Math  /  Numbers & Operations

QuestionEvaluate 753(4+12÷2)23+275-\frac{3(4+12 \div 2)^{2}}{3+2} by order of

Studdy Solution

STEP 1

What is this asking? We need to calculate the value of a long expression with parentheses, exponents, division, addition, and subtraction, respecting the order of operations. Watch out! It's easy to mess up the order of operations, so we need to be super careful and follow PEMDAS/BODMAS!

STEP 2

1. Simplify Inside Parentheses
2. Exponent Calculation
3. Numerator Calculation
4. Denominator Calculation
5. Fraction Calculation
6. Final Subtraction

STEP 3

Alright, let's **start** with the innermost parentheses: 4+12÷24 + 12 \div 2.
Remember PEMDAS/BODMAS!
Division comes before addition.
So, 12÷2=612 \div 2 = 6.
Now we have 4+64 + 6, which equals **10**.

STEP 4

So, the expression becomes 753(10)23+275 - \frac{3(10)^{2}}{3+2}.
Much cleaner, right?

STEP 5

Now, we handle the **exponent**. 10210^2 means 101010 \cdot 10, which is **100**.
Our expression now looks like 7531003+275 - \frac{3 \cdot 100}{3+2}.

STEP 6

Let's tackle the **numerator**: 3100=3003 \cdot 100 = \textbf{300}.
So, we have 753003+275 - \frac{300}{3+2}.

STEP 7

The **denominator** is simple: 3+2=53 + 2 = \textbf{5}.
Now, our expression is 75300575 - \frac{300}{5}.

STEP 8

Now, we divide the **numerator** by the **denominator**: 3005\frac{300}{5}.
Think of it as how many times 5 goes into 300.
That's **60**!
Our expression is now 756075 - 60.
Almost there!

STEP 9

Finally, we subtract: 7560=1575 - 60 = \textbf{15}.
We did it!

STEP 10

The value of the expression 753(4+12÷2)23+275-\frac{3(4+12 \div 2)^{2}}{3+2} is **15**.

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