DIVISION. In Articles 101, 102, and 114 the division of decimals by integers has been taught. These the pupil may review. To divide an Integer or a Decimal by a Decimal. 293. ILLUSTRATIVE EXAMPLE I. Divide 72 by 1.2 WRITTEN WORK. 1.2) 72.0 60 Explanation. Before dividing by a fraction, the dividend must be expressed in the same denomination as the divisor. The divisor is a number of tenths; the dividend expressed in tenths is 72.0 (720 tenths). 720 tenths divided by 12 tenths gives the same quotient as 720 divided by 12, which is 60. Ans. 60. 294. ILLUSTRATIVE EXAMPLE II. Divide 1.935 by 0.45 WRITTEN WORK. 0.45) 1.93,5 (4.3 180 135 135 0 Explanation. Here the divisor is a number of hundredths; the dividend expressed as hundredths is 193.5 hundredths (the denomination may be indicated in the written work by a caret). 193.5 hundredths divided by 45 hundredths gives the same quotient as 193.5 divided by 45, which is 4.3. Ans. 4.3. 295. From the preceding examples may be derived the following Rule. 1. To divide by decimals: Express the dividend in the same denomination as the divisor by putting a mark as many places to the right of the decimal point as there are decimal places in the divisor. 2. Divide as if the divisor were an integer, making a decimal point in the quotient, when the terms of the dividend have been used as far as the mark. NOTE. When there is a remainder after all the terms of the dividend have been used, the division may be continued, as in Articles 102 and 106. 296. Examples for the Slate. 107. How many books at $0.08 each can be bought for $3.84? 108. At $2.80 per yard, how many yards of muslin can be bought for $55.30 ? 109. How many rods, each 16.5 feet, are there in 99 feet? 110. One quart dry measure equals 67.2 cubic inches; one quart liquid measure equals 57.75 cubic inches: in a keg whose capacity is 5040 cubic inches, how many quarts dry measure? How many quarts liquid measure? 111. If coal is $6.67 per tón, how much coal can be bought for $3.335? 112. At $0.125 per yard for cotton cloth, how many yards. can be bought for $25? 137. Multiply 0.648 by 100; divide the product by ; divide this quotient by 0.001; and multiply the result by of 0.0362. 138. Find the sum of the following: 756.02; 18.3 × 100; 0.70.001; 8.1613; and 0.24 ÷ 16. For other examples in division of decimals, see page 135. 2. 25.75 3. Two hundred six ten-thousandths. 0.3504 Seven hundred, and eight tenths. 1.648 0.657 21. 1002. 4271, and 4271 ten-millionths. 22. 1.87 68 thousand, and 4 tenths. 0.6805 4.071 298. Exercises upon the Table. 177. Read the numbers expressed in E. 178. Read the numbers expressed in G. H 179. Write in figures the numbers expressed in F. 180. Change E to equiv. common fractions in lowest terms. 183. Add E and F. 184. Add F and G. 185. Add E F and G. 186. Find the difference of E and F. 195. Multiply E by 10; divide F by 100; add the results to G. 299. Questions for Review. What are DECIMAL FRACTIONS? How are their written expressions distinguished from those of integral numbers? What indicates the denomination of the decimal? How do you read a decimal expression? Read 7.05 as a mixed number; as a fraction. Read 0.504 and 500.004 so that they may be distinguished. How do you write decimals? What is the effect of annexing ciphers to a decimal expression? How do you change decimals to common fractions? Common fractions to decimals? What fractions cannot be changed wholly to a decimal form? What are they called when expressed decimally? How do you change a circulate to a common fraction? How do you add and subtract decimals? Perform an example in multiplication by a decimal, explain and give the rule. Perform an example in division by a decimal, explain and give the rule. How do you express the multiplication of a decimal by 10; 100; 1000; 0.1; 0.01; 0.001? How do you express the division of a decimal by 10; 100; 1000; 0.1; 0.01; 0.001? SECTION XI. WEIGHTS AND MEASURES. MEASURES OF LENGTH. 300. We measure the length of anything by applying to it a line of known length, as 1 foot, 1 yard, and finding how many such lengths it contains. The line of known length so used is a linear unit. 301. The length of a line is reckoned in linear units. 302. In measuring length we employ the mile (m.), rod (rd.), yard (yd.), foot (ft.), and inch (in.). These are NOTE I. The standard unit of length is the YARD. From this the other units of length are derived. NOTE II. For surveyors' and mariners' measures, see Appendix, page 306. 303. Oral Exercises. a. How many inches are there in 1 yard? in 2 yards? in half a yard? in a quarter? in an eighth? in a sixteenth ? b. What will it cost to grade a mile of road at $1 a rod? c. What is the length in feet of a hall that is 15 yards 2 feet long? d. How many feet in the length of a fence 5 rods long? e. One eighth of a mile is sometimes called a furlong. How many rods in a furlong? |