What is the fraction 3/2 squared in fraction form?
The Correct Answer and Explanation is :
To square the fraction ( \frac{3}{2} ), you multiply the fraction by itself:
[
\left( \frac{3}{2} \right)^2 = \frac{3}{2} \times \frac{3}{2}
]
When multiplying fractions, you multiply the numerators together and the denominators together. Thus:
[
\frac{3 \times 3}{2 \times 2} = \frac{9}{4}
]
So, ( \left( \frac{3}{2} \right)^2 = \frac{9}{4} ).
Explanation
Squaring a fraction involves a straightforward process, but it’s important to understand the underlying principles of fraction multiplication. A fraction is essentially a division of two integers: the numerator (the top number) and the denominator (the bottom number). The value of a fraction represents how many parts of the denominator are contained in the numerator.
In this case, the fraction ( \frac{3}{2} ) indicates that there are 3 parts of something divided into 2 equal parts. When we square the fraction, we want to determine how much of ( \frac{3}{2} ) we have when it is itself multiplied by the same amount.
Step 1: Multiply the Numerators
We multiply the numerators ( 3 ) and ( 3 ):
[
3 \times 3 = 9
]
Step 2: Multiply the Denominators
Next, we multiply the denominators ( 2 ) and ( 2 ):
[
2 \times 2 = 4
]
Step 3: Combine the Results
The results give us the new numerator and denominator, resulting in:
[
\frac{9}{4}
]
Conclusion
The fraction ( \frac{3}{2} ) squared equals ( \frac{9}{4} ). This can also be interpreted as ( 2.25 ) when converted to decimal form, highlighting the process of squaring a fraction as a means of scaling the value up by its own magnitude. Understanding this operation is essential in various mathematical applications, from simplifying expressions to solving equations.