When one of the numbers is an _aliquot part_ of 100, the process of
multiplication and division can often be very much shortened, as shown
below.
Find cost of 27 yards of goods at 16-2/3c ($1/6) per yard. At $1 per
yard, 27 yards cost $27; at $1/6, (27 ÷ 6), $4-1/2. _Ans._ $4-1/2.
Find cost of a bale of cotton, 528 pounds at 8-1/3c ($1/12) per pound.
At $1 per pound, 528 pounds cost $528; at $1/12 (528 ÷ 12) $44. _Ans._
$44.
Find cost of 1845 pounds of iron, at 3-1/3c ($1/30) per pound. Take 1/30
of 1845, since 3-1/3c is 1/30 of $1. (1845 ÷ 30 = 61-1/2). _Ans._
$61-1/2.
Find cost of 16 pounds of butter at 37-1/2c ($3/8) per pound. Here we
take 3/8 of 16. Say 1/8 of 16 is 2, and 3/8 is (2 × 3) 6. Or say 3 times
16 is 48, and 1/8 of 48 is 6. _Ans._ $6.
Find cost of 17-1/2 bushels of apples at 75c ($3/4) per bushel. The
shortest way to find 3/4 of $17.50 is to diminish it by 1/4 of itself.
4)17.50 at $1
------
4.37-1/2 at $1/4
13.12-1/2 at $3/4
_Ans._ $13.12-1/2.
At 6-1/4c per pound how much sugar will $5 buy? As 6-1/4c is 1/16 of $1,
evidently each dollar will buy 16 pounds. _Ans._ 80 pounds.
In multiplying by a fraction, write the quantity in a line with the
numerator and cancel common factors.
Find cost of 72 yards of carpet, at 87-1/2c ($7/8) a yard. Cancel 8,
also 72 and write 9 instead. _Ans._ $63.
7 × 7̸2̸ 9 = 63
-
8̸
Of 28 pounds of coffee, at 18-3/4c ($3/16) per pound. Cancel 28 and 16,
write 7 and 4. _Ans._ $5-1/4.
3 × 2̸8̸ 7 21
---- = -- or 5-1/4
1̸6̸ 4 4
At 66-2/3c ($2/3) per bushel, how many bushel of wheat will $34 buy?
_Ans._ 51 bushel.
3 × 3̸4̸ 17 = 51
-
2̸
In division, invert terms of fraction.
How much syrup, at 41-2/3c ($5/12) per gallon can be bought for $15?
_Ans._ 36 gallons.
12 × 1̸5̸ 3 = 36
--
5̸