Math Problem Statement

Evaluate this expression if a = 3 and b = 2: (4a - b) / (4 - b)

Solution

Let's evaluate the given expression step by step.

The expression is:

4ab4b\frac{4a - b}{4 - b}

We are given that a=3a = 3 and b=2b = 2.

Substituting these values into the expression:

4(3)242\frac{4(3) - 2}{4 - 2}

Simplifying the numerator:

4(3)=12122=104(3) = 12 \quad \Rightarrow \quad 12 - 2 = 10

Now simplify the denominator:

42=24 - 2 = 2

So, the expression becomes:

102=5\frac{10}{2} = 5

Thus, the number that belongs in the green box is 5.


Would you like further details or have any questions about this solution?

Here are 5 questions to expand your understanding:

  1. How does changing the values of aa and bb affect the result?
  2. What happens if b=4b = 4 in this expression?
  3. Can you explain the importance of simplifying both the numerator and the denominator separately?
  4. How would the result change if the expression were 4a+b4b\frac{4a + b}{4 - b}?
  5. How can you generalize this approach for more complex algebraic expressions?

Tip: Always simplify expressions step by step to avoid calculation errors, especially when dealing with multiple terms.

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Math Problem Analysis

Mathematical Concepts

Algebra
Substitution
Simplification

Formulas

(4a - b) / (4 - b)

Theorems

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Suitable Grade Level

Grades 6-8