SUBTRACTION

Subtraction may be defined in three ways: It is the procesE (a) of finding the difference between two numbers, (b) of taking one number from another, or (c) of finding what num ber must be added to a number to make a given number.

The number from which we subtract is called the minuend.
The number to be subtracted is called the subtrahend
The result is the difference, or the remainder.

NOTE. In the definition given in (c) the number corresponding to the minuend is a sum and the other two numbers are addends.

The sign

-, called minus, indicates subtraction.

Oral Work

Business men make change by the addition method of subtraction. Thus, if a purchase is made for $.69, and $1.00 is given in payment, the clerk will hand back a cent, a nickel, and a quarter, saying " 69, 70, 75, 1 dollar." The clerk makes change with the fewest pieces of money possible, handing out the smallest coins first.

Imagine that you are the clerk when the following purchases and payments are made, and count out the change to the customer in the above manner.

21-40. Subtract each of the numbers in examples 1-20

Keeping a Cash Account

Every pupil should form the habit of keeping an account in a small blank

The sum of the cash on hand and the receipts (left-hand side) is $14. The sum of the payments (right-hand side) is $1.90. The difference, $12.10, is written as Balance in the right-hand column below the last payment; and the column is then added, showing $14. As this amount is the same as the total of the receipts column, the account is correct. "Balance $12.10" is also written in the receipts column below the sum.

Make out and balance the following cash accounts:

1. Receipts: Feb. 4, cash on hand, $5.15; Feb. 5, shoveling snow, $.50; Feb. 6, tending furnace, $.25; Feb. 7, carrying bag, $.10; Feb. 8, chopping wood, $.15.

Payments: Feb. 5, repairing skates, $.50; Feb. 6, fountain pen, $2; Feb. 7, skating cap, $1.50; Feb. 8, muffler, $.75. 2. Receipts: July 1, cash on hand, $7.75; July 2, running errands, $.15; July 3, weeding garden, $.50.

Payments; July 1, fish line, $.50; July 3, bathing tights, $.55; July 5, ball, $.50; tennis racket, $5.

3. Receipts: Oct. 7, cash on hand, $4.25; Oct. 8, securing magazine subscriptions, $1; Oct. 9, making dresses for Helen's doll, $1.50; Oct. 11, weekly allowance, $.50.

Payments: Oct. 8, stationery, $.65; Oct. 9, car fare, $.10; Oct. 10, club dues, $1.

MULTIPLICATION

The process of taking one number as many times as there are units in another number is called multiplication.

The number multiplied is called the multiplicand.

The number by which we multiply is called the multiplier. The result of multiplication is called the product.

The multiplicand and multiplier are called factors of the product.

The sign indicates multiplication. It is read "times," when the multiplier precedes the sign. Thus, 3 x $5 is read "3 times 5 dollars."

A number used with reference to a particular object is called a concrete number; as, 5 days, 10 pounds, 8 inches.

A number used without reference to a particular object is called an abstract number; as, 5, 8, 20.

The multiplier is always regarded as an abstract number.

NOTE: The multiplicand may be either concrete or abstract. When it is concrete, the product has the same name as the multiplicand.

Compare the product of 8 × 6 with the product of 6 × 8; the product of 2 x 14 with the product of 14 × 2.

Either factor may be regarded as the multiplier.

How to multiply and divide by 10, 20, 100, etc.

1. Multiply 42 by 10. Annex a zero to the right of 42. Is there any difference in the products? Which of these two methods of multiplying is the shorter? Multiply 42 by 100. Annex two zeros to the right of 42.

2. Multiply each of the following numbers by 10; by 100: 43 26 75 96 283 694 786 813 465 710 634

To test multiplication, use the multiplicand for a multiplier and perform the multiplication again; or, divide the product by the multiplier.

2. How much will 48 chairs cost at $1.25 each?

$ 1.25

48

10 00

Multiply as before, and mark off from the right, in the product, two places for cents.

500

$60.00

4. 29 x 87 ft. =? 5. 46 x 215 doz.=? 6. 78 x $326 = ? 7. 86 $293 = ? 8. 91 x $145 = ? 9. 97 × 609 = ? 10. 85 x 987 = ? 11. 68 x 694 = ? 12. 65 x 45 = ? 13. 78 x 56=?