Answer:
−[−1 1/5 ÷ 0.6(1.3)] − 5/6
First, let's simplify the expression within the square brackets:
−1 1/5 ÷ 0.6(1.3)
To simplify this, let's convert the mixed number to an improper fraction:
−6/5 ÷ 0.6(1.3)
Next, we multiply 0.6 by 1.3:
−6/5 ÷ 0.78
To divide fractions, we can multiply by the reciprocal:
−6/5 * (1/0.78)
Now, let's multiply the numerators and denominators:
-6/5 * 1/0.78 = -6/5 * 1/0.78 = -6/3.9
To simplify this fraction, we can multiply both the numerator and denominator by 10 to eliminate the decimal:
-6/3.9 * 10/10 = -60/39
Now, let's simplify the expression further:
−60/39 − 5/6
To add or subtract fractions, we need a common denominator. In this case, the least common multiple (LCM) of 39 and 6 is 78:
−60/39 − 5/6 = −(60/39 * 2/2) − 5/6 = −120/78 − 5/6
Now, we can combine the fractions:
−120/78 − 5/6 = (−120 * 6)/(78 * 6) − 5/6 = −720/468 − 5/6
To subtract the fractions, we need a common denominator:
−720/468 − 5/6 = −720/468 − (5 * 78)/(6 * 78) = −720/468 − 390/468
Now, we can combine the fractions:
−720/468 − 390/468 = (−720 − 390)/468 = −1110/468
To simplify the fraction, we can divide both the numerator and denominator by their greatest common divisor, which is 78:
−1110/468 = (−1110 ÷ 78)/(468 ÷ 78) = −15/6
The simplified fraction is −15/6.
However, the question asks for the value as a simplified mixed number. To convert the fraction to a mixed number, we divide the numerator by the denominator:
−15 ÷ 6 = −2 remainder 3
Therefore, the value of the expression is -2 3/6, which can be further simplified as -2 1/2.
So, the value of the expression is -2 1/2.
Step-by-step explanation: