https://file.aiquickdraw.com/mathbot/file/1725694932861bhkbd476.jpg

The expression in the image is:

\[
\frac{2(7 + 2 \times 3) + 2}{\frac{1}{4}}
\]

Let's break it down step by step.

### Step 1: Evaluate the parentheses.
Inside the parentheses, you have:
\[
7 + 2 \times 3
\]
According to the order of operations (PEMDAS/BODMAS), you first multiply:
\[
2 \times 3 = 6
\]
So the expression inside the parentheses becomes:
\[
7 + 6 = 13
\]

### Step 2: Simplify the numerator.
Now substitute this back into the original expression:
\[
2(13) + 2 = 26 + 2 = 28
\]

### Step 3: Simplify the denominator.
The denominator is \(\frac{1}{4}\).

### Step 4: Divide the numerator by the denominator.
Dividing by \(\frac{1}{4}\) is the same as multiplying by 4:
\[
\frac{28}{\frac{1}{4}} = 28 \times 4 = 112
\]

So, the value of the expression is:
\[
\boxed{112}
\]

Do you want any further details or explanations on this? 

Here are 5 related questions to explore:
1. What is the general order of operations (PEMDAS/BODMAS) in mathematics?
2. How do you handle expressions with multiple fractions?
3. How would the result change if a different number replaced \(2 \times 3\) inside the parentheses?
4. What happens if the fraction in the denominator was flipped?
5. How can this expression be rewritten with all multiplication shown explicitly?

**Tip:** When dividing by a fraction, remember that dividing by \(\frac{a}{b}\) is the same as multiplying by \(\frac{b}{a}\).

Simplify the expression 2(7 + 2 × 3) + 2 divided by 1/4.

Learn how to simplify the expression 2(7 + 2 × 3) + 2 divided by 1/4 with step-by-step guidance. This problem demonstrates the use of order of operations and division by fractions, ideal for students in Grades 6-8.

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