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LESSON CXVI. 1. If 2 barrels of flour cost 10 dollars, what will 5 bar
rels cost? 2. 10 is 2 fifths of what number? 3. If 4 yards of cloth cost 40 cents, what will 9 yards cost ? 4. 90 is 9 times 1 fourth of what number? 5. If 5 books cost 60 ceats, what will 12 books cost? 6. 60 is 5 twelfths of what number? 7. 144 is 12 times 1 fifth of what number? 8. If 6 lead-pencils cost 36 cents, what will 11 lead
pencils cost ? 9. 36 is 6 elevenths of what number? 10. 66 is 11 times 1 sixth of what number? 11. If 7 quarts of cherries are worth 56 cents, what are
10 quarts worth? 12. 56 is 7 tenths of what number? 13. 80 is 10 times 1 eighth of what number? 14. If 8 boxes of strawberries are worth 160 cents, what
are 12 boxes worth ? 15. 160 is 8 twelfths of what number? 16. 240 is 12 times 1 eighth of what number? 17. If 9 pears are worth 27 cents, what are 5 of them
worth? 18. 27 is 9 times 1 fifth of what number? 19. 15 is 5 ninths of what number? 20. If a turkey weighing 10 pounds cost 120 cents, what
will a turkey weighing 7 pounds cost ? 21. 120 is 10 times 1 seventh of what number? 22. 84 is 7 tenths of what number? 23. William says to Henry, who is 10 years old, your age
is 1 eighth of 4 times my age; how old is William? 24. 10 is 1 eighth of 4 times what number? 25. 80 is 8 times 1 fourth of what number? 26. A lady being asked her age, answered, that her
youngest daughter was 12 years old, which was 1 twelfth of 3 times her own age; what was the lady's
27. 144 is 12 times 1 fourth of what number?
ADDITION. ADDITION is the method of finding the total number of units contained in two or more numbers, and
expressing them in one number, called the amount, or sum.
Illustration. - A man has three bags of money. No. 1 contains 950 dollars ; No. 2 contains 875 dollars ; No. 3 contains 764 dollars. What is the total amount or sum of money in the three bags ?
We begin at the bottom of the column of units, and add all the figures
in that column, and find the sum of 950
them to be 9 units, which we write 875
under the column of units. We then 764
add all the figures in the column of Ans. 2,589 dolls.
tens, and find the sum of them to be 18
tens, or 1 hundred, and 8 tens; we write the 8 (tens) under the column of tens, and then add the 1 (hundred) with the figures in the column of hundreds, and find the sum of them to be 25 hundred, or 2 thousand, and 5 hundred; we write the 5 (hundred) under the column of hundreds, and the 2 (thousand) at the left of the 5 hundred ; and find the whole amount or sum of money in the three bags to be 2,589 dollars.
From the above illustration, we obtain the following
RULE. — Write the numbers, placing units under units, tens under tens, hundreds under hundreds, and draw a line under them.
Begin at the bottom of the column of units, and add all the figures in that column in succession: if the amount does not exceed nine, write it under the column ; if the amount exceeds nine, write the right-hand figure of it under the column, and add the left-hand figure,or figures, with the figures in the next column.
Add the figures in each succeeding column in the same manner, and write down the whole amount of the last column.
EXERCISES TO BE PERFORMED ON THE SLATE.
Two short parallel lines (=) indicate equality : thus, 1 dollar 100 cents; which is read, 1 dollar is equal to 100 cents.
This cross (+) indicates addition: thus, 5+7=12; which is read, 5 plus 7 equal 12, or 5 and 7 equal 12. 13. What is the sum of 5,665 + 6,545 + 7,546 +
8,564 ? 14. What is the sum of 23,456 + 34,567 + 45,678 +
56,789 ? 15. What is the sum of 40,405 + 50,604 + 60,708 +
70,910? 16. What is the sum of 75,704 + 85,406 + 95,115+
48,412? 17. What is the sum of 48,444 +57,555 + 66,333+ LESSON CXIX. 1. In a school 25 girls learn to write, 20 learn arith
metic, 18 learn grammar, 15 learn geography, and 12 learn history ; what number of girls are there in
the school ? 2. There is an orchard in which there are 75 apple-trees,
25 peach-trees, 15 pear-trees, and 12 plum-trees ;
what is the whole number of trees in the orchard ? 3. There is a school in which there are 4 classes; in the
first class there are 125 girls, in the second 120, in the third 124, and in the fourth 175. What is the
whole number of girls in the school ? 4. A gardener has in his nursery 525 apple-trees, 375
peach-trees, 275 cherry-trees, 250 plum-trees, 175 pear-trees, and 750 other trees of various kinds;
how many trees are there in the nursery ? 5. In a certain farm there are 124 acres under cultiva
tion, 75 acres for mowing, 140 acres of pasture, and 175 acres of wood-land; what number of acres
are there in the farm ? 6. A man purchased a farm for which he paid 5,750
dollars; he afterwards paid 375 dollars for clearing
dollars did the farm cost him? 7. A mechanic owns five houses. No. 1 is worth 7,525
dollars ; No. 2, 6,475 dollars ; No. 3, 5,845 dollars; No. 4, 5,425 dollars ; No. 5,5,300 dollars. What
number of dollars are the five houses worth? 8. A teacher wished to know how many questions had
been performed by the first class in arithmetic during the last 5 weeks, and on inquiry, he found that the class had performed 75 questions during the first week, 85 during the second week, 95 during the third, 105 during the fourth, and 125 during the fifth week. How many questions had they per
formed during the last five weeks ? 9. Three trains of cars started from Boston on the same
day; the first train carried 525 passengers, the second 675, and the third 750.
How many passengers were there in the three trains ?
SUBTRACTION. SUBTRACTION is the method of taking a less number from a greater, to find the remainder, or difference.
The less number is called the subtrahend, and the greater, the minuend.
The number found by taking a less number from a greater is called the remainder, or difference, and it shows how many the greater number exceeds the less.
Subtraction is performed, when each figure of the less number is smaller than the corresponding figure of the greater, by taking each figure of the less number from the corresponding figure of the greater, and writing the reremainder underneath ; the several remainders will express the whole difference.
Illustration. — A merchant purchased 765 yards of cloth, and has since sold 523 yards of it; what number of yards has he remaining unsold ?
We first write down the 765 No. of yards purchased. greater number; then we 523 No. of yards sold. write the less number under 242 No. of yards unsold.
the greater, placing units
under units, tens under tens, and hundreds under hundreds. We then take 3 units from 5 units, and 2 units remain, which we write directly under the units. Then 2 tens from 6 tens, and 4 tens remain, which we write under the tens. Lastly, 5 hundred from 7 hundred, and 2 hundred remain, which we write under the hundreds. The whole remainder or difference is 242.
When any figure of the less number is larger than the corresponding figure of the greater number, the following question and its illustration will show the method of performing the operation :
A man borrowed 94 dollars, and has paid 46 dollars ; how many dollars remain unpaid ?
We cannot take 6 units from Borrowed 94 dollars.
4 units; and as 10 units of any Paid 46 dollars.
lower order are equal to 1 unit