Solving -7+[-5+2 X (3-8x5)] - (-3) (-1) +9 A Step-by-Step Guide
Hey guys! Ever stumbled upon a mathematical expression that looks like it belongs in a cryptic puzzle? Well, today we're diving headfirst into one such enigma: -7+[-5+2 x (3-8x5)] - (-3) (-1) +9. Buckle up, because we're about to embark on a mathematical expedition where we'll dissect this beast, unravel its secrets, and emerge victorious with the correct answer. Think of it as a treasure hunt, but instead of gold, we're chasing numerical enlightenment.
Decoding the Order of Operations: Our Treasure Map
Before we even think about crunching numbers, we need to arm ourselves with the golden rule of mathematical expeditions: the order of operations. This isn't just some arbitrary set of instructions; it's our treasure map, guiding us through the maze of parentheses, exponents, multiplication, division, addition, and subtraction. Remember the acronym PEMDAS (or BODMAS, depending on where you're from)? It's our trusty compass, ensuring we don't get lost in the numerical wilderness.
PEMDAS: Our Guiding Star
- Parentheses (or Brackets): These are our first priority. We tackle everything inside the parentheses before moving on.
- Exponents (or Orders): Next up are exponents. Think of them as mathematical power-ups.
- Multiplication and Division: These guys are on equal footing. We work from left to right, like reading a sentence.
- Addition and Subtraction: Just like multiplication and division, these are also equal partners. We move from left to right.
With our treasure map in hand, let's zoom in on our mathematical expression and start our descent.
Navigating the Labyrinth: Step-by-Step Solution
Our quest begins with the innermost sanctum of our expression: -7+[-5+2 x (3-8x5)] - (-3) (-1) +9. Let's break it down piece by piece, like a master puzzle solver.
1. The Innermost Parentheses: (3 - 8 x 5)
According to PEMDAS, we start with the parentheses. But hold on! There's more than one operation inside. We have subtraction and multiplication vying for our attention. Multiplication wins the day, so we tackle 8 x 5 first.
- 8 x 5 = 40
Now our parentheses look a little simpler: (3 - 40).
- 3 - 40 = -37
We've conquered the innermost parentheses! Our expression is starting to look less intimidating: -7+[-5+2 x (-37)] - (-3) (-1) +9.
2. The Brackets: [-5 + 2 x (-37)]
Next up are the brackets, which are just parentheses in disguise. Inside, we have addition and multiplication. Multiplication takes precedence once again.
- 2 x (-37) = -74
Now our brackets are feeling the heat: [-5 + (-74)].
- -5 + (-74) = -79
We've cleared another hurdle! Our expression is slimming down: -7 + (-79) - (-3) (-1) + 9.
3. Multiplication: (-3) (-1)
Now we spot some multiplication lurking outside the parentheses. Let's deal with it.
- (-3) x (-1) = 3
Remember, a negative times a negative equals a positive! Our expression is morphing into something much more manageable: -7 + (-79) - 3 + 9.
4. Addition and Subtraction: The Final Stretch
We've reached the home stretch! All that's left is addition and subtraction. We work from left to right, just like reading a book.
- -7 + (-79) = -86
- -86 - 3 = -89
- -89 + 9 = -80
We've done it! We've navigated the labyrinth and arrived at our destination.
The Grand Finale: -80 is Our Treasure!
After our exhilarating mathematical journey, we've finally unearthed the answer: -80. It might have looked like a daunting challenge at first, but by following the order of operations and taking it step by step, we conquered the expression and claimed our numerical treasure. Remember, guys, every complex problem is just a series of smaller, manageable steps. Keep your treasure map (PEMDAS) handy, and you'll be solving mathematical mysteries in no time!
Why is Order of Operations Crucial? Mastering PEMDAS/BODMAS
You might be wondering,