Math Problem Statement

Write an equivalent expression for the expression: b/2 + b/2

Solution

The given expression is:

b2+b2\frac{b}{2} + \frac{b}{2}

To simplify this, notice that both terms have the same denominator. So, you can combine them:

b2+b2=b+b2=2b2\frac{b}{2} + \frac{b}{2} = \frac{b + b}{2} = \frac{2b}{2}

Now, simplify the fraction:

2b2=b\frac{2b}{2} = b

Thus, the equivalent expression is simply b.

Explanation: Since the two terms have the same denominator, they can be combined by adding their numerators. This results in the expression 2b2\frac{2b}{2}, which simplifies to bb.

Would you like further details or have any other questions?

Here are five related questions:

  1. What happens if the denominators are not the same?
  2. How would you handle a case like b3+b4\frac{b}{3} + \frac{b}{4}?
  3. How do you combine fractions with different variables?
  4. Can you subtract two fractions like b2b2\frac{b}{2} - \frac{b}{2}? What is the result?
  5. How can you generalize this process for combining more than two fractions?

Tip: Always check if terms in fractions have the same denominator before adding or subtracting them!

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Math Problem Analysis

Mathematical Concepts

Algebra
Simplification of fractions

Formulas

Addition of fractions with the same denominator
Simplification of expressions

Theorems

Basic fraction addition theorem

Suitable Grade Level

Grades 6-8