Visual Fraction Comparison: Identifying Sections Greater Than 1/5

Fraction Comparison with Visual Rectangle Models

In which example below does the colored section account for more than a 15 \frac{1}{5} of the shape as a whole?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Choose the shapes where the marked part is larger than the given fraction
00:04 In each shape, count the colored amount and divide by the number of parts
00:10 Compare to the given fraction and select the shapes that are larger than the fraction
00:14 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

In which example below does the colored section account for more than a 15 \frac{1}{5} of the shape as a whole?

2

Step-by-step solution

To find the shape where the colored section accounts for more than 15 \frac{1}{5} of the whole, we'll follow these steps:

  • Step 1: Count the total number of sections in each shape.
  • Step 2: Count the number of sections that are colored.
  • Step 3: Calculate the fraction represented by the colored sections.
  • Step 4: Compare this fraction with 15 \frac{1}{5} .

Let's apply this to the given choices:

**Choice 1:**
The shape is comprised of 6 sections, with 2 sections being colored.
The fraction of the shape that is colored is 26=13 \frac{2}{6} = \frac{1}{3} .
Since 13 \frac{1}{3} is greater than 15 \frac{1}{5} , this choice meets the condition.

**Choice 2:**
The shape is similar but has only 1 section colored out of 6 in total.
The fraction is 16 \frac{1}{6} , which is less than 15 \frac{1}{5} . This does not satisfy the condition.

**Choice 3:**
Here, 1 out of 5 sections is colored.
The fraction is 15 \frac{1}{5} , which is exactly 15 \frac{1}{5} but not more than 15 \frac{1}{5} .

**Choice 4:**
This shape has 1 out of 6 sections colored.
The fraction is 16 \frac{1}{6} , which is less than 15 \frac{1}{5} .

Therefore, in the example corresponding to Choice 1, the colored sections indeed account for more than 15 \frac{1}{5} of the entire shape.

The correct answer is Choice 1.

3

Final Answer

Key Points to Remember

Essential concepts to master this topic
  • Visual Rule: Count colored sections and total sections to form fraction
  • Technique: Convert fractions to compare: 26=13 \frac{2}{6} = \frac{1}{3} vs 15 \frac{1}{5}
  • Check: Cross multiply to verify: 1×6=6>5=5×1 1 \times 6 = 6 > 5 = 5 \times 1

Common Mistakes

Avoid these frequent errors
  • Comparing fractions by looking only at denominators
    Don't assume 16>15 \frac{1}{6} > \frac{1}{5} because 6 > 5 = completely backwards! Larger denominators mean smaller pieces. Always compare by cross-multiplying or converting to decimals: 15=0.2>0.167=16 \frac{1}{5} = 0.2 > 0.167 = \frac{1}{6} .

Practice Quiz

Test your knowledge with interactive questions

Without calculating, determine whether the quotient in the division exercise is less than 1 or not:

\( 5:6= \)

FAQ

Everything you need to know about this question

How do I count the sections correctly in these diagrams?

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Look for the grid lines that divide the rectangle. Count all the equal-sized pieces, then count how many are colored. Each complete square is one section!

What's the easiest way to compare fractions like 1/3 and 1/5?

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Use cross multiplication! For 13 \frac{1}{3} vs 15 \frac{1}{5} : multiply 1×5=5 and 1×3=3. Since 5>3, we know 13>15 \frac{1}{3} > \frac{1}{5} .

Why does 2/6 equal 1/3?

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Both fractions represent the same amount! You can simplify 26 \frac{2}{6} by dividing both top and bottom by 2: 2÷26÷2=13 \frac{2÷2}{6÷2} = \frac{1}{3} .

What if a fraction equals exactly 1/5?

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The question asks for more than 15 \frac{1}{5} , so exactly 15 \frac{1}{5} doesn't count! It has to be greater than, not equal to.

Can I convert to decimals instead?

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Absolutely! 15=0.2 \frac{1}{5} = 0.2 , 130.33 \frac{1}{3} ≈ 0.33 , 160.17 \frac{1}{6} ≈ 0.17 . Decimals make comparing much easier for some students!

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