(d) How many 2's are in the prime factors of 100? in the factors of 8? (e) Show why sixteenths end in 1. (f) Which of these aliquot parts end in thirds? Factor these numbers and show why they must end in thirds. 6. What aliquot part of $1.00 is each of the following 7. What is a short way to multiply by 12? by 331? by 87? by 163? by 81? by 371⁄2? by 621? by 663? V. Test Problems Give an estimate of the following products, then multiply and compare results with the estimates. 7. If 1 yard of lace costs 12, what will 7 yards cost? 8. If pencils cost 50¢ a dozen, what will 3 dozen cost? 9. Flour sells for 7¢ a pound. How much will 7 pounds cost? 10. Dressed turkey sells for 351⁄2¢ a pound. How much will a 10-pound turkey sell for? Chicken is worth 28 a pound. How much is a 5-pound chicken worth? Which is less expensive, one turkey or two chickens? How much less expensive? 11. The price of milk is 6 for a pint, if milk tickets are bought. If a pint of milk is used each day, what would be the amount of the January milk bill? 12. Meat is 271⁄2¢ a pound. What will a 5-pound roast cost? 13. Canned tomatoes sell for 12¢ a can in the store. What is the cost of a dozen cans? If tomatoes put up at home cost 7¢ a can, how much is saved on a dozen cans? 14. A boy works 1 hours after school each day and 31 hours on Saturday at the rate of 163¢ an hour. How much does he earn each week? 15. A girl needs 13 yards of lace for a large doily and of a yard for a small one. What will the lace for one large and six small ones cost at 371⁄2¢ a yard? 16. A girl buys tulip bulbs at 4¢ each. How much will 3 dozen cost? G. RAPID CALCULATION IN DIVISION I. Division of Integers and Decimal Fractions 1. What is division? 2. What name is given to the number to be divided? 3. What name is given to the number by which the other is divided? 4. What name is given to the result of division? 5. In all calculations, it is necessary to keep your figures well spaced and in the right places, but it is especially necessary in division. 6. Divide 7568 by 16. 16 7568 Above which digit should the first figure of the quotient be placed? How do you find what this first figure is? How do you know that 5 is too large? 7. (a) Divide 75.68 by 1.6. (b) Write this problem as a fraction, 75.68 1.6 (c) Multiply both numerator and denominator by 10. What change is made in the position of the decimal points? 1.6 10 16. (d) Does multiplying by 18 change the quotient? Why? (e) To divide by a decimal, it is most convenient to change the decimal point in the divisor so as to make it a whole number. If the decimal point in the dividend is moved to the right the same number of places, the quotient is not changed. (f) Instead of erasing the decimal points, cancel them, and put others in the new positions. (g) Before dividing, place the decimal point in the quo tient directly over the new one in the dividend. 47.3 1/6. 75/6.8 64 11 6 11 2 48 48 8. Divide 75.68 by .016. How can you move the decimal point in the dividend the necessary three places to the right? 9. Divide 25,689 by 119. 21510 119 25689 238 188 119 699 595 104 The remainder from this division may be written over the divisor and added to the quotient. This is usually done when the remaining fraction can be changed to a simple one in halves, thirds, fourths, fifths, eighths, tenths, or even sixteenths. But such a fraction as 1 is not easily handled, therefore it is customary to carry the division out to one, two, or three decimal places and then drop the remainder. 215.87+ 119 25689.00 238 188 119 699 595 1040 952 880 833 2. (a) In the foregoing problems how does each divisor compare with the one before it? (b) How does each quotient compare with the pre ceding one? (d) Show why 120 120 x 2 = 240. = 3. How may any problem in division be changed to one in multiplication? 4. How many eighths of an inch are in 1 inch? in of an inch? in 14 inches? 5. How many dish towels of a yard long can be cut from a 12-yard bolt of crash? 6. A sheet of tablet paper is 7 inches wide. Into how many spaces of an inch wide can it be ruled? 7. One piece of summer dress goods sells for 87 a yard. Another sells for 62. If a girl buys a dress from the first piece, how many times more expensive is it than one from the second piece? 8. What part of 4 is 2? 9. (a) What part of 7 is 5? (b) What part of is? |