5. Give decimal form to the fractions in these : 11. 31.04 . 12. .000185 13. 3.00160 14. 4627 14 15. 189911 ADDITION. INDUCTIVE STEPS. 1. lo + to = what? what? .7 + .2 = what? .7 + .02 = what? .7 + .32= what? 2. If .7 +.02 = .72, and if .7 +.32 = 1.02, does the = addition of decimals differ from the addition of integers? Obviously, the addition of decimals and the addition of integers are governed by the same principles. EXERCISES. 1. What is the sum of 4.18, .005, and 5.6057 ? Process. 4.18 4.1800 .005 .0055 5.6057 5.6057 9.7912 Explanation. By writing the decimal points in a vertical column the digits of like orders fall in the same column, and we proceed as in addition of integers. To mark the place of tenths in the sum we put a decimal point therein under the column of points. RULE. Write the decimals so that the decimal points will fall in a vertical column; add as in addition of integers, and place a point in the sum under the column of points. 2. Find the value of: 1. 87.79 + 47.05 + 245.406. 125. 15 5 PROBLEMS. 1. A wagon cost $25.37, a horse $180.90, a set of harness $10.05, a mowing machine $85.37, a cow $28.08, and a pair of mules $225.75. What was the entire cost? 2. If I purchase a penknife for 871 cents, a quire of paper for 25 cents, a bottle of ink for 18 cents, and a box of pens for 624 cents, how much money will pay the bill? ? 3. Add ten thousand and one millionth, four hundredthousandths, ninety-six hundredths, forty-seven million sixty thousand and eight billionths. 4. Five pieces of silver weigh as follows: .33 pounds, 1.275 pounds, .5 pounds, 2.375, and 1.324 pounds. How much do the five pieces weigh ? 5. Find the sum of 2 decimal units of the 2d order, 21 of the 3d order, 41 of the 4th order, 3} of the 5th order, 51% of the 6th order, and 9 of the 7th order. SUBTRACTION. 1. What is the difference between 10 and y? Between .9 and .7? 2. What is the value of .94 .02? Of .94 ..06 ? Obviously, the subtraction of decimals and the subtraction of integers are governed by the same principles. EXERCISES. 1. From 86.71 take 27.004. Process. Explanation. 86.710 The numbers being written with the decimal points in a 27.004 vertical co the digits of like orders fall in the same column, and the subtraction proceeds as in the case of in59.706 tegers. The 7 tenths must be separated from the 9 units by the decimal point. RULE. Write the decimals so that the decimal points will fall in a vertical column; subtract as in subtraction of integers, and place a point in the difference under the column of points. 2. Subtract: (1.) 82.19 14.21 (2.) 274.684 217.423 (3.) 8468.3684 1764.8342 (4.) 8.4062 .6434 (5.) 4256.85 .00564 (6.) 3. Subtract 284.7654 from 321.07659. 4. Subtract 17.2398 from 27.06. 5. Subtract 29.9189 from 240.775. 6. Subtract 70.2574 from 365.71. 7. Subtract .006 from .00609. 8. Subtract 204.01 from 889.009. 9. Subtract 89.009 from 204.01. 10. Subtract 8.0999 from 1000. 11. Subtract 24.869 from 36. 12. Subtract 84 ten-millionths from 84 millionths. 13. Subtract 9 dollars 37 cents 5 mills from 27 dollars 8 cents. 14. Subtract 406.375 from 2370.001. — 100 PROBLEMS. 1. A man's income is $3000 a year; he spends $487.50. How much does he lay up? 2. I bought a farm for $2560; paid at one time $1046, and at another time $807.87. What remains unpaid ?. 3. A gentleman's income was $12,384.16, and his expenses the same year were $9864.18. How much of his income was left? 4. A man did .37 of a piece of work the first day and .33 of it the second day. „What part of the work was left for him to do the third day? 5. John walks 3.475 miles and James 3.8005 miles. Which walks the farther, and how much ? 6. Simplify: 1. 8.763 4.12 + 78.326 68.0816. 5 MULTIPLICATION. 1. B X Too = what? .3 x .07 = what? 2. How many decimal places in both factors ? 3. How many decimal places in their product ? PRINCIPLE. The product of decimal factors has as many decimal places as the factors. EXERCISES. Process. 1. Multiply 9.06 by .045. 9.06 Explanation. .045 4530 9.06 1667; 10X 1060 = 40770 since the factors have 2 + 3 or five decimal places, the 3624 166; .045 906 100 4 5 1000 Or, product must have five decimal places (Principle). .40770 RULE. Multiply without regarding the decimal point, but in the product point off from the right as many places for decimals as there are decimal places in the factors. NOTE.-Should the result of a multiplication not contain as many figures as the factors contain decimal places, we must supply the deficiency by prefixing ciphers, as in .02 X .003 = .00006. |