19. At an election 12572 votes are taken, of which the successful candidate received 7391. How many votes did the other candidate receive? Ans. 5181 votes. 20. And what was the first one's majority? Ans. 2210 votes. 21. The coinage of the United States mint for 1843 was in value 11967830 dollars, and in 1846 it was 6633965 dollars. How much greater in value was the coinage in 1843 than in 1846? Ans. 5333865 dollars. 22. The total number of pieces coined in 1843 was 114640582, and in 1844 it was 9051834. How many more pieces were coined in 1843 than in 1844? Ans. 105588748 pieces. 23. In the year 1846, the value of the gold coin produced at the mint was 4034177 dollars; the value of the silver coin was 2558580 dollars; and the copper coin, was 41208 dollars. How much greater was the value of the gold than the silver, and how much greater the copper? Also, how much did the silver exceed the copper? Gold exceeded silver by 1475597 dollars. 24. In 1835, the number of post offices in the United States was 10770; extent of post roads 112774 miles; in 1845, the number of offices was 14183; and extent of roads 143940 miles. How many offices were added during these 10 years, and how many additional miles of road were added? 25. In 1840 the population of New York was 2428921, and in 1830 it was 1913006. What was the increase during this 10 years? Ans. 515915. QUESTIONS INVOLVING ADDITION AND SUBTRACTION. 1. A lets B have 60 bushels of wheat, worth 70 dollars, a fine horse worth 150 dollars, and 37 dollars' worth of butter. B in turn gives A his note for 110 dollars, and the rest in cash. What is the amount of cash? Ans. 147 dollars. 2. A borrows of B, at one time, 375 dollars; at a second time he borrows 95 dollars, and at a third time he borrows 413 dollars; he has paid him 319 dollars. How much does he still owe him? Ans. 564 dollars. 3. A person left a fortune of 10573 dollars to be divided between two sons and one daughter; the first son received 4309 dollars, the other son had 4987 dollars. How much did the daughter receive? Ans. 1277 dollars. 4. Two persons are 375 miles apart; they travel towards each other; at the end of one day, one has travelled 93 miles, and the other 57 miles. How far apart are they? Ans. 225 miles. 5. A farmer sold a span of horses for 150 dollars, a cow for 27 dollars, some cheese for 83 dollars, and 7 tons of hay for 56 dollars. He purchased 10 yards of broadcloth worth 45 dollars, a cook stove for 23 dollars, and a pleasure carriage for 80 dollars How much money will Ans. 168 dollars. he have left? 6. In the year 1840, the coinage of the United States mint was as follows: 1675302 dollars of gold, 1726703 dollars of silver, and 24627 dollars of copper. In the year 1841 the gold coin amounted to 1091597, the silver to 1132750, and the copper to 15973. How much was the whole value for each year? How much greater was the whole coinage in 1840 than in 1841? In each year, how mich greater was the value of the silver than that of the gold and copper respectively? 1840 1840 { 66 exceeded 1841 by silver exceeded gold by 51401. 1841 { silver exceeded gold by 41153. 66 66 copper" 1116777. 1186312. 66 copper" 1702076. MULTIPLICATION OF SIMPLE NUMBERS. 14. MULTIPLICATION teaches to repeat one of two num. bers as many times as there are units in the other. The number to be repeated is called the multiplicand. The number denoting how many times the multiplicand is to be repeated, is called the multiplier. Both multiplicand and multiplier are called factors.* The symbol for multiplication is x; this written be(ween two numbers, indicates that they are to be multiplied together. Thus, 3 x 7 denotes that 3 is to be repeated 7 times, or, which is the same thing, 7 is to be repeated 3 times From a Latin word, meaning to make; because, multiplied together they make the product. 4 By the assistance of this symbol, we niay form the The foregoing table should be committed to memory by the pupil. f * This table uses no factor consisting of more than one digit. I am aware that many tables of this kind are extended as far as 12 times 12, and others as far as 25 times 25, and even further; but I see no good reason why it should terminate at 12 times 12, any more than 13 times 13. I have therefore thought it better to limit it to 9 times 9, this being as far as it can extend by using but one digit as a factor. Still I have no objection to pupils committing to memory the products of as large factora as they may wish. 15. The pupil must also bear in mind that the multiplier and multiplicand may be interchanged without altering the product. Thus : 4x8=8x4=32 9x7=7x9=63 4×6=6×4=24 What does multiplication teach? The number to be repeated is called what? The number denoting how many times the multiplicand is to be repeated is called what? What are the multiplicand and multiplier sometimes called? The result obtained is called what? What is the symbol for multiplication? Can the multiplier and multiplicand exchange places without altering the product? When the multiplicand consists of more than one figure, and the multiplier has but one figure, we proceed as follows: Multiply 697 by 3. Place the multiplier under the multiplicand, units under units. First, multiply the 7 units by the 3 units; we obtain 21 units, or 2 tens and 1 unit. Write the 1 under the unit column, and the 2 under the tens' column. Next, mul OPERATION. Thousands. Tens. → Units. 9 7 multiplicand. 27 2 7 tens. 2 0 9 1 product. tiply the 9 tens by the 3, and we have 27 tens; equal to 2 hundred and 7 tens. Write the 7 tens under the tens' column, and the 2 under the hundreds' column. Finally, multiply the 6 hundreds by the 3 and we have 18 hundreds, which is the same as 1 thousand and 8 hundreds. Write down the 8 under the hundreds' column and carry the 1 to the thou sands' place; that is, write down the whole 18 |