Final answer:
The given expression 2/5(a-c) + b evaluates to -1 22/75 when substituting a = 2/3, b = -1.2, and c = 0.9. The steps involve fraction subtraction, multiplication, and addition to reach the final mixed number.
Step-by-step explanation:
To evaluate the expression 2/5(a-c) + b with given values
a = 2/3,
b = -1.2, and
c = 0.9, we first substitute the values into the expression.
- Calculate a - c: (2/3) - 0.9 = (2/3) - (9/10)
- Find a common denominator and subtract the two fractions: (20/30) - (27/30) = -7/30
- Multiply by 2/5: (2/5) * (-7/30) = -14/150 = -7/75 after simplifying
- Add b: -7/75 + (-1.2) or -7/75 + (-6/5)
- Convert -6/5 to a fraction with a denominator of 75: -90/75
- Add the fractions: -7/75 + (-90/75) = -97/75
- Convert to a mixed number: -1 22/75
Therefore, the evaluation of the expression 2/5(a-c) + b with the given values is -1 22/75.