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Question
Evaluate.

−[−1 1/5÷0.6(1.3)]−5/6

What is the value of the expression?

Enter your answer as a simplified mixed number in the box.

User Robterrell
by
7.3k points

2 Answers

5 votes

Final answer:

To evaluate the expression, we simplify it step-by-step following the order of operations. The value of the expression is -4.61.

Step-by-step explanation:

To evaluate the expression, we follow the order of operations: parentheses, exponents, multiplication/division (from left to right), and addition/subtraction (from left to right).

Let's simplify the expression step-by-step:

-[−1 ÷ 1/5 × 0.6(1.3)] − 5/6

-[-1 ÷ 0.2 × 0.6(1.3)] − 5/6

-[-1 ÷ 0.2 × 0.78] − 5/6

-[-1 × 0.39] − 5/6

0.39 − 5/6

To subtract mixed numbers, we need to find a common denominator. The common denominator between 6 and 1 is 6.

0.39 × 6/6 − 5/6

2.34/6 − 5/6

0.39 - 5/6

Converting 5 to a fraction with a denominator of 6:

0.39 - 30/6

0.39 - 5

-4.61

Therefore, the value of the expression is -4.61.

User Jugal Thakkar
by
6.6k points
4 votes

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:

User Sven Bluege
by
7.0k points
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