Solving a Complex Arithmetic Expression
To solve the expression given in the image, follow the order of operations, commonly remembered by the acronym PEMDAS (parentheses, exponents, multiplication and division from left to right, and addition and subtraction from left to right).
The expression to solve is:
\[ 4 \times \frac{10 - 27 \times 2}{1+1 \times 5} \div \frac{6}{3} \]
Step 1: Solve multiplication and divisions as they appear from left to right.
For the numerator of the fraction:
\[ 27 \times 2 = 54 \]
Step 2: Continue with the subtraction in the numerator and the addition in the denominator:
For the numerator:
\[ 10 - 54 = -44 \]
For the denominator:
\[ 1 + 1 \times 5 = 1 + 5 = 6 \]
Step 3: Now you have the fraction:
\[ 4 \times \frac{-44}{6} \]
However, the division by 6 is not finished yet. At this point, divide 6 into the numerator -44:
\[ \frac{-44}{6} = -\frac{44}{6} = -\frac{22}{3} \]
Step 4: Now multiply 4 by the result of the fraction:
\[ 4 \times -\frac{22}{3} \]
Divide 4 by 3 before multiplying to simplify the computation:
\[ \frac{4}{3} \times -22 = -\frac{88}{3} \]
Step 5: Solve the division by the fraction \(\frac{6}{3}\):
\[ \frac{6}{3} = 2 \]
Step 6: Now put together the multiplication and the division:
\[ -\frac{88}{3} \div 2 = -\frac{88}{3} \times \frac{1}{2} = -\frac{88}{6} \]
Step 7: Simplify the fraction by dividing both the numerator and the denominator by 2:
\[ -\frac{88}{6} = -\frac{44}{3} \]
Thus, the answer to the given expression is:
\[ -\frac{44}{3} \]
or in decimal form:
\[ -14.67 \] (rounded to two decimal places)
