1. Quick Mental Test (10 minutes) gross are how many dozen? 2. 9 cu. ft. are what part of a cubic yard? 3. A cake of ice 2' by 1' by 1' contains how many cubic feet? 4. How many square sheet 6 inches long and 4 inches of paper are there in a inches wide? 5. A piece of wire screen is 2 ft. wide. How long must it be to contain 15 sq. ft.? 6. A piece of carpet 25 ft. long contains how many yards? 7. 12 ounces are what part of a pound? 8. 3 pints are how many quarts? 9. When 3 lb. of sugar cost 20, what will 9 lb. cost? 10. Three fish weigh 10, 12, and 8 ounces. What is their average weight? Short Written Tests I. 1. Add 247% and 542 2. Subtract 293 from 6877 II. Find: 3. × 8 × 7 × 18 = ? 4. 37 16% = ? 1. The cost of 500 lb. of coal at $6.72 a ton. 2. The number whose factors are 35% and 221. 3. Tom's weekly wages when he earns $173 in 3 weeks. 4. The width of a 6-acre field that is 48 rods long. III. Find the answers and test them in · 3. 793429 +387 + 605 + 803 + 786 4. 83 ÷ 92 - minutes: SIXTH GRADE FIRST HALF DECIMALS NOTE. Classes beginning the 6th grade work will do well to review the last six pages of the 5th grade course. In the study of integers, we have learned that the value of a figure depends upon its place in a number, that each removal of a figure one place to the left increases its value tenfold, and that each removal of a figure one place to the right diminishes its value tenfold. We have used this principle thus far in dealing with integers only; but it holds true also for numbers smaller than one. Thus, Notice that we place the decimal point (.) at the right of units' place. This shows where the integer ends and the fraction begins. READING AND WRITING DECIMALS The places at the right of the decimal point are called decimal places and are named much like those at the left, thus: 1. Read .8; .49; .786; .4923. 2. Read 500; 50; 5; .5; .05; .005; .0005. 3. Read .25; .36; .39; .47; .365; .3; .7; .403; .07; .009. 4. How many cents make one dollar? What part of a dollar is one cent? 7 cents? 19 cents? 41 cents? 97 cents? How would 5. We write 25 cents, $.25, because it is 25 hundredths of a dollar. One dime is 1 tenth of a dollar. you write it? Write 5 dimes; 7 dimes. 6. 4321.648 is read 4321 and 648 thousandths. Notice that and is used between the integer and the fraction. Read: 6.42; 17.5; 4.23; 583.97; .640; 7.640; 439.018; 9341.215; 68.43; 70.9; 893.047; 903.03; 642.008; 95.249. Read: 3.4; .0034; .987; 2048.017; .00315; 200.02. Write in words on the blackboard: 35.08; 6.5; .084; .6082; 235.235; 64.105; 308.02; 56.081; 30.130. DECIMALS 2 X 2 = 4 3 × 3 × 3 = 27 2 X2 X2 = 8 10 x 10 = 100 Since 4, 8, 27, and 100 are obtained by multiplication, what are they called? How do the factors of 4 compare with each other? Of 8? Of 27? Of 100? The product of equal factors is a power. Name the powers given above. Name two other powers of 10. A fraction whose denominator is 10 or a power of 10 is a decimal fraction; e.g., 188, .25, .3421. 59 Only decimal fractions can be expressed by use of the decimal point as in the last exercise. When a decimal fraction is thus expressed, how may we tell what the denominator is? Name some decimal fractions not given here. A number that is composed of an integer and a decimal fraction is called a mixed decimal; e.g. 2.5; 130.35; 21.007. A fraction that is expressed by writing the numerator above and the denominator below a line is a common fraction; e.g. 3, §, 7, 18, fo. 2 5 Change to the decimal form: 8 Write, first as common fractions, or mixed numbers, then as decimals: 36. Four tenths. 37. Seventy-five hundredths. 38. One hundred twenty-five thousandths. 39. Sixteen, and forty-eight hundredths. 40. Twelve, and four tenths. 41. Six tenths. 42. Six hundredths. 43. Six thousandths. 44. How many decimal figures are required to express thousandths? Hundredths? Tenths? 45. Read the numerators only in examples 36 to 43. Write the following as decimals, and read the numerator and denominator of each: 46. Two hundred eighty-two thousandths. 47. Fifty-six hundredths. 48. Seven tenths. 49. Five hundred eight thousandths. 50. Six hundred thousandths. |