Visual Representation of Improper Fraction 27/12: Choose the Correct Image

Q: How do I know when a fraction is improper?

A fraction is improper when the numerator (top number) is larger than or equal to the denominator (bottom number). Since 27 > 12, $ \frac{27}{12} $ is improper.

Q: Why do I need to convert to a mixed number?

Mixed numbers make it easier to visualize! $ 2\frac{1}{4} $ clearly shows you need 2 whole circles plus one-quarter of another circle.

Q: How do I simplify the fractional part?

Find the greatest common factor (GCF) of the numerator and denominator. For $ \frac{3}{12} $, the GCF is 3, so $ \frac{3}{12} = \frac{1}{4} $.

Q: What should I look for in the visual representation?

Look for diagrams showing exactly 2 completely filled circles and one circle with exactly 1/4 shaded. Count carefully - some options might show different amounts!

Q: Can I work backwards to check my answer?

Yes! Convert your mixed number back: $ 2\frac{1}{4} = \frac{8}{4} + \frac{1}{4} = \frac{9}{4} $. Then multiply by 3: $ \frac{9}{4} \times \frac{3}{3} = \frac{27}{12} $ ✓

Improper Fractions with Visual Circle Models

Choose the option that visually represents the following fraction:

$\frac{27}{12}$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Choose the correct visual representation for the given fraction

00:03 In black, we see the number of parts into which the whole is divided

00:07 And in red is colored the given part, meaning the numerator

00:11 For each option, we'll find the mathematical representation and choose the appropriate one

01:26 Let's reduce what we can from the given fraction

01:32 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Choose the option that visually represents the following fraction:

$\frac{27}{12}$

Step-by-step solution

To solve this problem, we'll first convert the improper fraction $\frac{27}{12}$ into a mixed number. Dividing 27 by 12, we get:

27 ÷ 12 = 2 with a remainder of 3.

This means $\frac{27}{12} = 2 \frac{3}{12}$ . We can simplify $\frac{3}{12}$ to $\frac{1}{4}$ . Thus, the mixed number is $2 \frac{1}{4}$ .

Next, we look for the visual representation that displays this value. A correct representation will show two full circles and an additional quarter of a circle shaded.

Reviewing the provided options, the correct option visually representing $\frac{27}{12} = 2 \frac{1}{4}$ is option 3, which shows two fully shaded circles and one circle shaded to one-quarter.

Therefore, the solution to the problem is choice 3.

Final Answer

Key Points to Remember

Essential concepts to master this topic

Convert: Change improper fraction to mixed number first
Division: 27 ÷ 12 = 2 remainder 3, so $\frac{27}{12} = 2\frac{3}{12}$
Visual Check: Count 2 full circles plus $\frac{1}{4}$ of third circle ✓

Common Mistakes

Avoid these frequent errors

Not converting improper fraction to mixed number
Don't try to visualize $\frac{27}{12}$ as just parts of one circle = impossible representation! You need more than one whole. Always convert to mixed number first: 27 ÷ 12 = 2 $\frac{3}{12}$ = 2 $\frac{1}{4}$ to see you need 2 full circles plus a quarter.

Practice Quiz

Test your knowledge with interactive questions

Write the fraction as a mixed number:

$\frac{10}{7}=$

FAQ

Everything you need to know about this question

How do I know when a fraction is improper?

A fraction is improper when the numerator (top number) is larger than or equal to the denominator (bottom number). Since 27 > 12, $\frac{27}{12}$ is improper.

Why do I need to convert to a mixed number?

Mixed numbers make it easier to visualize! $2\frac{1}{4}$ clearly shows you need 2 whole circles plus one-quarter of another circle.

How do I simplify the fractional part?

Find the greatest common factor (GCF) of the numerator and denominator. For $\frac{3}{12}$ , the GCF is 3, so $\frac{3}{12} = \frac{1}{4}$ .

What should I look for in the visual representation?

Look for diagrams showing exactly 2 completely filled circles and one circle with exactly 1/4 shaded. Count carefully - some options might show different amounts!

Can I work backwards to check my answer?

Yes! Convert your mixed number back: $2\frac{1}{4} = \frac{8}{4} + \frac{1}{4} = \frac{9}{4}$ . Then multiply by 3: $\frac{9}{4} \times \frac{3}{3} = \frac{27}{12}$ ✓

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