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 (f) In a problem the divisor is $146 and the quotient is 27. 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. of 37 = (a) Three fourths of 984 feet are how many feet? (b) Three fourths of 985 = (c) Three fourths 986 = feet. feet. 37 ft. are three 38 ft. are 3 of (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? 4. Harris paid $4 for chickens at of a dollar each. He 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 $1g a barrel. How many barrels did he buy? 5. Ellis sold 2 cords of wood at $4 a cord; he should receive for the wood 4 means, 2 times 4 (1) A man sold 12 dollars. (2 times and acres of land at $561 an acre. How much should he receive for the land? * Think of x as standing for the money his father gave him. Then he spent 1 half of x and 1 third of x, or 5 sixths of x, and had of x 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. $10.60 Value of .04 of an acre. (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. DENOMINATE NUMBERS. 1. From March 26th to April 2d, it is March 26th is Monday, April 2d is days. If days, or 2. From April 20th to May 5th, it is weeks and day. If April 20th is Friday, May 5th is 3. From April 20th to May 12th it is — days, or weeks and day. If April 20th is Friday, May 12th is (a) How many days from April 20th to June 9th ? (b) If April 20th is Friday, what day of the week is June 9th? (c) June 12th? 4. In a year in which there is a Feb. 29th, there are 5. In a year in which there is no Feb. 29th, there are days, or weeks and day. 6. If the first day of February of a common year is Monday, the first day of February of the next year is 7. If the first day of February of a leap-year is Monday, the first day of February of the next year is 8. If the tenth of February of a leap-year is Saturday, the tenth day of February of the next year is 9. If the 17th day of April of a leap-year is Wednesday, the 17th day of April of the next year is *Think as suggested in the following; April 10 to Apr. 30, 20 days; Apr. 30 to May 31, 31 days, May 31 to June 30, 30 days; June 30 to July 4, 4 days. 20 days +31 Sidewalk MEASUREMENTS. The following diagram of a house and lot is drawn on a scale of 24 feet to an inch. North side of Lot HOUSE (a) How many feet long is the lot, not including the walk? (b) How many feet wide is the lot? (c) How many feet from the sidewalk to the house? (d) How far from the house to the back of the lot? (e) How far from the house to the north side of the lot? (f) How many feet long is the house? (g) How many feet wide is the front of the house? (h) How many feet wide is the rear of the house? (i) How far from the south side of the lot to the house? (j) How wide is the sidewalk? (k) How much will the sidewalk cost at 124 per square foot? * (1) How much is the lot worth at $25 a foot front ? † * There are 306 square feet in the walk. In finding the cost the pupil may think that at 14 a foot it would cost $3.06, and at 12¢ a foot, 12 times $3.06; or he may think that if 1 foot costs 124, 306 feet would cost 306 times 124. The expression "foot front" stands for a strip 1 foot wide and as long as the lot is " deep." Back of Lot. |