%2F(-2%2F3)x(-4-1%2F2).jpeg "(-8/9)/(-2/3)x(-4 1/2)")
Solving the Expression: (-8/9)/(-2/3)x(-4 1/2)
This article will guide you through solving the expression (-8/9)/(-2/3)x(-4 1/2). We will break down the steps and explain the concepts involved.
Understanding the Order of Operations
Before we dive into the calculations, let's remember the order of operations, commonly known as PEMDAS or BODMAS:
- Parentheses ( Brackets)
- Exponents ( Orders)
- Multiplication and Division (from left to right)
- Addition and Subtraction (from left to right)
Step 1: Division of Fractions
The first part of the expression is (-8/9)/(-2/3). Dividing by a fraction is the same as multiplying by its reciprocal. Therefore:
(-8/9)/(-2/3) = (-8/9) * (-3/2)
Now, we multiply the numerators and the denominators:
(-8/9) * (-3/2) = 24/18
We can simplify this fraction by dividing both numerator and denominator by their greatest common factor, which is 6:
24/18 = 4/3
Step 2: Multiplication with a Mixed Number
The next step is to multiply the result from step 1 by -4 1/2. First, we need to convert the mixed number into an improper fraction:
-4 1/2 = (-4 * 2 + 1) / 2 = -9/2
Now, we multiply the fraction 4/3 by -9/2:
(4/3) * (-9/2) = -36/6
Step 3: Simplifying the Result
Finally, we simplify the fraction by dividing both numerator and denominator by their greatest common factor, which is 6:
-36/6 = -6
Conclusion
Therefore, the solution to the expression (-8/9)/(-2/3)x(-4 1/2) is -6. By carefully following the order of operations and applying the rules for fractions, we were able to arrive at the correct answer.