mainder* of 2 rd.; 2rd. equal 33 ft. 33 ft. plus 12ft. equal 4

One fourth of 45 ft. equals 11 ft.with a remainder of 1 ft.; 1 12in.; 12 in. plus 8 in. equals 20 in. One fourth of 20 in. ec One fourth of 46 rd. 12 ft. 8 in. equals 11 rd. 11 ft. 5 in.

PROBLEM.

The perimeter of a square garden is 46 rd. 12 ft. 8 in. across one side of it?

139. MISCELLANEOUS.

Tell the meaning of each of the following, solve, expl state in the form of a problem the conditions that would gi each number process.

1. Multiply 64 rd. 14 ft. 6 in. by 8. 2. Divide 37 rd. 15 ft. 4 in. by 5. 3. Divide $675.36 by $48. 4. Divide $675.36 by 48. 5. Divide $675.36 by .48 6. Divide $675.36 by $4.8 7. Divide $675.36 by 4,8 8. Divide $675.36 by $.48 9. Multiply $356,54 by .36 10. Multiply $356.54 by 3.6 11. Multiply $356.54 by 36. 12. Multiply $275.56 by 2.25. 13. Multiply $275.56 by 24.

14. Can you multiply by a number of dollars? 15. Can you divide by a number of dollars?

* The word remainder in this connection suggests incomplete division the division is complete there can be no remainder.

4. Divide 3 ab3 + 6a2b2 + 9 ab by 3 ab.

5. Multiply the quotient of problem 4, by 3 ab. 6. Verify problems 4 and 5, by letting a = 3, ar

8. Multiply the quotient of problem 7, by xy. 9. Verify problems 7 and 8, by letting x = 2, an

10. Divide 5 a3y2 - 2 a2y3 + ay by ay.

11. Multiply the quotient of problem 10, by a3y. 12. Verify problems 10 and 11, by letting a = 1, a

13. Divide 3 b1x + b3 x2 - 3 b2x3 by bx.

14. Multiply the quotient of problem 13, by bx. 15. Verify problems 13 and 14, by letting b = x = = 4.

Observe that when the divisor is a positive numbe term of the quotient has the same sign as the term dividend from which it was derived.

of

1. A triangle has

2. A right triangle has one right angle; that is, one angle

degrees.

3. An isosceles triangle has two angles that are equal and two sides that are equal.

4. An equilateral triangle has equal sides and equal angles. 5. Find in the above figures all the angles that are right angles; all that are less than right angles; all that are greater than right angles.

6. Cut from paper a triangle similar to the one shown in Fig. 5. Then cut it into parts as shown by the dotted lines. Re-arrange the 3 angles of the triangle as shown in Fig. 6. Compare the sum of the 3 angles with 2 right angles as shown in Fig. 6. Convince yourself that the three angles of this triangle are together equal to two right angles.

7. Cut other triangles and make similar comparisons, until you are convinced that the sum of the angles of any triangle is equal to two right angles.

1. If in figure 1, the angle a is a right angle, angle b is equal to the angle c, the angle b is an angl many degrees?

2. If in figure 2, the angle d is an angle of 95° angle e is an angle of 40°, the angle ƒ is an angle many degrees?

3. If in figure 3, the angle x is an angle of 75°, ti w is an angle of how many degrees?

4. If in an oblong there are ab square feet, and the is a feet long, it is feet wide. ab ÷ a =

5. If in a rectangular solid there are abc cubic f the solid is a feet long and b feet wide, it is

thick. abc ab:

C =

=

6. Verify problems 4 and 5 by letting a = 3, b

= 2.

7. There is a field that contains 1736 square rods 28 rods long. How wide is the field?

8. There is a solid that contains 4320 cubic inches 24 inches long and 15 inches wide. How thick is the

9. How many square inches of surface in the so scribed in problem 8?

10. How many inches in the perimeter of the large of the solid described in problem 8?