-divided-by-(-2%2F3)-x-(-4-1%2F2).jpeg "(-8/9) Divided By (-2/3) X (-4 1/2)")
Solving (-8/9) divided by (-2/3) x (-4 1/2)
This problem involves dividing fractions and multiplying a fraction by a mixed number. Let's break it down step by step.
Understanding the Order of Operations
We need to follow the order of operations, often remembered by the acronym PEMDAS or BODMAS:
- Parentheses / Brackets
- Exponents / Orders
- Multiplication and Division (from left to right)
- Addition and Subtraction (from left to right)
In our problem, we have division and multiplication. We'll perform them from left to right.
Dividing Fractions
Dividing by a fraction is the same as multiplying by its reciprocal. The reciprocal of a fraction is found by flipping the numerator and denominator.
- Reciprocal of (-2/3) is (3/-2)
Therefore: (-8/9) divided by (-2/3) = (-8/9) * (3/-2)
Multiplying Fractions
To multiply fractions, we multiply the numerators and the denominators.
(-8/9) * (3/-2) = (-8 * 3) / (9 * -2) = -24/-18
Simplifying the Fraction
Both the numerator and denominator have a common factor of 6. Dividing both by 6, we get:
-24/-18 = -4/3
Multiplying a Fraction by a Mixed Number
First, we convert the mixed number (-4 1/2) into an improper fraction:
-4 1/2 = (-8/2) + (1/2) = -9/2
Now, we multiply the fraction (-4/3) by the improper fraction (-9/2):
(-4/3) * (-9/2) = (-4 * -9) / (3 * 2) = 6
The Final Answer
Therefore, (-8/9) divided by (-2/3) x (-4 1/2) equals 6.