WRITTEN EXERCISES. 1. From 5334 take 2726. PROCESS. Min., 5334 Since 6 units can not be taken from 4 units, add 10 units to the 4 units, making 14 units; then subtract 6 units from 14 units, and write 8 units, the difference, below. To balance the 10 units (equal 1 ten) added to the minuend, add 1 ten to the 2 tens of the subtrahend; then subtract 3 tens from 3 tens, and write 0 tens, the difference, below. Add 10 hundreds to the 3 hundreds of the minuend, making 13 hundreds; subtract 7 hundreds from 13 hundreds, and write 6 hundreds, the difference, below. To balance the 10 hundreds (equal 1 thousand) added to the minuend, add 1 thousand to the 2 thousands of the subtrahend; subtract 3 thousands from 5 thousands, and write 2 thousands, the difference, below. The difference is 2608. This process may be shortened, thus: 6 units from 4 units plus 10 units, or 14 units, leave 8 units; 2 tens and 1 ten are 3 tens, and 3 tens from 3 tens leave 0 ten; 7 hundreds from 3 hundreds plus 10 hundreds, or 13 hundreds, leave 6 hundreds; 1 thousand and 2 thousands are 3 thousands, and 3 thousands from 5 thousands leave 2 thousands. The difference is 2608. NOTE. The teacher should show that the adding of 10 to a term of the minuend and 1 to the next higher term of the subtrahend increases both minuend and subtrahend equally, and does not affect the difference. 12. From fourteen thousand and forty-four take six thousand and sixteen. 13. A man whose income is $1850 expends annually $1365: how much does he lay up? 14. The number of youth of school age in a certain city is 1234, and only 756 pupils are enrolled in the schools: how many youth do not attend school? 15. The number of pupils enrolled in the public schools of Ohio, in 1867, was 704767; in Pennsylvania, 789389: how many more pupils were enrolled in Pennsylvania than in Ohio? LESSON IV. New Subtrahend Figures, 8 and 9. MENTAL EXERCISES. 1. How many is 9 less 8? 11 less 8? 13 less 8? 10 less 8? 14 less 8? 12 less 8? 2. How many is 16 less 8? 26 less 8? 56 less 8? 17 less 8? 27 less 8? 67 less 8? 3. How many is 11 less 9? 13 less 9? 12 less 9? 16 less 9? 17 less 9? 15 less 9? 4. How many is 16 less 9? 26 less 9? 36 less 9? 15 less 9? 25 less 9? 45 less 9? 5. Begin with 50 and count back to 2 by subtracting 8 successively. 6. Begin with 57 and count back to 3 by subtracting 9 successively. 7. A school has enrolled 65 pupils, and 8 are absent: how many are present? 8. Mr. Smith is 44 years of age and his youngest son is 8 years of age: what is the difference in their ages? 9. A school contains 9 more girls than boys: if there are 56 girls, what is the number of boys? WRITTEN EXERCISES. 1. From 800000 take 238. 2. From forty million take eighty thousand. 3. A nursery contains 705 peach trees and 428 plum trees: how many more peach trees than plum trees in it? 4. The Pilgrims landed at Plymouth in 1620, and our National Independence was declared in 1776: how many years between the two events? 5. The first steam-boat was made in 1807, and the Atlantic Cable was laid in 1866: how many years between the two events? 6. Mont Blanc in Europe is 15668 feet high, and Mount Sorata in South America is 21286 feet high: what is the difference in the height of these two mountains? 7. A man who owned 3408 sheep, sold 1897 of them how many sheep had he left? : 8. Mt. Etna is 10874 feet high, and Mt. Vesuvius 3948 feet: how much higher is Etna than Vesuvius? 9. America was discovered in 1492, and the Pilgrims landed at Plymouth in 1620: how many years intervened? 10. The population of the State of New York in 1860 was 3881000, and that of Ohio, 2340000: how many more people in New York than in Ohio? LESSON V. REVIEW. 1. From a cask containing 45 gallons of molasses, 39 gallons were sold: how many gallons remained unsold? 2. An orchard contains 56 apple trees and 48 peach trees: how many more apple trees than peach trees in the orchard? 3 A grocer sold 57 pounds of butter from a firkin containing 65 pounds: how many pounds remained in the firkin? 4. In a school, 63 pupils are enrolled and 54 are present: how many pupils are absent? 5. If a man earn $45 a month, and spend $36, how much does he lay up? 6. A man gave $75 for a watch and $22 for a chain: how much did the watch cost more than the chain? 7. Charles has 17 marbles and John 8: how many more marbles has Charles than John? 8. A teacher asked his class 52 questions, and 8 were answered incorrectly: how many were answered correctly? 9 In a term of 64 days, Charles attended school 55 days: how many days was he absent? back to 3. 10. Subtract by 4's from 62 back to 2. back to 5. WRITTEN EXERCISES. 1. From 202380 take 165436. 2. 4308560 1674805 how many? 3. Illinois contains 55409 square miles, and Missouri 67380: how much more area has Missouri than Illinois? 4. By the census of 1850 the entire population of the United States was 23191876, and by the census of 1860 it was 31224885: what was the increase in 10 years? 5. In 1862 there were 10869 miles of railroad in Great Britain, and 33222 miles in the United States: how many more miles in the United States than in Great Britain? 6. An army of 30340 men lost 7568 in battle: how many men did it then contain? 7. In 1862 Ohio produced 35442858 pounds of butter and 20637235 pounds of cheese: how much more butter than cheese was produced? 8. A merchant having $11315 in bank, drew out $978: how much remained in the bank? DEFINITIONS, PRINCIPLES, AND RULE. Art. 29. Subtraction is the process of finding the difference between two numbers. The Difference or Remainder is the number found by subtracting one number from another. The Minuend is the number diminished. The Subtrahend is the number subtracted. Art. 30. Only Like Numbers can be subtracted. Three pencils can not be subtracted from 7 books, nor 3 units from 7 tens. Art. 31. The Sign of Subtraction is It is read minus or less. It shows that the number after it is to be subtracted from the number before it. Art. 32. RULE FOR SUBTRACTION—1. Write the subtrahend under the minuend, placing units under units, tens under tens, hundreds under hundreds, etc. 2. Begin at the right, and subtract each term of the subtrahend from the term above it, and write the difference underneath. |