119. Complex Fractions.-Either or both terms of a fraction may themselves be fractions, or operations with fractions and whole numbers. These fractions are called

Since a fraction is an indicated division, a complex fraction may be simplified by merely treating it as the numerator divided by the denominator. Thus,

14. The unit of electrical resistance is called the ohm.

If r1 is 6 ohms and r2 is 8 ohms, what is R?

15. If A and B had been connected with three wires whose resistances were r1, r2, and rз each, then,

16. Find R when r1 is 2, r2 is 3, and r, is 4. 17. The velocity with which water will flow from an opening at the base of a stand-pipe is given by the formula to the right. Change the fraction from the compound to a simple fraction.

18. Explain the interest equation, I =

V2

=

ᏢᎡᎢ

From

100

Change this to a simple fraction.

19. What principal will give $ 60 in 2 yr. at 5 % interest?

120. Picture Graphs.-The above pictures give an easy comparison of the amount of corn raised in each of several states during the year 1916. Any drawing used to show comparisons in this manner is called a graph. Graphs like the above are called picture graphs. Why? Be on the lookout for graphs in books, magazines, and newspapers while studying this chapter.

Read the above numbers. Do the numbers or the pictures show the comparisons the more easily? the more exactly?

121. Football Graph.-The plays in a football game can

be shown clearly by a graph.

1. How many yards was the ball "punted " toward the goal of the East Junior High? toward the goal of the West Junior High?

2. What was the actual distance that the ball was "punted" in each of the above two instances?

3. The distance "punted" by East Junior High toward their opponents' goal was what per cent of the total distance punted by East Junior High?

4. Answer 3 for West Junior High.

5. How far was the ball carried toward the goal of the East Junior High? toward the goal of the West Junior High?

6. What was the total distance that the ball was carried by the West Junior High? What per cent of this distance was toward their opponents' goal?

7. Answer Ex. 6 for the East Junior High.

8. Express the percentages in Exs. 3 and 4 as decimals carried out to .001.

9. Express the percentages in Exs. 6 and 7 as decimals carried out to .001.

10. Draw a football field several times larger than the one on page 124. Graph the following data, taking your school and some other school that you know for the two teams:

Team A kicked off to team B and the ball was caught on the 20-yard.line 25 yd. from the right side-line. Team B carried the ball directly toward A's goal 15 yd. before it was 66 down." First down, 3 yd. forward and 10 yd. to the left. Second down, 2 yd. forward and 20 yd. to the left. Third down, 3 yd. forward and 30 yd. to the right. Fourth down, punt 35 yd. forward and 10 yd. from right side-line. The ball was brought forward by team A 10 yd. First down, 5 yd. forward and 20 yd. to the left. Second down, 8 yd. forward and 5 yd. to the left. First down, 15 yd. forward, and 10 yd. from right side-line. First down, thrown back 5 yd. and 25 yd. to the left. Second down, 11 yd. forward and 10 yd. to the left. Third down, 7 yd. forward and 5 yd. to the right. First down, end run across goal-line and down behind goal-line 20 yd. from the left side-line.

11. Make up a set of six plays coming one after the other for the class to graph. The class will graph the most interesting plays. Try to make yours the one to be graphed.

Hold a number contest on adding and subtracting frac