1. Change to twelfths. SOLUTION. To change 4 to 12, it must be multiplied by 3. To preserve the same value of the fraction, the numerator must also be multiplied by 3. 7. To what common denominators can and be reduced? Dividing both terms by 2, and the result by 2 again, the resulting fraction is . These terms have no common divisor, and hence are the lowest terms of the fraction. Illustrate by a square or a line on the blackboard, divided into fourths and sixteenths. 71 1. Three-fifths and two-fifths and four-fifths are how many fifths? 17. Find the sum of 2 and 3. NOTE.- Add the integer and fractions separately, then add the two sums; or, reduce the fractions to improper fractions, and add as in proper fractions. What is the sum of 18. 2 and 33 19. 3 and 41 20. 5 and 3 21. 5 and 42 22. 7 and 18 23. 8 and 95 24. 10 and 5 25. 6 and 87 27. A triangular piece of land had sides 8 rods, 63 rods, and 74 rods in length. How many rods around the land? 28. A coat cost $22 dollars, a vest cost $81, and trousers cost $11. What did the whole suit cost? 29. A lady went shopping, and spent at one store $43, at a second store $5, and at a third store $24. How much did she spend at the three stores? 30. A traveler walked 23 miles one day, 15 miles another day, and 10 miles the third day. How many miles did he walk in the three days? 72 1. A man owned of a mill and sold ğ of it. the mill did he still own? What part of 2. A boy had a dollar and spent of it. How much did he then have? SOLUTION. In $1 there are . SOLUTION. The subtrahend fraction being larger, a unit is taken from the 4 and added to 10. 10 45 542=5410 313=313 4 5 21 18-31-31 24. +++= 73 6 dozen oranges at 163 cents a dozen? 13. 5 acres of land at $423 an acre? 14. 12 hats at $34 apiece? 15. 10 cords of wood at $34 a cord? 16. At 90 cents a pound, what will of a pound of tea cost? SOLUTION. of a pound will cost of 90 cents, or 30 cents. of a pound will cost 2 times 30 cents, or 60 cents. 3 1. Show by illustration that is the result of dividing by 3. 2. Divide 24 by 5. 10 SOLUTION. 24=15 3. What is the cost of 1 ton of coal, if 7 tons cost $311? 4. If 10 barrels of fruit cost $374, what is the cost of 1 barrel? 5. If 7 men can mow 113 acres in a day, how many acres can 1 man mow in a day? 6. A boy earned $93 in 12 days. How much did he earn in a day? 7. If a boy earns $33 dollars a day, how many days will be required to earn $10? 8. At $ a pound, how many pounds can be bought for $10? 9. What is the cost of a ton of hay, if ton cost $10? 10. How many coats can be made from 30 yards of cloth, if one coat requires 24 yards? 11. If 1 arithmetic costs $3, how many arithmetics can be bought for $? SOLUTION. As many as are contained times in ; or 4 arithmetics. 12. Divide by . SOLUTION. The divisor is of 1, or of 5. Dividing by 5 gives. But the divisor is of 5. Having divided by a divisor 6 times the true divisor, the quotient is only as large as it ought to be. Hence, multiply by 6 to obtain the true quotient. It is observed |