*17. Subtract from 843 the sum of 244 and 181.

*18. From 143 + 123, subtract 8+48.

37. Changing the Minuend in Subtraction

I

In order to pay a half-dollar or a quarter out of a two-dollar bill, it is necessary to change the bill. In like manner, when a fractional part is to be taken from a whole number, the form of the whole number must be changed.

What number is left when the fraction is taken from 8?

13. How many yards are left when of a yard is taken from 2 yards?

14. From a line 12 inches long, 82 inches are erased. How many inches are there in the line that is left?

15. From a box containing 5 pounds of candy, 24 pounds are taken. How many pounds are left in the box?

CHANGING THE MINUEND IN SUBTRACTION

II

57

How much longer is a line 143 yards long than one 93 yards long?

8

9

9

8

In solving this problem, the fractions are first changed to a common denominator: = 12; 4 = 12. Then, since 12 cannot be subtracted from 12, 1 is taken from the integer in the minuend and added to the fraction in the minuend. The 14 is changed to 1313. The 1, or 12, added to the makes. The problem then stands: 139 - 91%

=

?

Notice that when fractions have unlike denominators, as in the problem above, they are reduced to a common denominator before the change is made in the integer.

21. From a fish line 40 yards long, a piece 18 yards long is cut. How many yards are left?

22. In one part of its course a stream is 44 rods in width; in another part, 2 rods. What is the difference in the width of the stream at the two points named?

23. How much deeper is a swimming pool that is 8 feet deep than one that is 5 feet deep?

38. Test and Graded Practice

This test is to help you find out and overcome your difficulties in the addition and subtraction of fractions. If you fail to get the right answer to a problem in the test, practice solving the problems in the set below having the same letter. If you have no trouble with the test, improve your work by solving the starred problems in exercise H.

To play the game "Over-the-top" with any of these exercises, write the problems in the form of a ladder with the first problem at the bottom. Race with your classmates to get the right answers. The first one to do so goes over-the-top first.

G.

37.7-31.

[Use pencil only when needed.]

1. What is the increase in a boy scout's walking record if on a tramp he extends his record of 81⁄2 miles to one of 12 miles?

2. What is the distance covered in a day by a group of campfire girls who walk 5 miles in the morning and 41⁄2 miles in the afternoon?

3. A mountain trail is 6 miles long. How far from the upper end of the trail are boys who have climbed 4 miles?

4. A lake is 22 miles across. How far from the farther shore is a canoe which has been paddled 13 miles across the lake?

5. John and his brothers row three miles. They cover the first mile in 12 minutes, the second mile in 14 minutes, and the third mile in 10 minutes. What is their record in minutes for the three miles?

6. How much greater is the distance covered by a boy who swims mile at a stretch than that covered by a boy who swims 220 yards (of a mile)?

7. What is the difference in time made in a hundred-yard swimming contest, between a record of 553 seconds and a record of 1 minute?

8. In a walking contest, the winner walked a mile in 8 minutes; the boy next in the contest took 10 minutes. What was the difference in the time?

40. On the Athletic Field

[Use pencil only when needed.]

1. A ball player takes 43 seconds to get to first base, 43 seconds to get to second base, 43 seconds to get to third base, and 43 seconds to get to the home plate. How many seconds does it take him to make a home run?

2. The time taken for the home run (problem 1) is how many seconds over a quarter of a minute?

3. In a relay race, the first boy takes 5 seconds for his part of the course; the second boy, 5 seconds; the third boy, 4 seconds. How much less than a half-minute was needed for the race?

4. What is the difference in the length of a running track 1% of a mile long, and one of a mile long?

5. Find the difference in time between a record of 43 minutes for a mile run and one of 54 minutes.

6. Fred can take a running jump over a pole 5 feet from the ground; his brother can jump over the pole at 4 feet. What is the difference in the height of the jumps?

7. Albert can make a running broad jump of 121 feet; Charles's record is 145 feet. Find the difference.

*8.. Use this table for making problems of your own. Solve your problems and then report your results to your classmates.