This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Here are the rational numbers written in their standard form: a) Given fraction: (-36)/(-63) Step 1: Simplify the signs. (-36)/(-63) = (36)/(63) Step 2: Find the greatest common divisor (GCD) of 36 and 63. The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, 36. The factors of 63 are 1, 3, 7, 9, 21, 63. The GCD of 36 and 63 is 9. Step 3: Divide both the numerator and the denominator by their GCD. (36 ÷ 9)/(63 ÷ 9) = (4)/(7) The standard form is (4)/(7). b) Given fraction: (-12)/(30) Step 1: The denominator is already positive. Step 2: Find the GCD of 12 and 30. The factors of 12 are 1, 2, 3, 4, 6, 12. The factors of 30 are 1, 2, 3, 5, 6, 10, 15, 30. The GCD of 12 and 30 is 6. Step 3: Divide both the numerator and the denominator by their GCD. (-12 ÷ 6)/(30 ÷ 6) = (-2)/(5) The standard form is (-2)/(5). c) Given fraction: (24)/(-64) Step 1: Make the denominator positive by multiplying both the numerator and the denominator by -1. (24)/(-64) = (24 × (-1))/(-64 × (-1)) = (-24)/(64) Step 2: Find the GCD of 24 and 64. The factors of 24 are 1, 2, 3, 4, 6, 8, 12, 24. The factors of 64 are 1, 2, 4, 8, 16, 32, 64. The GCD of 24 and 64 is 8. Step 3: Divide both the numerator and the denominator by their GCD. (-24 ÷ 8)/(64 ÷ 8) = (-3)/(8) The standard form is (-3)/(8). d) Given fraction: (-14)/(49) Step 1: The denominator is already positive. Step 2: Find the GCD of 14 and 49. The factors of 14 are 1, 2, 7, 14. The factors of 49 are 1, 7, 49. The GCD of 14 and 49 is 7. Step 3: Divide both the numerator and the denominator by their GCD. (-14 ÷ 7)/(49 ÷ 7) = (-2)/(7) The standard form is (-2)/(7). Send me the next one 📸