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20;

5;

180

=

Therefore when the L. C.D. of several fractions cannot be easily found by inspection it may be found as follows: 1. Change , ze to their L. C. D.

MODEL. 9 = 3 X 3

36 2 X 2 X 3 X 3

5=1 x 5 2 x 2 x 3 x 3 x 5 = 180 = L. C. M. of the denominators, which is the L. C. D. to which the fractions may be reduced. 4 x 20 80

7 x 5 35 180 = 9 =

180 : 36
9 x 20 180

36 x 5
4 x 36 144
180 : 5 = 36;

5 x 36 180 Change to their L. C. D.: 2. d, s, 16 5. 1, 12, 35 8. , . 3. 3, 32, 6 6. 5, 15, 1 9. 27, 15, 12 4. , }, % 7. 11, 4, 21 11. When is a fraction said to be in its lowest terms? 12. How do you reduce a fraction to its lowest terms ? 13. Change 54 to an improper fraction. Give analysis.

14. In practice, how do we change a mixed number to an improper fraction?

15. How many 4ths of a yard in 98 yards? 16. Change i to 5 equivalent fractions.

17. Name several denominators to which 6ths and 8ths may be reduced.

ADDITION

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LESSON 42

Add:
1. Å and 12
2. } and }

3. $ and s
4. } and 1

5. } and 6. I and

7. j and 1 10. Á and I 13. and 8. } and } 11. and

14.5 and 1 9. & and 14 12. 1 and

15. } and 11 16. John spent of a dollar for a pair of gloves and 10 of a dollar for a collar. What part of a dollar did both cost him?

17. A boy rode of a mile and walked if of a mile. How far did he go ?

18. How much silk are 31 yards and 43 yards ?

MODEL. 3 yards + 4 yards = 7 yards. 1 yard + s yard = yards, or 1} yards. 7 yards + 14 yards = 81 yards.

19. How many gallons are 3] gallons and gallon ?
20. How many inches are 34 in. and 21 in. ?
21. Add by 11 from 1 to 151.

22. A farmer sold i dozen eggs to one man, j dozen to another, and ó dozen to another. How many dozen did he sell ?

23. How many pounds are 53 lb. and 45 lb. ?
24. What is the sum of $3, $4, and $12?
25. Add }, }, 1 ; 1; 1; 1; 1; 1; 1; }, 1, 1.

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2. Add }, }, and so 7. Add }, 11, and 33. 3. Add á, ig, and . 8. Add is, /, and 31 4. Add , , and is 9. Add 5, 1], and . 5. Add , 33, and 18 10. Add já, , and I. 6. Add 5, 33, and a.. 11. Add i 3, and it 12. Find the sum of 73, 86, and 1872.

MODEL. 7 + 8 + 18 33, sum of integers.

+* + 12 = 11 = 171, sum of fractions.

Entire sum = 3435. Find the sum of: 13. 43, 92, and 1827 17. 513, 615, and 9 14. 25., 318, and 223 18. 293, 463, and 2145 15. 184, 93, and 21 19. 1441, 26,3, and 43}} 16. 115, 214, and 15,5 20. 473, 435, and 1943

21. A man bought 3 loads of coal. The first load weighed 11 tons, the second 1} tons, and the third 11 tons. How many tons did he buy?

22. I bought a coat for $35, a vest for $93, shoes for $8, and a hat for $44. How much did I pay for all ?

48

SUBTRACTION

LESSON 44

What is the value of : 1. {-}?

6. 1 - ? 2. ģ- 1?

7. } - ? 3. 1-3?

8. - ģ? 4. {-1?

9. - ib? 5. } -17

10. - ?

11. 5 - 4 ? 12. - 3 ? 13. ģ-ia? 14. {-}? 15. - ? ?

8 9 7 10

16. If I spend } and } of my money, what part of my money remains ?

17. ß inch and how many 8th-inches make 31 inch ? 18. 7] inches and how many inches make 12 inches ? 19. From s take To.

MODEL. L. C. D. = 90

8 x 10 80
9 x 10

90
7 x 9 63
10 x 9 90
63

Ans.

90 90 90 20. 12- =?

3 =? 28. 18 - 1o =?

12 21. _- =? 25. 13 - 5 = ? 29.23 - =? 22. j1 - =? 26. 2. - 'o = ? 30.57 -4 =? 23. 11 – =? 27. 3. - 16 =? 31. 13 - 5 = ? 32. From 12 take a

MODEL. 12 11%; 11- 5 = 114 Ans. 33. 13 – 5 = ? 35. 22 - $ = ? 37. 39 – 11 = ? 34. 18 – 12 = ? 36. 28 – 13 = ? 38. 46 – } = ?

80

17

24. 11

LESSON 45

1. From 29 take 16%. 5. From 17% take 7. MODEL. 29 = 28%;

Model. 17} = 1675; = 45. 283 - 163 = 124 Ans.

163} - $5 = 163. Ans. 2. From 49 take 1841 6. From 29 8 take . 3. From 51 take 4915. 7. From 46-3 take

26 4. From 56 take 5415 8. From 5911 take $. 9. From 84 take 36. MODEL. 81 =778; 35 = 356.

788 -32 = 488 Ans.

13

10. 164 – 8,35 = ?

18. 72 – 65% = ? 11. 24 16 – 75 = ?

19. 1613 - 95 = ? 12. 9K1 - 3 = ?

20. 1311 - 154 = ? 13. 123-712 = ?

21. 919 – 276 = ? 14. 293 – 64 = ?

22. 953 – 45% = ? 15. 493 – 21% = ?

23. 58 - 43} = ? 16. 17 – 9 = ?

24. 425 – 28.5 = ? 17. 2816 - 19,4 = ? 25. 98% – 37% ?

26. From a bin containing 964 bushels of wheat 495 bushels were sold. How many bushels remained in the bin ?

27. From a piece of cambric containing 653 yards there were sold at one time 164 yards, and at another time 175 yards. How many yards remained ?

28. Charles can build a certain fence in 127 days ; William can build it in 13 days less. In what time can William build it?

29. Four loads of coal weighed, respectively, 13 tons, 11 tons, 116 tons, and 1,5 tons. What was the entire weight?

LESSON 46 1. 28 – 74 + 2 ? 10. 1945 – 730 - 5= ? 2. 135 - +3} = ? 11. 184 +92 – 8,0 = ? 3. 73 – 61 +242 : ? 12. 83 + 713 - 95 = ? 4. 12 – į + 164 = ? 13. Hi - 42 + 3 = ? 5. 133 - 45 + 5 = ? 14. ^ + 9} – 2} = ? 6.75 + 8- 43 =

?

15. 1% + 83 – *} = ? 7. 177 + 8.1 – 12% = ? 16. 8} – } + 16) = ? 8. 93 – 36 – 23 = ? 17. 164 + 711 - 5 = ? 9. 120 – 952 + x = ? 18. 9] + 32 – 616 = ?

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