Convert Shaded Circle Portion to Fraction: Visual Mathematics Challenge

Q: How do I know which number goes on top and which goes on bottom?

The shaded parts always go on top (numerator) and the total parts go on bottom (denominator). Think: "1 out of 3 parts" becomes $ \frac{1}{3} $.

Q: Do I need to simplify my fraction?

Yes, always simplify! If you get $ \frac{2}{4} $, reduce it to $ \frac{1}{2} $ by dividing both top and bottom by their greatest common factor.

Q: What if the circle has unequal parts?

For this type of problem, assume all parts are equal in size. The lines divide the circle into equal sections, so you can simply count the total sections and shaded sections.

Circle Fractions with Visual Division

Write the fraction shown in the drawing, in numbers:

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Convert from drawing to simple fraction

00:03 To convert to a fraction, what's red will be in the numerator and black in the denominator

00:08 We can see that the whole is divided into 3 parts

00:13 Therefore we'll put 3 in the denominator

00:17 Out of all parts, only 1 is colored

00:20 Therefore we'll put 1 in the numerator

00:23 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

Write the fraction shown in the drawing, in numbers:

Step-by-step solution

The number of parts in the circle represents the denominator of the fraction, and the number of colored parts represents the numerator.

The circle is divided into 3 parts, 1 part is colored.

Hence:

$\frac{1}{3}$

Final Answer

$\frac{1}{3}$

Key Points to Remember

Essential concepts to master this topic

Rule: Total parts become denominator, shaded parts become numerator
Technique: Count all sections (3), then count shaded sections (1)
Check: Verify 1 out of 3 parts is shaded: $\frac{1}{3}$ ✓

Common Mistakes

Avoid these frequent errors

Confusing which number goes where in the fraction
Don't put total parts as numerator and shaded parts as denominator = flipped fraction like $\frac{3}{1}$ ! This makes the fraction greater than 1 when only part of the circle is shaded. Always put shaded parts on top (numerator) and total parts on bottom (denominator).

Practice Quiz

Test your knowledge with interactive questions

Write the fraction shown in the picture, in words:

FAQ

Everything you need to know about this question

How do I know which number goes on top and which goes on bottom?

The shaded parts always go on top (numerator) and the total parts go on bottom (denominator). Think: "1 out of 3 parts" becomes $\frac{1}{3}$ .

What if more than half the circle is shaded?

The same rule applies! If 2 out of 3 parts are shaded, you get $\frac{2}{3}$ . The fraction can be any value from 0 to 1 depending on how much is shaded.

Do I need to simplify my fraction?

Yes, always simplify! If you get $\frac{2}{4}$ , reduce it to $\frac{1}{2}$ by dividing both top and bottom by their greatest common factor.

What if the circle has unequal parts?

For this type of problem, assume all parts are equal in size. The lines divide the circle into equal sections, so you can simply count the total sections and shaded sections.

How can I double-check my answer makes sense?

Ask yourself: "Does my fraction represent less than the whole circle?" Since only part of the circle is shaded, your fraction should be less than 1 (numerator smaller than denominator).

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