Which fraction is not equivalent to 2/3?

Understand the Problem

The question is asking us to identify a fraction that does not hold the same value as 2/3. To solve this, we need to understand the concept of equivalent fractions and analyze given options to find one that does not match 2/3.

Answer

$ \frac{a}{b} $ where $ 2b \neq 3a $.

Steps to Solve

Understanding Equivalent Fractions

To find a fraction that does not equal $ \frac{2}{3} $, we must first recognize what equivalent fractions are. Equivalent fractions are different fractions that represent the same value.

Finding Non-Equivalent Fractions

To determine if a fraction is not equivalent to $ \frac{2}{3} $, we can cross-multiply. For a fraction $ \frac{a}{b} $, it is equivalent to $ \frac{2}{3} $ if $ 2b = 3a $. We will check this condition for various fractions.

Cross-Multiplication Example

Let’s denote the candidate fraction as $ \frac{a}{b} $. Then we check:

If $ 2b \neq 3a $, then $ \frac{a}{b} $ is not equivalent to $ \frac{2}{3} $.

Checking Suggested Fractions

Let’s analyze the suggested fractions one by one to see which ones do not satisfy the condition. Assume options are given, we apply the cross-multiplication rule to each.

Conclusion

After checking, we will conclude which fraction does not equal $ \frac{2}{3} $.

The fraction that does not hold the same value as $ \frac{2}{3} $ is whichever one fails the test $ 2b \neq 3a $ when evaluated.

More Information

Fractions can represent the same value but still look different. Understanding equivalent fractions helps to identify those that are not the same. This is crucial in simplifying problems in algebra, art, and real-life situations like cooking or finances.

Tips

Common mistakes include:

Assuming that simply having different numerators and denominators means the fractions are not equivalent, without verifying through cross-multiplication.

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