22. What is the greatest common divisor of 48, 84, and 90? 2148 84 90 324 42 45 8 14 15 2x3=6, the g. c. d. When the g. c. d. is not readily found by inspection, use this method. Arrange the numbers in a row and successively divide them by any number that will exactly divide all of them. Repeat the process with the resulting quotients. Continue the division until there is no number that will exactly divide all of the quotients. The product of the several divisors is the greatest common divisor. 2 and 3 are common divisors of all the numbers. Their product, 6, is the greatest common divisor of the numbers. Find the greatest common divisor of: A multiple of a number is a number obtained by using that number as a factor. Thus, 2, 4, 6, 8, 10, etc., are multiples of 2. 1. Name some multiples of 3. 2. Name some multiples of both 2 and 3. Since 6, 12, 18 are multiples of both 2 and 3, they are common multiples of 2 and 3. A number that is a multiple of two or more numbers is a common multiple of the numbers. The least multiple common to two or more numbers is their least common multiple (1. c. m.). Name the least common multiple of: 11. Find the least common multiple of 8, 10, and 12. 28 10 10 12 2 5 24 5 6 2 × 2 × 2 × 5 × 3 = 120 When the least common multiple is not readily seen, use this method. Divide the numbers by any factor common to two or more of them. Continue the division of the resulting quotients until no two of them have a common factor. The divisors and the remaining quotients are the factors of the least common multiple. Find, in the easiest way possible, the least common Operations in arithmetic are indicated by signs. The signs most commonly used are +, −, ×, ÷. When several operations are indicated in the same expression, operations indicated by x and are performed before operations indicated by + and Thus, in 8+ 6 × 2, first multiply 6 by 2, and then add their product to 8. 8+6x2=8+12=20. 23. Which is larger, 10+ 10+10 or 10-10 ÷ 10? 24. Show that 42+ 6+ 7 is equal to 42-7 x 4. 25. What is the value of 4×5+6x7-8÷4? 26. What is the sum of 66 ÷ 6 + 5 and 66 5 x 10? 27. What is the product of 8+ 56 ÷ 8 and 56 - 12 × 4? x 28. How many times is 32÷8+5 contained in 32+ 8 x 5? CANCELLATION 1. Divide 7 × 8 × 12 by 4 × 6. 2 2 7 × 8 × 12 2. What factors are common to both dividend and divisor? 3. Does striking out or canceling equal factors from both dividend and divisor affect the quotient? 5. 24 x 15 x 6 by 8 × 5 × 3 9. 36 × 32 × 16 by 24 × 3 × 8 10. 64 × 35 × 42 × 40 by 8 × 56 × 12 × 10 11. 72 x 81 x 45 x 28 by 90 × 144 × 63 Beginning with any number in the margin and going in either direction, rapidly add the numbers until 100 or any given number is reached. Beginning with 100 or any given number, rapidly subtract the successive numbers. 9 4 12 7 20 15 8 6 10 8 31 7 10 6 11 8 FRACTIONS A unit is a single thing; as 1 apple. A fraction is one or more of the equal parts of a unit; as of an apple. of an apple means that an apple has been divided into 4 equal parts and 3 of these parts taken. In a fraction: (1) The figure below the line is the denominator; it denominates or names the number of equal parts into which the unit is divided; it is the namer. (2) The figure above the line is the numerator; it numerates or tells the number of parts taken; it is the numberer. The numerator and denominator are the terms of the fraction. 1. In the fraction : What does it show? 2. Read aloud and tell what the terms of each fraction show: 1. Which do you prefer, of a dollar or of a dollar ? § of a pound of candy or å of a pound of candy? 2. Are and alike in form? Are they alike in value ? |