Calculate the Shaded Region: Rectangle Grid Proportion Problem

Q: How do I tell the difference between grid lines and sections?

Think of sections as boxes or rectangles formed by the grid lines. If you see 8 vertical lines, they create 7 sections between them. Count the spaces, not the lines!

Q: What does it mean when the fraction equals 1?

When a fraction equals 1, it means the entire shape is shaded. For example, $ \frac{7}{7} = 1 $ means all 7 sections are shaded - the whole rectangle!

Q: Why does the answer say 'Answers a + b'?

This means both answer choices a and b are correct! Since $ \frac{7}{7} $ and $ 1 $ represent the same value, both answers describe the shaded region accurately.

Q: How can I double-check my section counting?

Try counting from left to right, then right to left. Also look for patterns - if sections appear equal in size, the total should make sense with what you see shaded.

Q: What if the shaded region doesn't cover complete sections?

In this problem, the shading covers complete sections perfectly. But if partial sections were shaded, you'd need to estimate the fractional part of each section that's colored.

Fraction Representation with Grid Sections

What is the marked part?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find the marked part

00:03 Let's count the colored amount

00:09 Let's put this amount in the numerator

00:13 Now let's count the total number of parts that make up the whole

00:19 Let's put this number in the denominator

00:25 We colored the entire whole, so we'll get 1

00:30 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

What is the marked part?

Step-by-step solution

Let's begin:

Step 1: Upon examination, the diagram divides the rectangle into 7 vertical sections.

Step 2: The entire shaded region spans the full width, essentially covering all sections, so the shaded number is 7.

Step 3: The fraction of the total rectangle that is shaded is $\frac{7}{7}$ .

Step 4: Simplifying, $\frac{7}{7}$ becomes $1$ .

Therefore, the solution is marked by the choice: Answers a + b.

Final Answer

Answers a + b

Key Points to Remember

Essential concepts to master this topic

Grid Analysis: Count total sections and shaded sections carefully
Technique: Compare shaded sections to total: 7 out of 7 sections = $\frac{7}{7}$
Check: Verify by simplifying: $\frac{7}{7} = 1$ means entire rectangle is shaded ✓

Common Mistakes

Avoid these frequent errors

Misreading the number of sections in the grid
Don't count grid lines instead of sections = wrong denominator! Lines divide space into sections, but the sections themselves are what matter for fractions. Always count the actual rectangular sections, not the dividing lines.

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 tell the difference between grid lines and sections?

Think of sections as boxes or rectangles formed by the grid lines. If you see 8 vertical lines, they create 7 sections between them. Count the spaces, not the lines!

What does it mean when the fraction equals 1?

When a fraction equals 1, it means the entire shape is shaded. For example, $\frac{7}{7} = 1$ means all 7 sections are shaded - the whole rectangle!

Why does the answer say 'Answers a + b'?

This means both answer choices a and b are correct! Since $\frac{7}{7}$ and $1$ represent the same value, both answers describe the shaded region accurately.

How can I double-check my section counting?

Try counting from left to right, then right to left. Also look for patterns - if sections appear equal in size, the total should make sense with what you see shaded.

What if the shaded region doesn't cover complete sections?

In this problem, the shading covers complete sections perfectly. But if partial sections were shaded, you'd need to estimate the fractional part of each section that's colored.

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