140

FRACTIONS-COMMON DENOMINATOR

35

I. In 1900, of all the farms in New Jersey contained less than 10 acres; contained from 10 to 99 acres.

21 35

How is this found? 335 + 31/3 = 35· What part of the whole number of farms contained less than 100 acres?

35

2. 1. 35-34? What part of the whole number of farms in New Jersey contained 100 acres or more?

3. On of the total number of farms the principal source of income was vegetables; on 4, live stock; on, dairy produce; what part of the whole number had none of these as the principal source of income?

4. Before adding or subtracting the fractions in the above exercises, how were the fractions changed?

When fractions are to be added or subtracted they should be changed to fractions having the same denominator. This denominator is called their common denominator.

A

Change the fractions of each row to equal fractions having the common denominator as indicated:

II. In Exercises 5-10 select those in which the new denominator is the least number that could be used thus. What is the least common multiple of the given denominators in each exercise?

The least common multiple of the given denominators is called the least common denominator (1. c. d.) of the fractions. Find the least common denominators of :

Change to fractions equal to the given fractions with 1. c. d. and add:

13. A man sold of an acre at one time, of an acre at another, and at another; 37 how many acres did he sell altogether?

14. If a farmer laid of a mile of drain-tile one year, of a mile the second year, and ğ of a mile the third year, how many miles did he lay in three years?

15. If from of a bolt of silk of the whole bolt are sold, what part of the whole bolt remains?

Reduce to least common denominator and add:

24. From a bolt of cloth a merchant sold at one time, at another, and at another; how much did he sell in all? 25. A rectangle is of a foot on one side and on another; what is the length of its perimeter?

50 lb.

= hr.

lb. =

lb.

In adding or subtracting mixed numbers it is usually more convenient to treat the fractions and whole numbers separately than to change the numbers to improper fractions.

3. A man walked 11 miles on Monday and 6,7 miles on Tuesday; how many miles did he walk altogether?

4. William is 113 years old and Thomas is 9152 years old; William is how much older than Thomas?

5. A gold dollar contains 2311 grains of gold and 2,58 grains of alloy; what is the weight of the gold dollar?

6. The half-eagle or 5-dollar gold piece contains 9922 more grains of gold than the gold dollar; how much gold does the half-eagle contain?

FRACTIONS-PROBLEMS

Why?

1. From a jar containing 18 lb. of butter 7 lb. are sold; how many pounds remain in the jar? 18 lb. = 179 lb. 2. A park contains 637 acres of which 131 acres are given to lakes and lagoons, how many acres are dry land? 631 acres =

6218 acres.

3. Mary bought 12 yards of cloth and used 75 yards for a dress; how many yards had she left?

4. A man traveled 125 miles one day, 250 miles the next, and 113 miles the next; how many miles did he travel in the three days?

5. Charles walks 14 miles to school and George walks of a mile; who walks the farther, and how much?

6. From a jar containing 20 lb. of butter, a grocer sold 3 lb. to one customer and 65 to another; how many pounds are left in the jar?

7. From 20 yards of cloth a merchant sold 10 yards, 51 yards, and 23 yards; how many yards had he left?

144

PROBLEMS-SEWING

1. Small triangular pieces of cloth used to shape garments are called gussets. They are of various triangular shapes. How many gussets like Figure 1 can

be cut from a 4-in. square?

2. State the size of the smallest piece of

Figure 3.

4. Show by drawings the shape of the pieces of cloth mentioned in Exercises 2 and 3, and how the gussets should be cut.

5. A breadth of a skirt is 231 in. wide after a seam of in. has been made along each edge; how wide was the cloth?

6. A tape loop sewed to a band has a free length of 21

22 IN.

in. as shown in the pic

ture. If in. is turned

under at each end, and

the tape is stitched down

in. from each end, how long was the piece of tape?

7. If a finished pillow-case is 17 in. wide and 263 in. long, in which in. is taken in for seams and 3 in. + in. for a hem, how much cloth is needed for 1 pillow-case? For a dozen such pillow-cases? What is the cost of one pillowcase if the cloth cost 1214 per yard? What is the cost of 6 pairs?