DENOMINATE NUMBERS. (a) Copy, complete, and receipt the following Bill: 1. 500 sheets of paper are 1 ream and sheets. 8. When hay is $8 a ton, 5000 lb. cost dollars. (b) Load of straw, gross weight, 3380 lb.; tare, 1580 lb. Find the value at $5.50 a ton. (c) Multiply 40 sq. rods by 24 and divide the product by 160 square rods. Story. (d) Multiply 24 cubic feet by 8 and the product thus obtained by 6. Divide the last product by 128 cu. ft. Story. 2 in. MEASUREMENTS. 31 in. This diagram represents a piece of land." It is drawn on a scale of inch to the rod. 18 1. The land represented by the above diagram is rods long. It is rods wide. (a) Find the perimeter of the piece of land represented by the diagram. (b) Find its area in square rods. (c) Find its area in acres. (d) How much is the land worth at $40 an acre? 2. Draw carefully upon your slate or paper, on a scale of gin. to the rod, a diagram of a rectangular piece of land that is 30 rods by 36 rods. (e) Find the perimeter of the land represented by the diagram you have drawn. (f) Find its area in square rods. (g) Find its area in acres. (h) How much is the land worth at $60 an acre? (i) How much will it cost to build a fence around it at 50¢ a rod? (j) Find its area in square yards. In each such problem as (e), the number that follows the word of always becomes the denominator. 120 is 118 = }} = § of 140. 6. 63 is 7% (7 hundredths) of (f) 364 is 7% of what? (g) 635 is 5% of wha? 7. 72 is 9% (9 hundredths) of (h) 657 is 9% of what? (i) 584 is 8% of what? *Lead the pupil to observe that he has already learned to solve "Case 3" problems in percentage in two ways. Sometimes he has found what part one number is of another and has changed the fraction thus obtained to hundredths. See problems 11 to 17, page 57. Sometimes he has found one per cent of the base and has used this number as a divisor to obtain the required result. See page 58, problem (0); page 68, problems 3 to 5; page 78, problems 4 to 6. The "Case 3" problems on this page and the greater number of those that follow in Part I., can be most readily solved by the second method. 12 is what % of 200? One % of 200 is 2; therefore 12 is 6 per cent of 200; 13 is 61 per cent; 54 is 27 per cent, and 45 is 221 per cent. PERCENTAGE. 1. Three % of $620 = 2. Eighteen is 3% of = (a) Find 9% of $620. 3. Eighteen is -% of 600. (c) 138 is what % of 600? (d) Find 8% of $738. 5. Forty-eight is 8% of (e) $76 is 4% of what? 6. Thirty-six is % of 600. (f) 174 is what % of 600? (g) A farmer had 825 sheep; he sold 8% of them. How many sheep did he sell? (h) How many sheep did he have left? (i) A dealer bought some sheep and immediately sold 72 of them; these were 8% of all he purchased. How many sheep did he purchase? (j) How many sheep did he have left? (k) Mr. B had 400 sheep; he sold 48 of them. What % of his sheep did he sell? (1) A man had $485; he spent 7% of his money. How much money did he spend? (m) How much money did he have left? (n) Peter Gray paid $35.50 for a suit of clothes; this was 5% of all he earned in a year. How much did he earn in a year? (0) Judge Branson had $600 in the bank; he drew out $198. What % of his deposit did he draw out? 7. A lawyer collected $800; he retained as his commis dollars, sion $56 of this sum and paid the remainder, to the man for whom he collected the money; the lawyer's commission for collecting was %. (p) A lawyer collected $850; he retained as his commission for collecting $51 of this sum. What per cent did the lawyer charge for making the collection? |