A cord of wood is as much wood as is contained in a pile measuring 4 ft. x 4 ft. x 8 ft. A cord 128 cu. ft. in space. = The wood is piled as it comes, and the space not actually taken by wood counts just as much as the solid wood. A cord foot is 4 ft. x 4 ft. x 1 ft. 1. How many cord feet are there in a cord? 2. Will's father bought 20 cords of wood. If this was piled 4 ft. wide and 8 ft. high, how long would the pile be? 3. What part of a cord is 2 cord feet? 3 cord feet? 4. A pile of wood 4 ft. x 12 ft. x 12 ft. was offered to John Douglas at $5 a cord. He found the amount of the bill in this way: 4 x 12 x 12 = 4 x 3 x 4 x 3 x 4 = 4 x 4 x 4 x 3 x 3 = cord x 92 cords = 4 $5 × 41 = $201 = $20.50. = cd. Can you follow these steps? ADDITION In addition, the numbers to be added are called addends. Tell the addends, the subtrahends, the minuends, and differences; the multiplicands, the multipliers, and the products; the dividends, the divisors, and the quotients; the ratios and the fractions in the following questions: 1. A farmer bought 6 cows at $30 each from a trader, 4 cows at $32 each from a neighbor, and 2 cows at $75 each from a fancy stock farmer. He then had in all 15 COWS. How many cows had he to begin with? much did all the new cows cost him? How 2. In a regiment of 708 men there were 120 veterans, and the rest were raw recruits. The average age of the veterans was 38 yr., while that of the recruits was 15 yr. less. How many raw recruits were there? What was their average age? 3. A boy bought two saws, a hammer, a hatchet, a file, a plane, a try-square, two chisels, a vise, and a 2-foot rule. These cost respectively $1.50 and $1 for the saws; 75¢, 904, 20, $1.35, 40%, for the next tools; 40 and 30¢ for the chisels; $2 and 30 for the last articles. How many tools did he buy? At what total cost? At the same general prices, how much would 33 tools have cost? 4. One girl had 7 paper dolls, another 3 times as many, another as many as the second, and a fourth as many as the second and third together. How many paper dolls had they altogether? If they could have sold them at 2¢ each, how much would each of them have received for her dolls? How much would all have received for all the dolls? 1. Read the multiplication table of each number, beginning 2 × 1 = 2, 2 × 2 = 4, 2 × 3 = 6, and so through 2's; then 3 × 1 = 3, and so on through all numbers. 2. Read the division facts in this way, beginning 422, 6 ÷ 2 = 3, 8 ÷ 2 = 4, and so through the first column; then 632, 9÷ 3 = 3, 12 ÷ 3 = 4; and so on through all the numbers. 3. Read the columns down, 2, 4, 6, 8, and so on; 3, 6, 9, 12, and so on, telling in what multiplication table we find these numbers. 4. What numbers multiplied together give 144, 132, 121, 120, 110, 108, 100, 99, and so on through all these numbers? DIVISION If we divide one number by another, we find how many times the divisor is in the dividend. Let us divide 10 into 2's: ::::: = 5 2's. Dividing is separating into parts. When we divide 48 by 12, we find 4 parts of 12 units each. If we wished to separate 360 into parts of 10 each, how hard it would be to find the answer in this way: 360 – 10 = 350, 350 — 10 = 340, 340 — 10 – 330, etc.; and then to count all the 10's! Instead, we can write 10)360 36' 2. Divide six millions by three millions. Cancel the millions. = 2. 3. If New York City had in 1900 about 3 millions of people, and the whole United States had in 1800 7 millions, what was the ratio of population in all the United States then to New York one century later? Divide: 4. 64,000 by 8000. 5. 15,000,000 by 3,000,000. DIVISION Division finds how many times one number is contained in another. The number to be divided is called the dividend. The number we divide by is called the divisor. The result obtained by division is called the quotient. It shows how many times the divisor is contained in the dividend. When the dividend does not contain the divisor an exact number of times, the part of the dividend left undivided is called the remainder, which is always less than the divisor. The sign of division, ÷, shows that the number before it is to be divided by the number after it. Thus, 1052. Ten divided by five is two. Division is also indicated by writing the dividend above a line and the divisor below it; thus, 10 = 2. The sign) also is used to indicate division. Thus 5)10(2 shows that 10 divided by 5 equals 2. We sometimes show by this form, 8)64, that division is desired. Proof. Multiply the quotient by the divisor and add the remainder, if any. If the result equals the dividend, 216 dividend Divide 433 by (1) 5; (2) 7; (3) 19. By introducing the fraction we may secure exact division always. To do this we treat the remainder as a fraction of which the divisor is the denominator and the remainder the numerator. 8)65 8x8 (8 × 8) + (8 × }) = 64 + 1 = 65. 81 |