Convert Circle Sector to Fraction: Reading the Shaded Region

Sector Fractions with Visual Circle Diagrams

Write the fraction shown in the diagram as a number:

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:03 Let's learn how to convert a drawing into a simple fraction.
00:08 To make a fraction, we'll put what's red in the numerator, or top part.
00:14 And we'll put what's black in the denominator, or bottom part.
00:18 This whole drawing is divided into 3 equal parts.
00:22 So, we'll place 3 in the denominator.
00:26 There are 2 parts colored red.
00:29 That means we'll put 2 in the numerator.
00:32 And there you have it. That's how we solve the problem!

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Write the fraction shown in the diagram as a number:

2

Step-by-step solution

The number of parts in the circle represents the denominator of the fraction, while the number of coloured parts represents the numerator.

The circle is divided into 3 parts and 2 parts are coloured.

Hence:

23 \frac{2}{3}

3

Final Answer

23 \frac{2}{3}

Key Points to Remember

Essential concepts to master this topic
  • Fraction Rule: Denominator counts total parts, numerator counts shaded parts
  • Counting Method: Circle has 3 equal sectors, 2 are red/shaded
  • Verification: Check that 2 shaded + 1 unshaded = 3 total parts ✓

Common Mistakes

Avoid these frequent errors
  • Counting the unshaded parts as the numerator
    Don't count the 1 white part as numerator = 13 \frac{1}{3} ! The numerator must represent what you want to show (the colored/shaded portion). Always count the shaded parts for the numerator and total parts for the 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?

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The denominator (bottom) is always the total number of equal parts the circle is divided into. The numerator (top) is the number of parts that are shaded or colored.

What if the circle looks like it has different sized parts?

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For fraction problems, we always assume the parts are equal in size. Count the sections created by the lines, not their visual appearance. This circle has 3 equal sectors.

Can the fraction be bigger than 1?

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In circle diagrams like this one, the fraction is usually less than 1 because you're showing part of a whole. If more than the whole circle were shaded, then yes, you could get fractions greater than 1.

Do I need to simplify the fraction?

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Always check if your fraction can be simplified! In this case, 23 \frac{2}{3} is already in lowest terms since 2 and 3 share no common factors other than 1.

What if I can't tell exactly how many parts there are?

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Look for the lines or boundaries that divide the circle. Count the sections they create. In this diagram, there are 3 clear lines from the center creating 3 sectors.

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