## (4/3)/2 in Fraction Form?

To express (4/3) divided by 2 in fraction form, follow these steps:

- Write (4/3) as a fraction.
- Divide the numerator (4) by 2.
- Keep the denominator (3) the same.
So, (4/3) divided by 2 is (4/3) * (1/2), which simplifies to (4/6). Further simplifying the fraction by dividing both numerator and denominator by their greatest common factor, we get (2/3).

## Simplifying Complex Fractions

In algebra, we often have to work with complex fractions that contain fractions in both the numerator and denominator. Simplifying these complex fractions relies on applying fraction operations step-by-step to convert them into a standard single fraction.

Let’s look at simplifying the complex fraction (4/3)/2 to a standard fraction:

- Identify the numerator and denominator fractions:Numerator: 4/3 Denominator: 2
- To divide fractions, invert the denominator and multiply:(4/3) / 2 Becomes: (4/3) * (2/1)
- Multiply across the numerators and denominators:(4 * 2) / (3 * 1)
- Simplify the resulting fraction:8/3

Therefore, the complex fraction (4/3)/2 simplifies to 8/3 in standard fractional form.

## Why This Works

Dividing by a fraction is the same as multiplying by its reciprocal.

Inverting the denominator fraction 2/1 and multiplying converts the division to multiplication.

This allows us to simplify complex fractions using standard fraction operations.

## Checking the Work

To verify the simplified fraction is equivalent, we can divide it by 2:

8/3 / 2 = 4/3

Getting back the original numerator 4/3 confirms that 8/3 is the correct simplified form of (4/3)/2.

Being able to work comfortably with complex fractions makes fraction arithmetic much more manageable. Understanding the logic behind simplifying builds essential algebra skills.

In summary, simplify a complex fraction by inverting the denominator and multiplying to convert division to multiplication, then simplifying the resulting fraction.

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