Add the following rational numbers: a) -2/5 and 4/5, b) -7/3 and 1/3, c) -11/8 and 5/8, d) -6/11 and -4/11, e) 5/6 and -1/6, f) [omitted]

Here are the solutions to your addition problems: 1. Add the following rational numbers: a) (-2)/(5) and (4)/(5) Step 1: Add the numerators since the denominators are the same. (-2)/(5) + (4)/(5) = (-2+4)/(5) Step 2: Simplify the numerator. = (2)/(5) The sum is (2)/(5). b) (-7)/(3) and (1)/(3) Step 1: Add the numerators. (-7)/(3) + (1)/(3) = (-7+1)/(3) Step 2: Simplify the numerator. = (-6)/(3) Step 3: Simplify the fraction. = -2 The sum is -2. c) (-11)/(8) and (5)/(8) Step 1: Add the numerators. (-11)/(8) + (5)/(8) = (-11+5)/(8) Step 2: Simplify the numerator. = (-6)/(8) Step 3: Simplify the fraction by dividing the numerator and denominator by 2. = (-3)/(4) The sum is (-3)/(4). d) (-6)/(11) and (-4)/(11) Step 1: Add the numerators. (-6)/(11) + (-4)/(11) = (-6-4)/(11) Step 2: Simplify the numerator. = (-10)/(11) The sum is (-10)/(11). e) (5)/(6) and (-1)/(6) Step 1: Add the numerators. (5)/(6) + (-1)/(6) = (5-1)/(6) Step 2: Simplify the numerator. = (4)/(6) Step 3: Simplify the fraction by dividing the numerator and denominator by 2. = (2)/(3) The sum is (2)/(3). f) (-17)/(15) and (-1)/(15) Step 1: Add the numerators. (-17)/(15) + (-1)/(15) = (-17-1)/(15) Step 2: Simplify the numerator. = (-18)/(15) Step 3: Simplify the fraction by dividing the numerator and denominator by 3. = (-6)/(5) The sum is (-6)/(5). 2. Add the following rational numbers: a) (3)/(4) and (-3)/(5) Step 1: Find the least common multiple (LCM) of the denominators 4 and 5, which is 20. Step 2: Convert the fractions to equivalent fractions with the common denominator. (3)/(4) + (-3)/(5) = (3 × 5)/(4 × 5) + (-3 × 4)/(5 × 4) = (15)/(20) + (-12)/(20) Step 3: Add the numerators. = (15-12)/(20) Step 4: Simplify the numerator. = (3)/(20) The sum is (3)/(20). b) (5)/(8) and (-7)/(12) Step 1: Find the LCM of 8