the pupil to find the total number of pounds, as well as dollars, for the whole number of years given, or for any particular years within the limits of the table; and as it is very desirable for the pupil to be quick and accurate in the addition of numbers, it will be well for the teacher to extend to considerable length the exercises which may be diawn from the above statistics. SUBTRACTION OF SIMPLE NUMBERS. 12. SUBTRACTION is taking a less number from a greater. The greater number is called the minuend, and the smaller number is called the subtrahend ; the result is called the remainder or difference. The symbol for subtraction is –. When this symbol is placed between two numbers, it indicates that the second is to be subtracted from the first. Thus, 8–5, denotes that 5 is to be taken from 8. The remainder being 3, we have 8-5=3. The symbol – is generally read minus ; a Latin word meaning less. What is Subtraction? What is the greater number called? What is the sma.ler Qumber called ? What is the result called ? What symbol is used to deuote Subtraction ? By using this symbol, we may form the following EXAMPLES OPERATION. co ~ Hundreds. Tens. 1. In which no figure of the subtrahend is larger than the corresponding figure in the minuend. From 796 subtract 375. Place the subtrahend directly under the minuend, so that units may stand under units, Lens under tens, hundreds under hundreds. 7 9 6 minuend. Then commence at the 3 1 5 subtrahend units' column and subtract 4 2 1 difference. 5 from 6 leaves 1 ; place the one i under the units' column, and so proceed with each succeeding column. From 687 subtract 486. Ans. 201. From 7949 subtract 5438. Ans. 2511. From 69975 subtract 59831. Ans. 10144. From 879465 subtract 729355. Ans. 150110. From 987654321 subtract 821350011. Ans. 166304310. 2. In which some of the figures of the subtrahend are larger than the corresponding figures of the minuend. From 867 subtract 496. OPERATION. Hundreds. 7 hindred, 16 tens, and 7 units, [7] [16]: =3 hundred, 6 tens, and 7 units, $ $ 7 minuend. 4 9 6 subtrahend 3 g 1 difference Place the minuend and subtrahend as in the preceding example. Begin at the units' column; 6 from 7 leaves 1. · Passing to the tens' figure of the subtrahend, which is 9, we see that it cannot be subtracted from the corresponding figure of the minuend. But we know (Art. 10,) that 1 of any order is equal to 10 of the next lower order. We therefore take 1 from the hundreds' figure, leaving that figure 7, (which we place in brackets over the 8, marking out the 8,) and counting the 1 hundrei as 10 tens, we add it to the 6 tens, making 16 tens, which sum we place in brackets over the 6 and mark out the 6. We now say 9 from 16 leaves 7; 4 from 7 leaves 3. From 959 subtract 678. Ans. 281. From 767 subtract 349. Ans. 418. From 8965 subtract 7774. Ans. 1191. From 52475 subtract 19304. Ans. 33171. 3. We will now give an example of a more difficult operation. From 8053 subtract 4967. OPERATION [7] [Y] [4] [13] fore take 1 from the tens' $ $ $ $ minuend. figure of tho minuend, 4 9 6 7 subtrahend. leaving that figure, 4, (which we place' in / 3 0 8 6 difference. brackets over the 5, marking out the 5,) and counting the 1 ten as ten units, we ... Thousands. Hundreds. Tens. Units. add it to the 3 units, making 13 units, which sum we place in brackets over the 3 and mark out the 3. We can now subtract the 7 from the 13. We next seek to subtract the 6 from the 4, which we cannot do. We must then seek one from the hundreds' place to be added to the 4. But there are no hundreds there. We then go to the thousands' place. - Taking one from the 8, we have 7 left. Place the 7 in brackets over the 8 and mark out the 8. The 1 thousand we carry to the hundreds' place, where it counts 10 hundred; place the 10 over the zero and mark out the 0... Then take 1 hundred from the 10 in the brackets, leaving 9, which, place in second brackets above, and mark out the 10; then add the 1, counting it as 10 tens, to the 4, and you have 14 tens, which place within second brackets over the 4 and mark out the 4. Now we proceed with the subtraction; 6 from 14 leaves 8; 9 from 9 leaves 0; 4 from 7 leaves 3. It will be noticed that the minuend'appears in three different forms; yet the sum is the same in all. Thus, in the minuend proper, the sum is 8 thousands, 0 hundreds, 5 tens, 3 units; in the minuend in the first brackets, the sum is 7 thousands, 10 hundreds, 4 tens, 13 units; in the second brackets, 7 thousands, 9 hundreds, 14 tens, 13 units : each form being equal to 8053. Note.-The preceding explanations are intended to show the reasons of the process. The pupil should perform simiar opera. tions without writing down the steps. From 8275 subtract 7189. Ans. 1086. Ans. 772. Ans. 89999. |