Grid-Based Fraction Identification: Converting 3/7 from Visual to Numeric Form

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

The numerator (top number) is always the part you're focusing on - in this case, the 3 shaded rectangles. The denominator (bottom number) is the total number of equal parts.

Q: What if some rectangles are partially shaded?

Count only completely shaded rectangles for the numerator. If a rectangle is half-shaded, you'd need to count it as $ \frac{1}{2} $ and use more advanced fraction addition.

Q: Why are there 7 rectangles but the choices show different denominators?

The choices test your counting skills! Always count carefully - there are exactly 7 equal rectangles in this grid, making 7 the only correct denominator.

Q: How can I double-check my counting?

Count the rectangles in two different ways: Left to right across the rowLook for patterns (like groups of rectangles) Both methods should give you the same total.

Q: What does this fraction mean in real life?

$ \frac{3}{7} $ means 3 out of every 7 parts. If you had 7 pizza slices, you'd be eating 3 of them!

Visual Fraction Representation with Grid Models

Write the fraction shown in the drawing:

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Convert from visual representation to mathematical representation of the fraction

00:03 Count the division cells of the whole (denominator)

00:09 Count the number of colored parts (numerator)

00:13 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:

Step-by-step solution

To find the fraction represented by the shaded areas, follow these steps:

Step 1: Count the total number of rectangles. There are 7 rectangles in the drawing.
Step 2: Count the number of shaded rectangles. There are 3 shaded rectangles.
Step 3: Form the fraction, using the number of shaded rectangles as the numerator and the total number of rectangles as the denominator.

Therefore, the fraction of the drawing that is shaded is $\frac{3}{7}$ .

This value corresponds to option 4 in the provided choices, confirming $\frac{3}{7}$ is the correct answer.

Final Answer

$\frac{3}{7}$

Key Points to Remember

Essential concepts to master this topic

Count Total: Count all rectangles in the grid to find the denominator
Count Shaded: Count only the filled/colored rectangles for the numerator (3 out of 7)
Verify: Check that numerator is always less than denominator in proper fractions ✓

Common Mistakes

Avoid these frequent errors

Confusing numerator and denominator positions
Don't write the total count first as $\frac{7}{3}$ = improper fraction over 1! This reverses the fraction meaning completely. Always write shaded parts over total parts: $\frac{3}{7}$ .

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

How do I know which number goes on top?

The numerator (top number) is always the part you're focusing on - in this case, the 3 shaded rectangles. The denominator (bottom number) is the total number of equal parts.

What if some rectangles are partially shaded?

Count only completely shaded rectangles for the numerator. If a rectangle is half-shaded, you'd need to count it as $\frac{1}{2}$ and use more advanced fraction addition.

Why are there 7 rectangles but the choices show different denominators?

The choices test your counting skills! Always count carefully - there are exactly 7 equal rectangles in this grid, making 7 the only correct denominator.

How can I double-check my counting?

Count the rectangles in two different ways:

Left to right across the row
Look for patterns (like groups of rectangles)

Both methods should give you the same total.

What does this fraction mean in real life?

$\frac{3}{7}$ means 3 out of every 7 parts. If you had 7 pizza slices, you'd be eating 3 of them!

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