EXAMPLE 1. Multiply 62 by 68. 7×6= 42, the first two figures in the answer; therefore 62 times 68 is 4216. EXAMPLE 2. Multiply 24 by 26. 3 x 2 = 6, the first figure in the answer; therefore 24 times 26 is 624. EXAMPLE 3. Multiply 69 by 61. 7x6 = 42, the first figures in the answer; therefore 69 times 61 is 4209. To Multiply by 11. One or the other of the following cases can be used. Using the above rule find the following indicated products: CASE II. When the number consists of two figures whose sum is 10 or more. Rule. (1) Place the right-hand figure of the number as the right-hand figure of the answer. (2) Add the figures of the number and place the righthand figure of the sum in the tens' place. (3) Add the other figure of this sum to the left-hand figure of the number for the left-hand figure or figures of the answer. Using the above rule find the following indicated products: Division is the inverse of multiplication and is the process of finding the number of times one number is contained in another. In the statement "47 divided by 15 is 3,2," 47 is called the dividend, 15 is called the divisor, 3 is called the quotient, and 2 is the remainder. Check. mainder. EXAMPLE 3 quotient divisor 15)47 dividend 45 product of quotient and dividend 2 remainder Multiply the quotient by the divisor and add the reThe result is the dividend. Divisibility of Numbers. — It is an advantage to be able to tell at a glance whether a certain number will be contained in another an exact number of times. The following tests of divisibility are some of the most useful ones. 1. All even numbers are divisible by 2. 2. A number is divisible by 3 if the sum of its digits is divisible by 3. 3. A number is divisible by 4 if the number represented by the right-hand two digits is zero or is divisible by 4. 4. A number is divisible by 5 if it ends with a 5 or a 0. 5. A number is divisible by 6 if it is an even number and the sum of its digits is divisible by 3. 6. A number is divisible by 8 if the number represented by the right-hand three digits is divisible by 8. 7. A number is divisible by 9 if the sum of its digits is divisible by 9. 8. A number is divisible by 10 if it ends with a 0. 9. A number is divisible by 12 if it is divisible by 3 and 4. 10. A number is divisible by 11 if the difference between the sums of the odd-placed and even-placed digits is zero or is divisible by 11. Long Division. When all the steps in division are written down the process is called Long Division. Long division is generally used with divisors of two or more places. EXAMPLE 1 15918 46)7327 46 272 230 427 414 13 EXAMPLE 2 304 68)20675 Rule.—(1) Write the divisor at the left of the dividend. (2) Find how many times the divisor is contained in the smallest group of figures on the left of the dividend, that will contain it, and write the quotient over the right-hand figure of this group. (3) Multiply the divisor by this quotient and place the product under the group or partial dividend used. (4) Subtract this product, and to the remainder annex the next figure of the dividend. Treat the number so formed as a new partial dividend. EXAMPLE 3 3742 342)12745 204 1026 275 2485 272 2394 (5) If any partial dividend will not contain the divisor, write a zero in the quotient, then annex the next figure of the dividend, and proceed as before. (6) Divide as before, and continue the process until all the figures of the dividend have been used. (7) If there is a remainder after the last division, write it with the divisor under it as part of the quotient. Check. mainder. Multiply the quotient by the divisor and add the reThe result is the dividend. |