SECTION III. SUBTRACTION. ART. 25. Ex. 1. Charles having 15 cents, gave 6 conts for an orange how many cents did he have left? Solution.-6 cents taken from 15 cents leave 9 cents. Therefore he had 9 cents left. OBS. The preceding operation consists in taking a less number from a greater, and is called Subtraction. Hence, 26. SUBTRACTION is the process of finding the difference between two numbers. The answer, or number obtained by subtraction, is called the difference or remainder. OBS. 1. The number to be subtracted is often called the subtrahend, and the number from which it is subtracted, the minuend. These terms, however, are calculated to embarrass, rather than assist the learner, and are properly falling into disuse. 2. When the given numbers are all of the same kind, or denomination, the operation is called Simple Subtraction. 27. Sign of Subtraction (—). The sign of subtraction is a horizontal line (—), called minus, and shows that the number after it is to be subtracted from the one before it. Thus the expression 7-3, signifies that 3 is to be subtracted from 7; and is read, " 7 minus 3," or " 7 less 3." Read the following: 18-7-20-9. 23-10=16—3 35-8=31-4. Note.-The term minus is a Latin word signifying less. What is the answer called? Obs. QUEST.-26. What is subtraction? What is the number to be subtracted sometimes called? That from which it is subtracted? When the given numbers are of the same denomination, what is the operation called? 27. What is the sign of subtraction? What does it show? Note. What is the meaning of the term minus? OBS. This Table is the reverse of Addition Table. Hence, if the pupil has thoroughly learned that, it will cost him but little time or trouble to learn this. (See observations under Addition Table.) EXAMPLES. 28. When each figure in the lower number is smaller than the figure above it. 1. A farmer raised 257 bushels of apples, and 123 bushels of pears: how many more apples did he raise than pears? Operation. hund. units. 2 5 7 apples. 1 2 3 pears. Rem. 1 3 4 bush. Directions.-Write the less number under the greater, so that units may stand under units, tens under tens, &c., and draw a line beneath them. Beginning with the units or right hand figure, subtract each figure in the Lower number from the figure above it, in the following manner: 3 units from 7 units leave 4 units. Write the 4 in units' place under the figure subtracted. 2 tens from 5 tens leave 3 tens; set 3 in tens' place. 1 hundred from 2 hundred leaves 1 hundred; write the 1 hundred in hundreds' place. Solve the following examples in a similar manner: 29. When a figure in the lower number is larger than the figure above it. 11. A man bought 63 bushels of wheat, and afterwards sold 37: how many bushels had he left? It is bvious that we cannot take 7 units fr 3 uni's, for 7 is larger than 3; we therefore add 10 to the 3 units, and it w ll Lake 13 units; then 7 from 18 leave: 6; write the 6 in units' place First Method. 63 37 Rem. 26 bu. under the figure subtracted. To compensate for the 10 units we added to the upper figure, we add 1 ten to the 3 tens or next figure in the lower number, and it makes 4 tens; and 4 tens from 6 tens leave 2 tens: write the 2 in tens' place Ans. 26 bushels. We may also illustrate the process of borrowing in the following manner: 63 is composed of 6 tens and 3 units. Taking 1 ten from 6 tens, and adding it to the 3 units, we have 63=50+13. Separating the lower number into tens and units, Second Method. 63=50+13 37=30+7 Rem.=20+ 6, or 26 we have 37=30+7. Now, substracting as before, 7 from 13 leaves 6. Then as we took 1 ten from the 6 tens, we have but 5 tens left; and 3 tens from 5 tens leave 2 tens. The remainder is 26, the same as before. 30. The process of taking one from a higher order in the upper number, and adding it to the figure from which the subtraction is to be made, is called borrowing ten, and is the reverse of carrying ten. (Art. 22.) OBS. When we borrow ten we must always remember to pay it This may be done, as we have just seen, either by adding 1 to the next figure in the lower number, or by considering the next figure in the upper number 1 less than it is. 12. From 240 subtract 134, and prove the operation. Since 4 cannot be taken from 0, we borrow 10; then 4 from 10 leaves 6. 1 added to 3 (to compensate for the 10 we borrowed) makes 4, and 4 from 4 leaves 0. 1 from 2 leaves 1. PROOF.-We add the remainder to the smaller number, and since the sum is equal to the larger number, the work is right. Operation. 240 134 106 Ans. Proof. |