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If the numerator and denominator contain common factors, remove them in accordance with Principle 6 stated above.

This process is called cancellation.

EXAMPLE 3. Multiply by 4.

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If several fractions are to be multiplied together, the process is the

same.

EXAMPLE 4. Find the product of }, }, and š.

1 1 1

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Observe that as all the factors (except the l's) of the numerator are cancelled, the numerator of the answer is 1.

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ORAL DRILL In each of the following examples find the product of the numbers given : 1. 3, 7. , * 13. ,}

19., 25. § 2. Ķ, 8. , 14. ,}

20. , 言 26. , 3. ,} 15. 3, } 21. § }

27. , * 10. 4. }, } 16. , 1 / 22. 3 }

28. 11. , 5. 3, } 17. } 23.

29. 6. , 12.

23
18. 3,

30.
24. ,

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2 5 39 8

5 82

3

43

5 89

3 4)

5 89

Mixed Numbers. — To multiply

To multiply a fraction by a mixed number, or to multiply one mixed number by another, observe the following rule.

Rule. - (1) Express the mixed numbers as fractions, and (2) proceed as before.

EXAMPLE 1. Multiply by 31.

X 31 = {x}=i=116 EXAMPLE 2. Multiply 1ị by 45.

1

13 13
14 x 4 =

61.
3 2
1

Exercise In each of the following examples find the product of the numbers given:

1. 3}, 3 9. 51, 24 17. 53, 5 25. 2, 1, 4 2. 3}, 116 10. 54, 312 18. 25, 26 26. 41, 4, 36 3. 44, 215 11. 2,4 19. 6,33 27. 5, %, 1 4. 2, 3 12. 41, 2 20. 8, 44 28. 71, 2, 1} 5. 54,44 13. 5},5 21. , 3,5 29. 3, 21, 12 6. 13,211 14. 2}, í 22. 1, 4, 5 30. 24, 31, 6 7. 4}, 33 15. 31, 6 23. 1, 13, 9 31. 41, 53, 36 8. 43, 431 16. 43, 41 24. 21, 24, 2 32. 121,81,120

Division of Fractions

Rule. — To divide one fraction by another, invert the divisor and proceed as in multiplication. EXAMPLE 1. Divide i by 15.

1 5 2 8 2

15 Х

11 3 15

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5 3 16 8

Exercise In each of the following examples divide the first number by the second one: 1. 43, 14 9. 9}, 24

17.

25. 100, 8} 2. 53, 27 10. 83,46 18. 11, 16 26. 100, 16% 3. 63, 3} 11. 8}, } 19. 4, 5 27. 100, 62 4. 73, 43 12. 103, 24 20. 41, 6 28. 1000, 11 5. 43, 13 13. 12, 31 21. 14, 41 29. 1000, 121 6. 53,23 14. 12, 3} 22. 10, 3} 30. 1000, 371 7. 63, 3 15. 20, 22 23. 10, 3 31. 1000, 621 8. 8}, 31 16.,

24. 100, 61 32. 1000, 871

3 89 8

Review Exercise

1. What is ã of 25 ? 2. What is į of 17į? of 33ş? 3. Which is the greater, į or ? How much greater ? 4. What is įí of 49 ? 50 is of what number?

5. What fractions equal to have for numerators 6, 51, 33, 39, 48?

6. If of a mine is worth $ 27,000, what is the entire mine worth?

7. If 38 yards of cloth are required to make a garment, how many such garments can be made from a piece containing 56 yards?

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8. If a tractor-drawn reaper travels 33 miles per hour, how many more miles will it travel in a 12-hour day than a horsedrawn reaper

that
goes two miles

per

hour? 9. Simplify á - } + - 16 - . 10. A boy being asked to find the value of 84 +27 + 3} +43, gave as his answer 18. How great an error did he make?

11. Seven cars carried respectively 247, 18, 15, 28, 174, 323, 27 tons of coal. Required the number of tons carried.

12. Simplify 31 x 51 x 154 x 153.
13. Which is the greater, į or 1, and how much ?

14. A man owns a 64 interest in a ranch. If he sells { of his share, what fraction of the whole will he still have ? If the entire ranch is worth $ 300,000 what is the value of his holding ?

15. A farmer had 480 bushels of corn. He put g of it into one bin and the rest into another. He sold ở of what was in the first bin and s of what was in the other. The rest he kept. How much did he keep?

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16. If a motor-boat goes 65.017 miles per hour, what is the time required to travel one mile?

17. How many minutes will it take a pipe supplying water at the rate of 25 gallons per minute to fill a tank holding 70 gallons ?

18. Express 18 as a fraction whose denominator is 320.

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