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254. Written Problems.

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1. Find the number of square feet in a walk 50 ft. long and 4 ft. wide.

How much will it cost at $.12 a square foot to lay a cement walk 50 ft. long and 5 ft. wide ?

3. Find the area of a walk 60 ft. long and 5 ft. wide.

4. How many square inches are there in 3 sq. ft. ? In 31 sq. ft. ?

5. How many square inches are there in 3 sq. ft. and 32 sq. in. ?

6. Find the number of square feet there are on the floor of your schoolroom.

7. Find the number of square rods there are in your school yard.

8. Find the number of square yards of blackboard there are in your schoolroom.

9. How much did the blackboard in your schoolroom cost at 18¢ a square foot ?

255. In your drawings, let 1 in. represent 2 ft.
Draw:
1. A square that will contain 16

sq.

ft. 2. A rectangle that will contain 16 sq. ft. 3. A square that will contain 36

sq. 4. A rectangle that will contain 36 sq. ft. 5. Find the perimeter of each of your figures.

ft.

BILLS AND ACCOUNTS

256. 1. Study the bill given in Sec. 78, p. 82.

2. A bill must always show the date of the transaction. What is the date of the transaction referred to in the bill in Sec. 78 ?

3. The debtor is the party who buys the goods. Who is the debtor in the bill referred to above?

4. The creditor is the party who sells the goods. Who is the creditor in the bill referred to above ?

5. An item is a separate debit or credit made in a bill. How many items are there in the bill referred

. to above ?

6. How many items are there in the bill in Sec. 257 ?

7. Name the debtor and the creditor in the bill in Sec. 257.

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1st BK ARITII-12

LONG DIVISION

258. When all the steps in division are written, the process is called long division.

Divide 173 by 3.
MODEL: 573

3 is contained in 17 five times. 3)173 Write 5 in the quotient above the 15 7, as in short division. Multiply 3 23 by 5 and write the product under 21 17, and subtract. The remainder is 2 2. Bring down the 3 of the divi

dend and find how many times 3 is contained in 23. This is 7 times. Multiply 3 by 7 and write the product under 23, and subtract. Treat the remainder as in short division.

CASE ONE

259. When the second figure* of the divisor is the same as or less than the first figure, as in 44, 63, 978, 658, etc.

1. Divide 2292 by 43.

First, find how many places at the left of 2292 it will take to contain 43 at least one time. It will take three places. The first figure of the quotient will be in tens'

place.

5313 MODEL: 43)2292

Step 1. 4 is contained in 22

five times with 2 remainder. 215

This remainder, with the next 142

figure of the dividend, is the 129

dividend of 3, the second figure 13

of the divisor. The dividend of

* In 63 regard 6 as the first figure and 3 as the second figure.

3 is 29. Is 3 contained in 29 as many as 5 times ? If it is, 5 is the trial quotient figure. 3 is contained in 29. as many as 5 times.

Write 5 in the quotient above 9. Step 2. Multiply 43 by 5, and write the product under 229.

Step 3. Subtract 215 from 229. The remainder is 14.

As this remainder is less than the divisor, the trial quotient figure is the true quotient figure.

Step 4. Bring down the next figure of the dividend. The new dividend is 142. Repeat Step 1. 4 is contained in 14 three times with 2 remainder. As 3 is contained in 22 as many as 3 times, 3 is the trial quotient figure. Write 3 in the quotient.

Repeat Step 2. Multiply 43 by 3 and write the product under 142.

Repeat Step 3. Subtract 129 from 142. The remainder is 13. Treat the remainder as in short division.

2. Divide 1806 by 43; 7877 by 96 ; 7877 by 82. 3. Divide 2806 by 65; 5927 by 97; 5927 by 51. 4. Divide 16,108 by 72; 18,191 by 85; 45,960

by 71.

49,8

5. Divide 2115 by 43.

First, find how many places at the left of 2115 it will take to contain 43 at least one time. MODEL :

Step 1. 4 is contained in 21 43)2115 five times with 1 remainder. As

172 3 is not contained in 11 as many 395 as 5 times, write 4 as the trial 387 quotient figure, and continue as

in the preceding exercise.

43

6. Divide 6748 by 76; 8432 by 54; 7667 by 99. 7. Divide 4084 by 72; 2094 by 93; 6456 by 77. 8. Divide 1243 by 22; 4527 by 33; 5468 by 76. 9. Divide 9247 by 95.

9 is contained in 92 ten times. 9

Use 9 as the trial quotient figure. MODEL: 95)9247

Complete the division. 10. Divide 7492 by 77; 6230 by 65; 9348 by 98. 11. Divide 6258 by 66; 5213 by 55; 8570 by 87.

Divide 5234 by 54; 7485 by 76; 8775 by 88.

12.

260. When the second figure of the divisor is the same as or less than the first figure, the trial quotient figure may be found as follows:

*

1. If the second figure of the divisor is contained in its dividend * as many times as the first figure is contained in its dividend, use this quotient figure as the trial quotient figure.

2. If the second figure of the divisor is not contained in its dividend as many times as the first figure is contained in its dividend, use as a trial quotient figure one less than the quotient figure obtained by dividing by the first figure of the divisor. This will be found to be the true quotient figure.

3. If the first figure of the divisor is contained in its dividend 10 times, use 9 as the trial quotient figure.t

* The number formed by annexing the next figure of the dividend to the remainder left after dividing by the first figure of the divisor is the dividend of the second figure of the divisor.

† The pupils should become perfectly familiar with these facts through illustration.

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