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EXPLANATION OF SIGNS.

THERE are many characters used to indicate arithmetical operations, among which are the following:

= The sign of equality, called equals or is equal to, signifies that the quantities between which it is placed are in value equal to each other.

+ The sign of addition, called plus or and, signifies that the numbers between which it is placed are to be added together. Thus 7 + 4 = 11 means that 7 added to 4 are equal to 11. It may be read either 7 plus 4 equals 11, or 7 and 4 are 11.

The sign of subtraction, called minus or less, signifies that the number following it is to be subtracted. Thus 9

6 means that 6 is to be subtracted from 9, and may be read 9 minus 6, or 9 less 6.

X The sign of multiplication, called times, or multiplied by, signifies that the quantities between which it is placed are to be multiplied together. 9 x 6 means that 7 and 6 are to be multiplied together, and may be read either as 7 times 6, or 7 multiplied by 6.

• The sign of division, called divided by, signifies that the quantity preceding it is to be divided by that which follows it. 12 : 3 means that 12 is to be divided by 3. It

may

be read as 12 divided by 3.

The parenthesis ( ) is used to enclose several quantities connected by the preceding signs, and to show that the result of the operations indicated within the parenthesis is to be regarded as the quantity affected by the signs preceding or following the parenthesis. Thus 6 X (2 + 4) signifies that 6 times the sum of 2 and 4 is to be obtained. Written without the parenthesis, thus, 6 X 2 + 4, it would mean that to times 2, 4 is to be added.

The vinculum, a straight line drawn above the written figures and signs, is often used in place of the parenthesis, and has the

Thus 6 x 2 + 4 has the same meaning as 6 x (2+4).

same use.

In this work the comma is used in connection with the above signs, to show that the result of all the indicated operations preceding it is to be considered in connection with the signs follow

ing it.

6 X 8, = 4, X3 + 7 x 2, signifies that 6 times 8, or 48, is to be divided by 4; that this result, 12, is to be multiplied by 3, and that to 36, the result thus obtained, 7 times 2, or 14, is to be added. The final result is therefore 50.

6 X 8, • 4 x 3 + 7 x 2, signifies that 6 times 8 is to be divided by 4 times 3, and that 7 times 2 is to be added to this quotient. The result is therefore 18.

6 X8, • 4, X3 +7, X 2, signifies that 6 times 8 is to be divided by 4, and this quotient multiplied by 3; that 7 is to be added to this result, and that the sum thus obtained is to be multiplied by 2. The final result is therefore 86.

We have also used commas in connection with figures and signs to indicate ellipses. For instance, in explaining the addi. tion of 7+8+3 + 9, we have written 8+7=15, + 3 18, +9 27, as a convenient way of expressing that 8

= 15, that 15 +3= 18, and that 18 + 9 =

= 27.

THE

DECIMAL SYSTEM OF NUMBEP

SECTION I.

A. 1. 10 + 10 = 2 tens, called TWENTY, written 20. 2. 2 tens + 10 = 3 tens, called THIRTY, written 30. 3. 3 tens + 10 = 4 tens, called FORTY, written 40. 4. 4 tens + 10 = 5 tens, called FIFTY, written 50. 5. 5 tens + 10 = 6 tens, called sixty,

written 60. 6. 6 tens + 10 = 7 tens, called SEVENTY,

written 70. 7. 7 tens + 10 = 8 tens, called Eighty, written 80. 8. 8 tens + 10 = 9 tens, called NINETY, written 90. 9. 9 tens + 10 = 10 tens, called ONE HUNDRED, written 100. Note. The period at the right of the above written numbers (20., 30., 40., &c.), is called the decimal point, and is used to denote the place of ones, or units. The first place at the left of the decimal point is the place of units, the second place is that of tens, and the third, that of hundreds. When the decimal point is omitted, it is understood to belong at the right of the figures representing the number.

B. 1. What do we call 8 tens? 9 tens? 6 tens? 7 tens ? 4 tens? 2 tens? 5 tens? 3 tens? 10 tens ?

2. How is twenty written by figures ? Sixty ? Forty ? Ninety? Eighty? Thirty ? Fifty ? Seventy ? One hundred ?

3. How many tens in 50 ? 80 ? 20 ? 90 ? 100 ? 70 ? 30 ? 60 ? 40 ? 10 ?

C. 1. 4 tens + 4 tens = how many tens ? Called what? How

many then are 40 + 40 ? 2. 7 tens + 2 tens = how many tens? Called what? How many then are 70 + 20 ? 3. 5 tens + 3 tens = how

many

tens? Called what? How many then are 50 + 30 ?

Let the pupil now read the following, supplying appropriate numbers in place of the stars.

4. 2 tens +5 tens = * tens, or * units; then 20 +50=*. 5. 4 tens + 5 tens =* tens, or* units; then 40+50=*. 6. 3 tens + 6 tens : tens, or * units; then 30+60=*. 7. 2 tens + 2 tens tens, or * units; then 20 + 20=*. 8. 3 tens + 7 tens =* tens, or * units; then 30+70=*. 9. 3 tens + 3 tens * tens, or * units; then 30+30=*. 10. 6 tens + 4 tens * tens, or units; then 60 + 40=*. 11. 2 tens + 3 tens + 4 tens * tens, or * units; then 20+30 +40=*.

12. 5 tens + 2 tens + 3 tens = * tens, or * units; then 50 + 20+30

13. 3 tens + 2 tens + 3 tens = * tens, or * units; then 30+20 + 30 =*

14. 5 tens + 1 ten + 2 tens = * tens, or * units; then 50+ 10+20=*.

15. 2 tens + 1 ten + 3 tens =* tens, or * units; then 20+ 10+30=*.

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1. 9 tens 6 tens = how many tens? How many units ? 90 60 ?

2. 7 tens 3 tens = how many tens? How many units ? 70-30?

3. 5 tens 4 tens how many tens ? How many units ? 50 - 40 ?

Read the following, supplying the proper numbers in place of the stars.

4. 8 tens 5 tens =* tens, or * units; then 80 — 50 =* 5. 9 tens 7 tens

* tens, or * units; then 90 70=* 6. 6 tens 3 tens =

* tens, or * units; then 60 30=*.

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