Express each of the following rational numbers in the form of (a)/(b) where a and b are integers and b != 0.

Here's the continuation of the solutions. 1. Express each of the following rational numbers in the form of (a)/(b) where a and b are integers and b ≠ 0. j) 0.123 Step 1: Let x be the repeating decimal. x = 0.1232323... Step 2: Multiply by 10 to shift the decimal just before the repeating block. 10x = 1.232323... Step 3: Multiply by 1000 to shift the decimal past one repeating block and the non-repeating digit. 1000x = 123.232323... Step 4: Subtract the equation from Step 2 from the equation in Step 3. 1000x - 10x = 123.232323... - 1.232323... 990x = 122 Step 5: Solve for x and simplify the fraction. x = (122)/(990) = (122 ÷ 2)/(990 ÷ 2) = (61)/(495) (61)/(495) 2. List twelve rational numbers which lie between: a) 1 and 0 Step 1: Express 0 and 1 as fractions with a common denominator greater than 12. We can use 13. 0 = (0)/(13) 1 = (13)/(13) Step 2: List twelve fractions between (0)/(13) and (13)/(13). (1)/(13), (2)/(13), (3)/(13), (4)/(13), (5)/(13), (6)/(13), (7)/(13), (8)/(13), (9)/(13), (10)/(13), (11)/(13), (12)/(13) b) 4 and 5 Step 1: Express 4 and 5 as fractions with a common denominator greater than 12. We can use 13. 4 = (4 × 13)/(13) = (52)/(13) 5 = (5 × 13)/(13) = (65)/(13) Step 2: List twelve fractions between (52)/(13) and (65)/(13). (53)/(13), (54)/(13), (55)/(13), (56)/(13), (57)/(13), (58)/(13), (59)/(13), (60)/(13), (61)/(13), (62)/(13), (63)/(13), (64)/(13) c) -3 and -4 Step 1: Express -3 and -4 as fractions with a common denominator greater than 12. We can use 13. -4 = -(4 × 13)/(13) = -(52)/(13) -3 = -(3 × 13)/(13) = -(39)/(13) Step 2: List twelve fractions between -(52)/(13) and -(39)/(13). Remember that for negative numbers, a smaller absolute value means a larger number. -(51)/(13), -(50)/(13), -(49)/(13), -(48)/(13), -(47)/(13), -(46)/(13), -(45)/(13), -(44)/(13), -(43)/(13), -(42)/(13), -(41)/(13), -(40)/(13) That's 2 down. 3 left today — send the next one.