Math Problem Statement

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

Solution

The expression in the image is:

2(7+2×3)+214\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+2×37 + 2 \times 3 According to the order of operations (PEMDAS/BODMAS), you first multiply: 2×3=62 \times 3 = 6 So the expression inside the parentheses becomes: 7+6=137 + 6 = 13

Step 2: Simplify the numerator.

Now substitute this back into the original expression: 2(13)+2=26+2=282(13) + 2 = 26 + 2 = 28

Step 3: Simplify the denominator.

The denominator is 14\frac{1}{4}.

Step 4: Divide the numerator by the denominator.

Dividing by 14\frac{1}{4} is the same as multiplying by 4: 2814=28×4=112\frac{28}{\frac{1}{4}} = 28 \times 4 = 112

So, the value of the expression is: 112\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 2×32 \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 ab\frac{a}{b} is the same as multiplying by ba\frac{b}{a}.

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Math Problem Analysis

Mathematical Concepts

Order of Operations
Arithmetic Operations
Division by Fractions

Formulas

PEMDAS/BODMAS
Division by a Fraction

Theorems

Basic Arithmetic Theorems

Suitable Grade Level

Grades 6-8