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 x 1 = 3, and so on through all numbers. 2. Read the division facts in this way, beginning 422, 623, 8÷ 2 = 4, and so through the first column; then 6 ÷ 3 = 2, 933, 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? A cord of wood is as much wood as is contained in a pile measuring 4 ft. x 4 ft. x 8 ft. 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: cd. 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 9cords = 4 $5 × 41 = $201 = $20.50. Can you follow these steps? 1. How many quires are there in 5 reams? 8? 20? 2. Mrs. Thompson paid 48¢ for 2 quires of paper. How much per sheet was this? 3. Mary asked for 5 quires of paper, but received only 5 score of sheets. What was the difference? LENGTHS Not all things to be measured are in straight lines. A clock spring 18 inches long would be coiled up like this. Coil up 3 yards of thread or string, and see how it looks. B C SAVING CORNERS If we If we wish to cross a street and to save time and distance, we cut corners. wish to go to C from A, we may go from A to B and from B to C. Make drawings of triangles and measure A to C. 4. If it is 2 in. from A to B and 3 in. from B to C, how long is the space from A to C? What is saved? = 5. A to B 3 in. and B to C 2. 2+3 5. Measure the distance A to C. 5 A to C = ? DECIMALS We found that we could write five dollars and twentyeight cents $5.28. We called the period or point between 5 and 2 the decimal point. Decimal means ten or tenth. In our notation we used these orders. We e can extend decimals to the fractions, tenth co Tens 6 3 and hundredth, by the use Hundreds 39.4 is read thirty-nine four tenths. 39.4 = 396. 39.42 is read thirty-nine forty-two hundredths. The whole number may be written 639-46. 100 1. Write in decimals 75684; $15.5%; 56% yd. 100 2. Read 15.3%; 2.7 hr.; 9.3 mo. 100 3. I bought 7.4 oz. of a very expensive kind of tea especially imported from China. I paid 10¢ an ounce. What was the cost? Multiplying decimals by tens or hundreds is very easy. 7.4¢ × 10 = [7 × 10] and [+ × 10] = 70 ¢ + 4 ¢ = 74¢. We can multiply a decimal by ten simply by moving the decimal point one place to the right, as you see. 4. If I had paid 20 ¢, what would have been the cost? 20 10 x 2. = 7.4 x 10 = 74¢. 74 x 2 = 148. Do you see that we can change cents to dollars by moving the decimal point 2 places to the left? 100 = $1. 148100 $1.48. = BILLS When we buy things at stores we often get bills. This is a bill of goods, sold to Mr. Thomas Davenport: 1. What is the ratio of $1 to 10? of 25¢ to $2? 2. What is the ratio of 1 ft. to 2 yd.? of 3 yd. to 2 ft.? of 2 ft. to 4 yd.? 3. What is the ratio of 1 gill to 1 gal.? of 2 gal. to 3 pt.? of 3 pt. to 1 gal.? 4. What fraction of 1 hr. is 2 min.? 5 min. ? 5. How many times larger is a bushel than a quart? 6. What is the ratio of a ton to five hundred pounds? 7. The ratio of the distance I ran to the number of feet in a mile was 4. How far did I run? Answer in feet and in miles. 8. What is the ratio of 10 quires to a ream? to 5 quires? Of a ream to 60 quires? Of a ream |