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

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ScanSolve AI Tutor · Accepted Answer

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

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

Step-by-step solution

Part a· 2 steps

Express 0 and 1 as fractions with a common denominator greater than 12.

List twelve fractions between $\frac{0}{13}$ and $\frac{13}{13}$ .

Part b· 2 steps

Express 4 and 5 as fractions with a common denominator greater than 12.

List twelve fractions between $\frac{52}{13}$ and $\frac{65}{13}$ .

Part c· 2 steps

Express $-3$ and $-4$ as fractions with a common denominator greater than 12.

List twelve fractions between $-\frac{52}{13}$ and $-\frac{39}{13}$ .

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