Ex. 2. What is the difference between 7372 and 3454? In Ex. 2, we cannot take 4 units from 2 units, then we say 4 from 12 (10+2) and 8 remain Carry 1 to 5, 6, now, 6 from 7 and 1 remains; 4 from 3, we cannot, but 4 from 13 and 9 remain; carry 1 to 3 make 4, 4 from 7 and 3. 7372 3454 3918 Ans. 22. REASON-The reason of the rule is obvious, and depends on the fact, that the difference of the corresponding parts of two numbers is equal to the difference of the numbers themselves. If we wish to take 59 from 161, we can say 161-150+11 and 59 50+9, hence we have (see note 2 at the end of the work) 23. PROOF.-I. Add the remainder to the smaller number, and the sum will be equal to the greater. Explanation. 161 = 150+11 102 50+ 9 100+2=102 II. Subtract the answer from the greater number, and the remainder will be equal to the less. The sign of Subtraction is, thus, 10-6=4, read 10 minus 6=4, and denotes that the number after the sign is to be taken from the number which precedes it. (5) 69086 760043 47979 569978 (1) From 78069 (2) (3) 86004 496736 19363 279687 (4) 24. How much is the highest peak of the Himalayas higher than the Alps, the former being 29002, the latter 15789 feet? Ans. 13213 feet. 25. From ten thousand and eleven take ninety-seven ? Ans. 9914. 26. How many years from the Norman Conquest, 1066, to the present time, 1860? Ans. 794 years. 27. How long is it since the subjugation of Ireland, 1172, and since the passing of Magna Charta, 1215? Ans. 668 and 645. 24. MULTIPLICATION is a short method of Addition when the addends are all alike. When the addends are all the same it is only necessary to set down one of them, now called the MULTIPLICAND, or number to be multiplied. The number showing how many addends are to be taken is called the MULTIPLIER. The answer, or what we have called the sum in Addition, is called the PRODUCT. The following example will sufficiently illustrate these definitions. Ex. 1 Multiply 7 by 4, in other words, add 7 four times? By Addition. 7+7+7+7=28 Ans. By Multiplication, 7×4 (read, 7 multiplied by 4) =28 7 is the multiplicand, 4 the multiplier, and 28 the product. 25. The numbers 7 and 4, which are multiplied together are also called factors, in reference to the product. Proof. The sign X implies that the numbers between which it is placed are to be multiplied. 26. The multiplier and multiplicand may change places, without affecting the product, since 7 times 4 4 times 7. SIMPLE MULTIPLICATION is confined to the same kind of quantities as Simple Addition. 2 3 4 5 6 7 8 9 10 11 12 13 19 taken, and nothing more. always indicates the number of times the multiplicand is to be The multiplier must invariably be an abstract number, as it MULTIPLICATION TABLE. 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 90 100 110 120 130 140 150 160 170 180 190 2 6 12 18 88 24. MULTIPLICATION is a short method of Addition when the addends are all alike. When the addends are all the same it is only necessary to set down one of them, now called the MULTIPLICAND, or number to be multiplied. The number showing how many addends are to be taken is called the MULTIPLIER. The answer, or what we have called the sum in Addition, is called the PRODUCT. The following example will sufficiently illustrate these definitions. Ex. 1 Multiply 7 by 4, in other words, add 7 four times? By Addition. 7+7+7+7=28 Ans. By Multiplication, 7×4 (read, 7 multiplied by 4)=28 7 is the multiplicand, 4 the multiplier, and 28 the product. 25. The numbers 7 and 4, which are multiplied together are also called factors, in reference to the product. Proof. The sign X implies that the numbers between which it is placed are to be multiplied. 26. The multiplier and multiplicand may change places, without affecting the product, since 7 times 4 4 times 7. = SIMPLE MULTIPLICATION is confined to the same kind of quantities as Simple Addition. |