Calculate (3/2)² : Square of a Fraction Problem

Q: How do I convert the improper fraction to a mixed number?

Divide the numerator by the denominator: $ 9 ÷ 4 = 2 $ remainder $ 1 $. So $ \frac{9}{4} = 2\frac{1}{4} $. The quotient becomes the whole number, the remainder becomes the new numerator!

Q: Can I leave my answer as an improper fraction?

Yes! $ \frac{9}{4} $ is mathematically correct. However, if the answer choices are in mixed number form like $ 2\frac{1}{4} $, you should convert to match the format expected.

Q: What's the difference between squaring a fraction and a whole number?

With whole numbers like $ 3^2 = 9 $, you just multiply the number by itself. With fractions, you must square both the numerator AND denominator separately: $ (\frac{a}{b})^2 = \frac{a^2}{b^2} $.

Q: How can I check if 2¼ is really the same as 9/4?

Convert the mixed number back: $ 2\frac{1}{4} = \frac{2 \times 4 + 1}{4} = \frac{8 + 1}{4} = \frac{9}{4} $. They match perfectly! Always verify your conversions this way.

Fraction Exponents with Mixed Number Conversion

$(\frac{3}{2})^2=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:04 Let's solve this math problem.

00:08 First, break down exponents into multiplication.

00:13 Remember, multiply numerator by numerator, and denominator by denominator.

00:18 And that's how you find the solution! Great job!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$(\frac{3}{2})^2=$

Step-by-step solution

To solve this problem, we will follow these steps:

Step 1: Square the numerator $3$ .
Step 2: Square the denominator $2$ .
Step 3: Simplify the resulting fraction if needed.

Let's solve the problem:

Step 1: The numerator is $3$ . Squaring $3$ gives us:

3^2 = 9

Step 2: The denominator is $2$ . Squaring $2$ gives us:

2^2 = 4

Step 3: We now write the fraction as:

\left(\frac{3}{2}\right)^2 = \frac{9}{4}

To express $\frac{9}{4}$ as a mixed number, we divide $9$ by $4$ :

$9$ divided by $4$ is $2$ with a remainder of $1$ . Thus, $\frac{9}{4}$ can be expressed as:

2\frac{1}{4}

Therefore, the solution to the problem is:

$2\frac{1}{4}$

The correct choice according to given possible answers is choice 4.

Final Answer

$2\frac{1}{4}$

Key Points to Remember

Essential concepts to master this topic

Rule: Square numerator and denominator separately when raising fractions to powers
Technique: $(\frac{3}{2})^2 = \frac{3^2}{2^2} = \frac{9}{4}$ then convert to mixed number
Check: Convert back: $2\frac{1}{4} = \frac{9}{4}$ matches our calculation ✓

Common Mistakes

Avoid these frequent errors

Adding the exponent to numerator and denominator instead of multiplying
Don't think $(\frac{3}{2})^2 = \frac{3+2}{2+2} = \frac{5}{4}$ ! Exponents mean repeated multiplication, not addition. Always apply the exponent by multiplying: $(\frac{3}{2})^2 = \frac{3}{2} \times \frac{3}{2} = \frac{9}{4}$ .

Practice Quiz

Test your knowledge with interactive questions

$$ 11^2= $$

FAQ

Everything you need to know about this question

Why do I square the top and bottom separately?

When you square a fraction, you're multiplying it by itself: $\frac{3}{2} \times \frac{3}{2}$ . This gives you $\frac{3 \times 3}{2 \times 2} = \frac{9}{4}$ . Each part gets squared independently!

How do I convert the improper fraction to a mixed number?

Divide the numerator by the denominator: $9 ÷ 4 = 2$ remainder $1$ . So $\frac{9}{4} = 2\frac{1}{4}$ . The quotient becomes the whole number, the remainder becomes the new numerator!

Can I leave my answer as an improper fraction?

Yes! $\frac{9}{4}$ is mathematically correct. However, if the answer choices are in mixed number form like $2\frac{1}{4}$ , you should convert to match the format expected.

What's the difference between squaring a fraction and a whole number?

With whole numbers like $3^2 = 9$ , you just multiply the number by itself. With fractions, you must square both the numerator AND denominator separately: $(\frac{a}{b})^2 = \frac{a^2}{b^2}$ .

How can I check if 2¼ is really the same as 9/4?

Convert the mixed number back: $2\frac{1}{4} = \frac{2 \times 4 + 1}{4} = \frac{8 + 1}{4} = \frac{9}{4}$ . They match perfectly! Always verify your conversions this way.

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