Grid Fraction Analysis: Identifying the 4/7 Shaded Region

Fraction Visualization with Grid Counting

What fraction does the part shaded in red represent?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Find the marked part
00:04 Let's count the colored amount
00:07 Place this amount in the numerator
00:11 Now let's count the number of parts that divide the whole
00:16 Place this number in the denominator
00:19 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

What fraction does the part shaded in red represent?

2

Step-by-step solution

To work out what the marked part is, we need to count how many coloured squares there are compared to how many squares there are in total.

If we count the coloured squares, we see that there are four such squares.

If we count all the squares, we see that there are seven in all.

Therefore, 4/7 of the squares are shaded in red.

3

Final Answer

47 \frac{4}{7}

Key Points to Remember

Essential concepts to master this topic
  • Rule: Count shaded parts, then count total parts for fraction
  • Technique: 4 red squares out of 7 total squares = 47 \frac{4}{7}
  • Check: Verify all squares are equal size and counted correctly ✓

Common Mistakes

Avoid these frequent errors
  • Counting rectangles instead of individual unit squares
    Don't count the shaded area as 1 rectangle out of 2 rectangles = wrong answer 12 \frac{1}{2} ! The grid shows individual squares, not rectangles. Always count each individual unit square to get the correct fraction.

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 know what to count as the 'parts' in a grid?

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Always count the smallest equal divisions shown in the grid. In this case, count individual squares, not larger rectangles or sections.

What if the shaded area looks like one big rectangle?

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Even if the shaded area forms a rectangle, you still need to count the individual unit squares within that rectangle. The grid lines show you exactly how many equal parts there are.

How can I double-check my counting?

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Try counting in a systematic way: count across each row, then down each column. For the shaded area: 4 squares across × 1 row = 4 shaded squares.

Why isn't the answer 12 \frac{1}{2} since half the grid is shaded?

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While the shaded area might look like half, you must count the actual units. There are 7 total squares, not 6 or 8, so half would be 3.57 \frac{3.5}{7} , which isn't one of our answer choices.

What if I miscount the squares?

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Count slowly and systematically! For total squares: count 4 squares across × 1 row = 4, plus 3 more squares = 7 total. For shaded: count the red squares carefully.

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