371. According to the census report of 1900, New York had a population of 7,268,894; Pennsylvania, 6,302,115; Illinois, 4,281,550; Ohio, 4,157,545; Missouri, 3,106,665; Texas, 3,048,710. states at that time? What was the total population of these 372. The population of the United States in 1800 was 5,308,483; in 1810, 7,239,881; in 1820, 9,633,822; in 1830, 12,866,020; in 1840, 17,069,453; in 1850, 23,191,876; in 1860, 31,443,321; in 1870, 38,558,371; in 1880, 50,155,783; in 1890, 62,622,250; in 1900, 76,303,387. What was the increase during each decade? What was the increase during the century? 373. What is the salary of the President of the United States for one day? 374. A house that costs $4000 rents for $50 a month. In how many years will the rent amount to the cost of the house? 375. A stockman bought 4182 head of cattle at $23 a head and sold them for $27 a head. How much did he gain? 376. From what number can 246 be subtracted 12 times and leave a remainder of 69? Five times and leave a remainder of 1? 377. An express train makes daily trips between two places 562 miles apart. How many miles does it run during the month of December? How many miles during the year? 378. A market gardener sets out 396 plants in each of 539 rows. How many rows would he have if 462 plants had been set in a row? How many rows if 99 plants had been set in a row? 383. What numbers will divide 12? What numbers will divide 18? Find a number that will divide both 12 and 18. Find another number that will divide both 12 and 18. NOTE. A number that will divide two or more numbers is called a common divisor. Why? 66 Find the largest number that will divide both 12 and 18. NOTE. Since this number is the greatest factor common to both numbers, it is called the greatest common divisor of 12 and 18. 384. What is the greatest common divisor of 16 and 24? SOLUTION 162 × 2 × 2 × 2 24= 2 × 2 × 2 × 3 The factors common to both numbers are underlined. Their product is the greatest common factor, or the greatest common divisor. Find the greatest common divisor (G. C. D.) of: 387. Find a multiple of 2; of 6; of 16; of 33; of 60. (See No. 70.) 388. Find a multiple of 5; of 8; of 15; of 26; of 50; of 400. 389. Find a number that can be divided by 5 and by 7. Find a number that can be divided by 7 and by 9. NOTE. A number that can be divided by two or more numbers is a common multiple of those numbers. 63 can be divided by 7 and by 9 and is, therefore, a common multiple of 7 and 9. 48 and 24 are each common multiples of 6 and 8. 24 is the smallest number that can be divided by both 6 and 8, and is called the least common multiple (L. C. M.) of 6 and 8. 390. Why is 24 called a common multiple? Why is it called the least common multiple? 391. What is the L. C. M. of 24 and 90? 24= 2 × 2 × 2x3 902 x 3 x 3 x 5 SUGGESTION What is the greatest number of times 2 is found as a factor of either number? What is the greatest number of times 3 is found as a factor of either number? 5? The product of these factors equals the L. C. M. 2 × 2 × 2 × 3 × 3 × 5360. 360 can be divided by 24 because it contains all the factors of 24. Why can 360 be divided by 90? Change each mixed number to the form of a fraction : 393. 3, 7, 10, 121, 3527. 394. 61, 99-16, 2501, 115, 777. Change to whole or mixed numbers: 395. 44, 12, 144, 1260, 785. 398. Write five mixed numbers and reduce them to fractional forms. 399. Write five fractional forms that can be reduced to whole numbers. 400. Write five fractional forms that can be changed to mixed numbers. 401. Write five fractions that can be reduced to lower terms. 402. Write a fraction whose numerator and denominator are both prime numbers. 403. Change 141 to 4ths; 23 to 56ths; 7 to 33ds. 404. Write a fraction whose denominator is 12 and whose value is 1. 405. Write a fraction whose denominator is 7 and whose value is 3. 406. Write a fraction whose denominator is 4 and whose value is 61. 1000 407. Reduce to lowest terms: 25, 18%, 66, 185, 1888 300 90' 150' 4500° NOTE. Divide both terms of the fraction by the same numbers. 408. Factor the terms of the above fractions and express in fractional form as here indicated, and reduce to lowest terms by casting out factors contained in both numerator 5x5x3x3 and denominator: 225 3 3 300 5 x 5 x 3 × 2 × 2 2 × 2 409. Solve in like manner 25 × 18 × 36 × 20 2 x 27 x 33 x 150 = 4 410. Express in the form of a fraction and reduce to lowest terms: (30 × 64 × 2) ÷ (8 × 18 × 144) 411. (25 × 60 × 12 x 7 x 8) ÷ (50 × 20 × 14 × 5×2×3) 412. Divide 4356 by 396, first dividing dividend and divisor by all common factors. 413. How many crates of berries, each containing 24 boxes, at 10 a box, must be given in exchange for four pieces of cloth, each containing 18 yards, at 20 a yard ? 414. Divide the product of 4, 15, 7, 8, and 24 by the product of 6, 4, 14, 8, and 10. |
