sum of the products above the line is equal to the product under it: 1. A printing press that prints 295 copies of a paper in a minute will print how many copies in 9 minutes? 295 the number of copies printed in 1 minute. 9 = 2655 the number of copies printed in 9 minutes. = 2. Find the cost of 375 tons of coal at $6 a ton. SUGGESTION. 375 x $6=6× $375. Exercise 15 I. At $175 an acre, what will a farm of 250 acres cost? 2. How much tuition is paid in a year by 900 students, if each pays $250 ? 3. How many pounds are there in 35 bales of cotton, each weighing 500 lb.? 4. What is the cost of 275 tons of coal at $5 a ton? 5. Light moves at the rate of 186,000 miles a second; how far will it move in 12 seconds? 6. A contractor built 24 houses and sold them for $3250 each; what did he receive for them? 7. If sound travels 1090 feet per second and you see the flash of a gun 6 seconds before you hear the sound, how far are you from the gun? 8. If one pipe discharges 40 gallons of water per hour, and another 86 gallons per hour; how much more will the second discharge than the first in 24 hours? 9. A man bought a farm of 80 acres at $58 an acre and built a house on it at a cost of $3250; he then sold the farm for $9000. What was the profit? 10. The following is a good ration for a cow: How many pounds of each of the food products given in the ration are required to keep 10 cows one week? |