and eight hundred and seventy-eight bushels of rye; how many bushels of grain did he raise ? LESSON III. SUBTRACTION. THE finding of the difference of two numbers is called SUBTRACTION. 2. The number we subtract is called the Subtrahend. The number we subtract from is called the Minuend. The result is called the Difference or Remainder. 3. The symbol is the sign of subtraction, and is called minus. Thus 8-62 is read "8 minus 6 equals 2.".,, CASE I. 4. To subtract when no term of the subtrahend is greater than the corresponding term of the minuend. 1. Subtract 24 from 58. SOLUTION.-We write the 24 under the 58, OPERATION. draw a line beneath, and begin at the right to subtract. 4 units from 8 units leave 4 units; 2 tens from 5 tens leave 3 tens. is 34. The difference 58 24 34 1. If I had 12 apples, and gave 8 of them away, how many apples remained? SOLUTION.-If I had 12 apples and gave 8 of them away, there remained 12 apples minus 8 apples, which are 4 apples. Therefore, etc. 2. Susan had 13 pins in a cushion, and took out 7; how many pins remained? 3. There were 16 words given out in the spelling class, and 7 were misspelled; how many were spelled correctly? 4. There were 28 leaves in Ellen's book, and a dog tore out 10 leaves; how many leaves remained in the book? 5. If you cut off 12 feet of a kite-string 23 feet long, how many feet of the string will remain? 6. A boy had 20 marbles, and in playing lost all of them but 5; how many did he lose? 7. Peter picked 21 peaches for his mother, and his brother took 8 of them; how many remained for his mother? 8. There were 25 robins in a cherry-tree, I shot 6, and the rest flew away; how many flew away? 9. Begin at 20 and count backward by 2's to nothing. Begin at 21 and count backward by 2's to 1. 10. Begin at 21 and count backward by 3's to nothing. Begin at 22 and count backward by 3's to 1. Begin at 23 and count backward by 3's to 2. 11. What is the value of 12-7? Of 18-8? Of 20 -12? Of 21-11? Of 24-12? Of 26-13? Of 6+8 -7? Of 8+9-10? 12. What is the value of 8+7-6? Of 4+9-5? Of 9+4-6? Of 8+7-12? Of 10+11-12? Of 12+11-10? WRITTEN EXERCISES. 1. If there are 48 boys and 36 girls in a school, how many more boys are there in the school than girls? SOLUTION. There are as many more boys than girls as the difference between 48 and 36, which is 12. Therefore, etc. 48 36 12 2. My father had 258 acres of land and sold 36 acres; now many acres of land remained? 3. From four thousand seven hundred and ninety-five subtract two thousand four hundred and forty-three. 4. What is the difference between eight thousand and eighty-eight and five thousand and seventy-four? 5. A man carted 3047 bricks from a pile containing 8797; how many bricks remained? 6. What is the difference between twelve thousand seven hundred and forty-six and five thousand and twenty-five? 7. Mary cried because she couldn't tell how many she must add to 1325 to make 5748; can you tell? 8. Sarah had saved four hundred and seventy-five cents, and spent two hundred and fifty-two cents; how much had she remaining? 9. A farmer raised one thousand eight hundred and fifty-eight bushels of corn, and sold five hundred and thirty-five bushels; how many bushels remained? CASE II. 5. To subtract when a term of the subtrahend is greater than the corresponding term of the minuend. 1. Subtract 28 from 52. SOLUTION. We write 28 under 52, draw a line beneath, and begin at the right to subtract. We cannot subtract 8 from 2; so we borrow 1 ten from the 5 tens, leaving 4 tens, and add it to the 2 units, making 12 units; 8 OPERATION. 52 28 24 units from 12 units leave 4 units; 2 tens from 4 tens leave 2 tens; hence the remainder is 24. NOTE. With the youngest pupils it may be merely shown that we add ten to the upper term, and then add one to the next lower term, without explaining the reason. 1. If there are 20 crows on a tree, and 12 fly away, how many crows are left? 2. A hunter saw 22 rabbits, and shot 8 of them; how many escaped? 3. Eva culled 18 roses, and gave Floy 12 of them; how many did Eva retain? 4. A boy had 6 apples, and picked 8 more, and then gave his brother 10 apples; how many apples had he then? 5. A boy had 10 cents, and found 12 cents, and then spent 11 cents; how many cents had he then? 6. Harry had 20 peaches, gave his sister 8 of them, and ate 6; how many peaches had he then? 7. Begin at 24 and count backward by 4's to naught; begin at 25 and count backward by 4's to 1; begin at 26 and count backward by 4's to 2. 8. Begin at 30 and count backward by 5's to naught; from 31 to 1; from 32 to 2; from 33 to 3; from 34 to 4. 9. What is the value of 6+3-4? Of 7+4—5? Of 8+5-7? Of 5+12-8? Of 7+9-6? 10. What is the value of 7-4+3? Of 8-5+4? Of 9 -2+7? Of 12-8+10? Of 20-8+10? Of 8+12-6? WRITTEN EXERCISES. 1. A drover bought 235 horses, and sold 162 of them; how many horses remained unsold? SOLUTION.-If a drover bought 235 horses, and sold 162 of them, there remained the difference between 235 horses and 162 horses, which we find by subtracting is 73 horses. OPERATION 235 162 73 |