33. Relation Between English and Metric Units.-Note carefully the above comparisons, as well as the following numerical relations: In solving the following exercises make use of these equivalents. State your estimates, as far as possible, without use of pencil and paper, as whole numbers or halves, but no smaller fractions. EXERCISES 1. In buying 10 lb. sugar you would ask for how many Kilograms? 2. How many meters would you ask for in buying 10 yd.? 6 yd.? 15 yd.? 100 yd. ? 3. How many metric tons would you buy if buying 4 T.? 12 T.? 20 T.? 15 T.? 4. In buying flour how many Kilograms would you ask for in order to get about 10 lb.? 24 lb.? 48 lb. ? 96 lb. ? 5. Gene had a letter from his brother Wendell in France saying that his brother had been on a march of 60 Km. About how many miles was this? 6. The Eiffel Tower is 300 m. high. About how many yards high is it? About how many feet high is it? The children of a class in a certain junior high school are sending semiyearly $ 18.25 to little Berthe, one of the fatherless children in France. 7. The value of each franc is 20 cents. How many francs will these children send Berthe each year? 8. There are 73 pupils in this class. How much does each contribute yearly to this fund? 9. They sent her $ 5.00 as a Christmas gift. francs was this? How many 10. There are 100 centimes in a franc. Berthe bought 3 m. of cloth for a dress with part of this money. She paid 2 francs 40 centimes per meter for the cloth. How much did she pay for the cloth? How much was this in United States money? The class received a letter from Berthe in which she said that she was 11 yr. old, weighed 28.6 Kg., and was 1.25 m. tall. 11. About what was Berthe's weight in pounds? 12. 13. About what was her height in feet and inches? Berthe also wrote that she lived 375 Km. from Bordeaux and 220 Km. from Paris. About how many miles does she live from Bordeaux? from Paris? 14. The average weight of the pupils of this class was 64 lb. How many Kilograms would they call this in writing to little Berthe? 15. Their average height was nearly 4 ft. What would this be in metric units? Hold a number contest, using metric measures. II LITERAL NUMBERS 34. Mathematical Shorthand.-Statements can be written very simply and so that they can be used in computations by the use of a mathematical shorthand. Letters and symbols are used in the place of words. For instance, the circumference of a circle equals two times π, radius, is written C = 2X TX R. EXERCISES Give the following in mathematical shorthand: 3. Minuend minus difference equals subtrahend. times its 4. Minuend minus subtrahend minus difference equals zero. 5. Dividend equals divisor times quotient plus remainder. Use D and d. 6. Dividend minus the remainder equals the divisor times the quotient. 7. Total sales equal purchase price plus profits, or purchase price less losses. 8. Money on hand at the beginning of the day's business plus sales equals money on hand at the end of the day's business plus expenditures. 9. The circumference of a circle divided by its diameter equals π. 35. Numerical and Literal Expressions.-A statement in only numerals and symbols is called a numerical expression, as 5 X 4+7. A statement also containing letters is called a literal expression, as 3 Xa+6xb+ 9. 36. Formulas.-Mathematical rules and laws can be stated very simply by literal expressions. Such literal statements are called formulas. The curved surface of a cone equals π times the radius of its base times its slant height. Or, 10. The number of bushels of oats a bin will hold equals length times width times height, all in feet, divided by 1.25. Express this by a formula. 11. To find how many tons of hard coal a rectangular bin will hold, multiply the length, width, and height together in feet and divide by 28. Express by a formula. 12. The price of any number of articles equals the price of one times the number of articles. Use P and p for the two prices and express this as a formula. 37. Evaluating Literal Expressions.-Literal expressions are evaluated by replacing the letters by their numerical values. Thus, to find the number of gallons held by a rectangular tank 9 ft. by 4 ft. by 1.5 ft., replace the corresponding letters in formula (2) on page 29. Hence, EXERCISES Find the value of each of the following literal expressions 29 13. Rewrite the formula for Ex. 8, page 28. Were there any errors in a store where for one day cash on hand in the morning was $56.17 and at night $124.12, sales $97.48, expenditures $29.53 ? cash on hand in the morning $ 35.67 and at night $ 65.68, sales $ 49.28, expenditures $ 18.27? 14. Express as a formula that the sum of two numbers less the smaller number equals the larger number. Find the larger number if the sum is 314 and the smaller number is 98; if the sum is 103 and the smaller number is 47. |