REVIEW. 1. From April 25th to May 5th it is days. (a) How many days from April 25th to August 5th? 2. From Feb. 20th of a leap-year to March 10th, it is days. (b) How many days from Feb. 20th of a leap-year to July 4th? (c) Divide 64 by . (d) Multiply 64 by 5. Compare the answers to problems (c) and (d). 3. = hundredths. == thousandths. (e) Change to hundredths. (f) Change to 1000ths. (g) Change to hundredths. (h) Change to 1000ths. Change the following decimal fractions to common fractions and reduce them to their lowest terms: 6. 250 brick @ $8. (o) 520 brick @ $6. 5. 5500 brick at $8 per M. (n) 7600 brick at $6 per M. (p) There is a 4-foot gravel walk around a rectangular grass plot that is 30 ft. by 40 ft. How many feet in the perimeter of the grass plot? (q) How many feet in the perimeter of the outside of the walk? (r) How many square feet in the grass plot? (s) How many square feet in the gravel walk? (t) If one ton of coal is worth $7.50, how much is 14 cwt. of coal worth? (u) If one hundredweight of corned beef is worth $4.50, 90 lb. of beef is worth how much? * Divide the numerator and the denominator of 37 by 124. MISCELLANEOUS PROBLEMS. 1. I am thinking of the surface of a box that is 6 in. long, 4 in. wide, and 3 in. high. The surface of the bottom square inches. The surface of one side is is square surface of the entire box-top, bottom, sides, and ends-is square inches. (a) Find the entire surface of a box that is 15 in. long, 12 inches wide, and 8 inches high. (b) Make a receipted bill of the following goods sold by yourself to your teacher: March 6, 150 lb. sugar @ 414; 7 lb. coffee @ 354; (c) A farmer sold 15 head of cattle weighing 19650 lb. at $5.40 cwt. How much did he receive for them? (d) What was the average weight per head? (e) If there is 1 half a ream in a package of paper, how many sheets in 6 such packages? (f) A merchant had $275 in the bank Monday morning. His deposits for the week were as follows: Monday, $86; Tuesday, $55; Wednesday, $72; Thursday, $64; Friday, $83; Saturday, $124. He drew from the bank during the week $354.24. How much remained on deposit? 2. I gave 3 doz. eggs, worth 154 a dozen, in part payment for 20 lb. sugar at 44 a pound. There remains unpaid cents. (g) I gave 2250 lb. hay at $10 per for 2 tons of coal @ $6.50 per ton. unpaid? ton in part payment. How much remains SIMPLE NUMBERS. 1. The sum of two numbers is 38; one of the numbers is 12; the other number is (a) The sum of two numbers is 12346; one of the numbers is 4734. What is the other number? 2. The difference of two numbers is 17; the less number is 45; the greater number is (b) The difference of two numbers is 547; the less number is 3476. What is the greater number? 3. The difference of two numbers is 14; the greater number is 45; the less number is (c) The difference of two numbers is 607; the greater number is 4045. What is the less number? 4. In a problem the multiplier is 6 and the product is $42; the multiplicand is ? multiplicand. 6 multiplier. $42 product. (d) In a problem the multiplier is fifteen and the product is nine hundred forty-five. What is the multiplicand? 5. In a problem the multiplicand is $25 and the product is $125; the multiplier is $25 multiplicand. ? multiplier. $125 product. (e) In a problem the multiplicand is two hundred thirtyfive dollars and the product is five thousand four hundred five dollars. What is the multiplier? 6. In a problem the divisor is $12 and the quo- $12)? tient is 8; the dividend is 27. 8 (f) In a problem the divisor is $146 and the quotient is What is the dividend? 7. In a problem the quotient is 12 and the $9) divisor is $9; the dividend is 12 COMMON FRACTIONS. 1. Three fourths of 36 feet are feet. 3 of 37 = (a) Three fourths of 984 feet are how many feet? (d) 576 ft. are three fourths of how many feet? (e) 577 is three fourths of what? (f) 578 is of what? 3. Paul spent of the money his father gave him for a book and of it for a knife, and had 12¢ left. Before he spent any money he had cents.* (g) A man spent of his month's wages for fuel and of it for groceries, and had $17.25 left. How much was his wages? (h) How much did he spend for fuel? (i) How much did he spend for groceries? He 4. Harris paid $4 for chickens at of a dollar each. bought chickens. 4 means, find how many times 2 fifths are contained in 4 (20 fifths). (j) A man paid $375 for wheat at $3 a bushel. How many bushels did he buy? (k) A man paid $368 for apples at $13 a barrel. How many barrels did he buy? 5. Ellis sold 2 cords of wood at $41 a cord; he should receive for the wood 41 means, 2 times 41 (1) A man sold 12 and dollars. (2 times and 1 half of 41.) acres of land at $561 an acre. How much should he receive for the land? *Think of a as standing for the money his father gave him. Then he spent 1 half of a and 1 third of x, or 5 sixths of x, and had of a remaining. DECIMAL FRACTIONS. 1. At $60 an acre, 3.2 acres of land are worth dollars. 3.2 times 60 means, 3 times 60, plus .2 of 60. (a) At $85 an acre, how much are 6.7 acres of land worth? (b) 6.2 acres at $75 an acre? 2. At $70 an acre, 3.02 acres of land are worth 3.02 times 70 means, 3 times 70, plus 2 hundredths of 70. (c) At $65 an acre, how much are 5.03 acres of land worth? (d) 8.06 acres at $95 an acre? 3. At $40 an acre, 2.24 acres of land are worth dollars. 2.24 times 40 means, 2 times 40, plus 2 tenths of 40, plus 4 hundredths of 40. (e) At $45 an acre, how much are 4.35 acres of land worth? (f) 7.26 acres at $64 an acre? Find the cost: (g) 5.34 acres @ $265. (h) 7.34 acres @ $465. $265 Price per acre. 5.34 Number of acres. (i) 6.23 acres @ $52.5. (j) 7.03 acres @ $325. (k) 3.27 acres @ $43.5. (1) 5.37 acres @ $54.6. (m) 1.56 acres @ $276. (n) 24.3 acres @ $342. (0) 32.6 acres @ $41.6. NOTE. While the pupil is multiplying by 4, a separatrix may stand between the 2 and 6 of the multiplicand; thus, $265. This will help him to remember that he is really multiplying $2.65, the value of 1 hundredth of an acre, by 4. When he is ready to multiply by 3, the separatrix should be erased and written thus: $265. This will help him to remember that he is really multiplying $26.5, the value of 1 tenth of an acre, by 3. After a time he can simply imagine the separatrix in its place. Require the pupil to write the decimal point in each partial product when, in the process of multiplication, he reaches the place where it belongs. The pupil may now be taught that when he has solved a problem in multiplication of decimals, if he has "pointed off" correctly, the decimal places in the product will be equal to those in the multiplicand and mutiplier counted together. |