Convert Shaded Blocks to Fraction: Visual Mathematics Exercise

Q: What does it mean when all rectangles are shaded?

When all parts are shaded, you have a complete fraction or whole number! $ \frac{10}{10} $ equals 1, meaning the entire shape is filled.

Q: How do I count rectangles without missing any?

Use a systematic approach: count left to right, then top to bottom. You can also lightly mark each rectangle as you count to avoid double-counting.

Q: What if some rectangles weren't shaded?

Then only count the shaded rectangles for the numerator, but still count all rectangles for the denominator. For example, 7 shaded out of 10 total would be $ \frac{7}{10} $.

Q: Can I simplify this fraction?

$ \frac{10}{10} $ simplifies to 1 since any number divided by itself equals 1. But in fraction problems, it's often fine to leave it as $ \frac{10}{10} $ to show your work.

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Write the mathematical representation of the given fraction

00:05 In black, the number of parts into which the whole is divided (denominator)

00:12 And in red, the given number of parts (numerator)

00:17 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

Write the fraction shown in the drawing:

2

Step-by-step solution

To solve the problem, we need to determine the fraction represented by the shaded and unshaded areas in the drawing.

Step 1: By closely examining the provided drawing, we note the arrangement of rectangles or sections.
Step 2: Count the number of fully shaded (red-colored) rectangles.
Step 3: Count the total number of rectangles in the drawing, both shaded and unshaded (i.e., all rectangles present).
Step 4: Form a fraction with the number of shaded rectangles as the numerator and the total number of rectangles as the denominator.
Step 5: Check for any interpretation errors and ensure all rectangles are counted properly.

Upon examining the given drawing:

There are 10 rectangles in total.
All 10 rectangles are shaded, implying the entire set is filled.

The resulting fraction is $\frac{10}{10}$ , which is derived by setting the numerator (shaded) equal to the denominator (total). This represents a whole fraction value of 1.

Therefore, the fraction shown in the drawing is $\frac{10}{10}$ .

Upon comparing with provided multiple-choice options, the correct choice is option 3, $\frac{10}{10}$ .

3

Final Answer

$\frac{10}{10}$

Key Points to Remember

Essential concepts to master this topic

Counting Rule: Count all shaded parts as numerator, total parts as denominator
Technique: Identify 10 total rectangles with all 10 shaded = $\frac{10}{10}$
Check: Verify by confirming every rectangle is shaded and counted once ✓

Common Mistakes

Avoid these frequent errors

Miscounting the total number of rectangles in the diagram
Don't rush through counting rectangles or miss some sections = wrong denominator! This makes your fraction incorrect even if you count shaded parts right. Always count systematically by going row by row or section by section.

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

What does it mean when all rectangles are shaded?

+

When all parts are shaded, you have a complete fraction or whole number! $\frac{10}{10}$ equals 1, meaning the entire shape is filled.

How do I count rectangles without missing any?

+

Use a systematic approach: count left to right, then top to bottom. You can also lightly mark each rectangle as you count to avoid double-counting.

Why is the answer not 9/9 or 8/8?

+

Those fractions suggest different total amounts! The diagram clearly shows 10 rectangles total, so the denominator must be 10. Always count carefully!

What if some rectangles weren't shaded?

+

Then only count the shaded rectangles for the numerator, but still count all rectangles for the denominator. For example, 7 shaded out of 10 total would be $\frac{7}{10}$ .

Can I simplify this fraction?

+

$\frac{10}{10}$ simplifies to 1 since any number divided by itself equals 1. But in fraction problems, it's often fine to leave it as $\frac{10}{10}$ to show your work.

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Convert Shaded Blocks to Fraction: Visual Mathematics Exercise

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