s. By 2's from 30; from 29. w. By 6's from 100; from 99.

IV. From each number expressed in columns i, j, k below, subtract 2, and notice the units of the remainders.

In the same way subtract 3; 4; 5; 6; 7; 8; 9.

v 90

98

81 52 83 94 85 96 87

V. From the numbers expressed in column k above, subtract any number from 3 to 9; in column 7 from 4 to 9; in column m from 5 to 9, and so on.

VII. Give the remainders in the following examples, both

in the columns and in the lines.

Illustrative Example. From 42 take 25.

SOLUTION. -42 less 20 are 22, less 5 more are 17.

VIII. In the following, subtract first by columns, then

IX. q. From 30 take 20; 10; 15; 27; 3; 12; 18; 21;

9; 26; 5; 23; 19.

r. From 60 take 40; 20; 15; 45; 12; 48; 24; 36; 54;
6; 37; 49.

s. From 100 take 70; 30; 65; 35; 25; 75; 17; 83; 33;
66; 45; 87; 54.

t. From 125 take 15; 17; 13; 12; 5; 8; 7; 16; 9; 11;
6; 14; 16; 18.

Examples for Written Work.

58. Illustrative Example. John started to walk a mile,
which is 5280 feet; after walking 4326 feet, how many more
feet had he to go?

WRITTEN WORK.

i

Minuend,

5280
Subtrahend, 4326

Remainder, 954
Proof,

5280

The minuend and subtrahend are written as
in the margin, units under units, tens under
tens, and so on. The subtracting begins with
the units.

As there are no units in the minuend, one of
the tens must be changed to 10 units; 6 units
from 10 units leaves 4 units, which is written

in the units' place; 2 tens from the 7 tens
remaining leaves 5 tens, which is written in the tens' place.

As there are but 2 hundreds in the minuend, one of the thousands
must be changed to 10 hundreds, making, with the 2, 12 hundreds;
3 hundreds from 12 hundreds leaves 9 hundreds; 4 thousands from the
4 thousands remaining leaves no thousands. The remainder is 954.
Ans. 954 feet.

The operation may be expressed briefly, thus: 6 from 10, 4; 2 from
7, 5; 3 from 12, 9; 4 from 4, 0. Ans. 954. In practice simply think

of results and write them down in order.

To prove the work, add together the remainder and subtrahend.
Their sum equals the minuend.

59. Illustrative Example. Mr. Graves received a salary of $3000, and his son received $268. What was the difference in their salaries?

WRITTEN WORK.

(2) (9) (9) (10) $3000 268

$27 32

To find the difference, a part of 3000 equal to 268 must be taken away.

As there are no units, no tens, and no hundreds in the minuend, one of the 3 thousands is taken (leaving 2 thousands) and changed to hundreds ; one of the 10 hundreds is taken (leaving 9 hundreds) and changed to tens; and one of the 10 tens is taken (leaving 9 tens) and changed to units. 3000 is thus changed to 2 thousands 9 hundreds 9 tens and 10 units, from which, taking 2 hundreds 6 tens and 8 units, 2732 remains. Ans. $2732.

In practice simply think "8 from 10, 2"; "6 from 9, 3"; "2 from 9, 7"; "0 from 2, 2"; and write the results in order.