Math Problem Statement

Simplify the mathematical expression: \( \frac{\frac{\sqrt{2}}{2}}{\frac{\sqrt{2}}{2}} \times \frac{\sqrt{2}}{\sqrt{2}} \).

Solution

The expression shown is:

2222×22\frac{\frac{\sqrt{2}}{2}}{\frac{\sqrt{2}}{2}} \times \frac{\sqrt{2}}{\sqrt{2}}

Let's simplify this step by step:

  1. Simplify the fraction:

    2222=1\frac{\frac{\sqrt{2}}{2}}{\frac{\sqrt{2}}{2}} = 1

  2. The next part 22\frac{\sqrt{2}}{\sqrt{2}} also simplifies to 1.

So, the entire expression simplifies to:

1×1=11 \times 1 = 1

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Math Problem Analysis

Mathematical Concepts

Fractions
Radicals
Simplification

Formulas

Simplification of fractions: \( \frac{a}{a} = 1 \) when \( a \neq 0 \)
Simplification of radicals: \( \frac{\sqrt{a}}{\sqrt{a}} = 1 \) when \( a > 0 \)

Theorems

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Suitable Grade Level

Grades 6-8