Find the Fraction: Identifying the Shaded Region in a 3x4 Grid

Q: What's the easiest way to find what number to divide by?

Find the Greatest Common Divisor (GCD) of both numbers. For $ \frac{3}{6} $, both 3 and 6 can be divided by 3, so divide both by 3!

Q: Why can't I just count the shaded squares and stop there?

You can count them, but you must always simplify your fraction to match standard mathematical form. $ \frac{3}{6} $ and $ \frac{1}{2} $ are equal, but $ \frac{1}{2} $ is the proper simplified form.

Q: How can I check if my simplified fraction is correct?

Look at the visual! If your answer is $ \frac{1}{2} $, then exactly half of the total grid should be shaded. Count to verify!

Q: What if I can't see the grid clearly?

Focus on the pattern: count how many equal parts are shaded versus the total number of equal parts. Then simplify that fraction using division.

Fraction Simplification with Grid Models

What is the marked part?

❤️ Continue Your Math Journey!

We have hundreds of course questions with personalized recommendations + Account 100% premium

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

00:07 Place this amount in the numerator

00:10 Now let's count the total number of parts that make up the whole

00:14 Place this number in the denominator

00:19 We want to reduce the fraction as much as possible

00:23 Let's break down 6 into factors 3 and 2

00:29 Let's reduce what we can

00:33 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

We can see that there are three shaded parts out of six parts in total,

that is - 3/6

But this is not the final answer yet!

Let'snotice that this fraction can be reduced,

meaning, it is possible to divide both the numerator and the denominator by the same number,

so that the fraction does not lose its value. In this case, the number is 3.

3:3=1
6:3=2

And so we get 1/2, or one half.
And if we look at the original drawing, we can see that half of it is colored.

Final Answer

$\frac{1}{2}$

Key Points to Remember

Essential concepts to master this topic

Visual Analysis: Count shaded parts versus total parts in the grid
Simplification: Divide both numerator and denominator by their GCD: $\frac{3}{6} = \frac{3÷3}{6÷3} = \frac{1}{2}$
Check: Half the grid should be shaded when simplified fraction is $\frac{1}{2}$ ✓

Common Mistakes

Avoid these frequent errors

Giving the unreduced fraction as final answer
Don't stop at $\frac{3}{6}$ = wrong answer! This fraction isn't in simplest form and doesn't match the answer choices. Always reduce fractions by dividing both parts by their greatest common divisor.

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 when a fraction needs to be simplified?

A fraction needs simplifying when both the numerator and denominator can be divided by the same number greater than 1. Look for common factors like 2, 3, 4, etc.

What's the easiest way to find what number to divide by?

Find the Greatest Common Divisor (GCD) of both numbers. For $\frac{3}{6}$ , both 3 and 6 can be divided by 3, so divide both by 3!

Why can't I just count the shaded squares and stop there?

You can count them, but you must always simplify your fraction to match standard mathematical form. $\frac{3}{6}$ and $\frac{1}{2}$ are equal, but $\frac{1}{2}$ is the proper simplified form.

How can I check if my simplified fraction is correct?

Look at the visual! If your answer is $\frac{1}{2}$ , then exactly half of the total grid should be shaded. Count to verify!

What if I can't see the grid clearly?

Focus on the pattern: count how many equal parts are shaded versus the total number of equal parts. Then simplify that fraction using division.

🌟 Unlock Your Math Potential

Get unlimited access to all 18 Simple Fractions questions, detailed video solutions, and personalized progress tracking.

📹

Unlimited Video Solutions

Step-by-step explanations for every problem

📊

Progress Analytics

Track your mastery across all topics

🚫

Ad-Free Learning

Focus on math without distractions

No credit card required • Cancel anytime