SIMPLE NUMBERS. 1. A number that has no exact integral divisors except itself and 1, is called a prime number. 1, 2, 3, 5, 7, 11, , , , , , are prime numbers. 2. Integral numbers that are not prime are said to be composite. 4, 6, 8, 9. , , , , are composite numbers. 3. 24 is a number. 23 is a 29 is a number. 26 is a 28 is a number. 27 is a 31 is a number. 37 is a number. 4. If an integral number is expressed by two or more figures, and the right-hand figure is 5, the number is ■ •. 5. Every even number, except 2, is . 6. Some odd numbers are , and some are . 9 is . 11 is . 13 is . 21 is . (a) Write all the prime numbers from 1 to 53 inclusive, and find their sum. * This means, find how many times $52 are contained in $7436. $52 are contained in $7436,143 times. Story—A man paid #7436 for land at fSt an acre; there were 343 acres. t This means, find 1 fifty-second of $7436. 1 fifty-second of $7436 is $143. Story— A man paid f7iS8 for St acres of land; one acre cost fliS. COMMON FRACTIONS. Reduce to their lowest terms: i-«= i!= A= A= A= H = (a)A= (b)AV= (c)twt = Reduce to whole or mixed numbers: 2. Y= 4,o-= »/ = "V-= -V-= -4/= ¥ = (d)l|l= (e)m= (9*^ = Reduce to equivalent fractions having a common denominator: 3. i, $, J. (Change to .)* * = | = ^ = (g) *. |, !• (h) *, f 1- (i) I, h f • 4. Add %, \, and }. (Change to ——ths.) (j) Find the sum of 75f, 86|, and 47|. 5. From -| subtract ^. (Change to ths.) (k) Find the difference of 946f and 388|. 6. Divide 7 by f. This means . Story.^ (1) Find the quotient of 36 divided by -|. Story.% (m)24 gallons)!.26 gallons. This means, find howmany times 2\ gallons are contained in 126 gal. (Change 2J and 126 to fourths.) Story.% (n) 4)276£ gallons. This means, find 1 fourth of 2761 gal Ions. Story—In 4 days Mr. Smith sold DECIMAL FRACTIONS. 276J gallons of milk; this was at the rate of gallons per day. * The pupil is expected to find by trial that he can change halves, thirds, and eighths, to twenty-fourths. t See note (4) page 6, and problem 4, page 22. t Mr. Brown put 36 bushels of peaches into J-bushel baskets; there were baskets. § Put 126 gal. of milk into 2i-gal. cans. 1. One tenth of $2.45 is . .2 of $2.45 = (a) Multiply $2.45 by 2.3. This means, find 2 time-, $2.45 plus 3 tenths of $2.45. Operation. Explanation. $2.45 One tenth of $2.45 is . 2.3 Three tenths of $2.45 are . Two times $2.45 are . $.735+ $4.90 = $5,035. If 1 ton of coal is worth $2.45, 1 tenth of a ton of coal is worth . 3 tenths of a ton of coal are worth . 2 tons of coal are worth . 2.3 tons of coal are worth . (b) Multiply $3.65 by 2.4.* (.1 of $3.65 is $.365.) (c) Multiply $52.8 by 3.2. (.1 of $52.8 is $5.28.) 2. I bought 7| yards of print at %$ a yd. and gave the salesman half a dollar; I should receive in change . (d) I bought 5.3 tons of coal at $4.20 a ton and gave the salesman 3 10-dollar bills. How much change should I receive? (e) (f) (g) Add. Subtract. Multiply. 64f 78 3.75 28.37 24.42 2.6 * Write the decimal point in each partial product immediately after making the figure that represents the tenths in that product. t This means, find how many times 5 tenths are contained in W5 tenths. % This means, find 1 fifth of $1,7.5. DENOMINATE NUMBERS. 1. One ton is pounds. 2. One tenth of a ton is pounds. 3. Three tenths of a ton are pounds. 4. Nine tenths of a ton are pounds. 5. One hundredth of a ton is pounds. 6. Three hundredths of a ton are pounds. 7. Seven hundredths of a ton are pounds. 8. One thousandth of a ton is pounds. 9. Two thousandths of a ton are pounds. 10. Six thousandths of a ton are pounds. 11. 2400 lb. = 1 and tenths (1.2) tons. 12. 2800 lb. = 1 and tenths ( ) tons. 13. 3200 lb. = 1 and tenths ( ) tons. 14. 2460 lb. = 1 and tons. 15. 2468 lb. = 1 and tons. (a) Change 4870 lb. to tons. (b) 4980 lb. (c) Change 5260 lb. to tons. (d) 5750 lb. (e) Change 6480 lb. to tons. (f) 7260 lb. 16. 2 tons are lb. .3 of a ton are lb. 17. 2.3 tons are lb. 2.4 tons are lb. 18. .03 of a ton are lb. .04 of a ton are lb. 19. 2.04 tons are lb. 2.03 tons are lb. 20. 2.34 tons are lb. 3.23 tons are lb. (g) Change 3.52 tons to lb. (h) 4.37 tons, (i) Change 5.18 tons to lb. (j) 3.72 tons. (k) Change 1.48 tons to lb. (1) 2.324 tons, (m) At ^ a cent a pound, find the cost of 3.45 tons of scrap iron. MEASUREMENTS. A / An \ An right angle / acute angle \ obtuK angle 1. When two lines meet at a point, they are said to form an angle. 2. When a jackknife is half way open, the handle and blade form a right angle. If it is less than half way open, they form an angle. If it is more than half way open, but not fully open, they form an —— angle. 3. A square D has 4 right angles. 4. An oblong □ has right angles. 5. Rectangular means right-angled. 6. A rectangular figure, or rectangle, may be a square, or it may be an oblong. 7. A rectangle 6 inches by 6 inches is a . 8. A rectangle 4 in. by 6 in. is an . 9. A rectangular surface 4 feet by 6 feet is an ;its area is square feet and its perimeter is feet. 10. A rectangular surface 8 feet by 8 feet is a ;its area is square feet; its perimeter is ft. 11. Which has the greater area, a 5-in. square, or an oblong 4 in. by 6 in.? Compare their perimeters. Find the area and the perimeter of each of the following rectangular surfaces: (a) 23 feet by 6 feet. (b) 25 inches by 7 inches, (c) 15 yards by 8 yards. (d) 32 feet by 23 feet. (e) 30 inches by 20 inches. (f) 21 yards by 24 yards. |