Fraction Problem: Calculate Total Storks When 2/3 Have Black Spots

Q: Why does 2/3 having spots mean 1/3 don't have spots?

Because all storks must add up to the whole group! If 2/3 have a certain trait, the remaining portion is $ 1 - \frac{2}{3} = \frac{1}{3} $ that don't have that trait.

Q: Can I solve this by working with the 2/3 that have spots instead?

You could, but it's much harder because you don't know how many have spots! Since you know the exact number without spots (130), always work with the known quantity first.

Q: What if the problem said 3/4 have spots and 65 don't?

Same method! If $ \frac{3}{4} $ have spots, then $ \frac{1}{4} $ don't have spots. Set up: $ \frac{1}{4}x = 65 $, so x = 65 × 4 = 260.

Q: How do I check if 390 is really correct?

Test both parts: $ \frac{2}{3} \times 390 = 260 $ storks with spots, and $ \frac{1}{3} \times 390 = 130 $ storks without spots. Since 260 + 130 = 390, it works perfectly!

Q: Why do I multiply by 3 instead of dividing by 1/3?

Both give the same answer! Dividing by $ \frac{1}{3} $ is the same as multiplying by 3. Most students find multiplying easier, so use whichever method feels more comfortable.

Fractional Parts with Complementary Sets

An bird watcher observes some wild storks.

He notes that $\frac{2}{3}$ of them have a black spot on their wings, while 130 of them do not.

How many storks does the bird watcher observe?

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Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

An bird watcher observes some wild storks.

He notes that $\frac{2}{3}$ of them have a black spot on their wings, while 130 of them do not.

How many storks does the bird watcher observe?

Step-by-step solution

To solve this problem, we'll execute the following steps:

Step 1: Define the variable for total stork count
Step 2: Express the condition using equations
Step 3: Solve the equation for the variable

Now, let's work through each step:

Step 1: Define $x$ as the total number of storks observed.

Step 2: According to the problem, $\frac{2}{3}x$ have a black spot, meaning $\frac{1}{3}x$ do not have a black spot. We know $\frac{1}{3}x = 130$ .

Step 3: Solve the equation for $x$ :
Dividing both sides by $\frac{1}{3}$ gives: $\frac{1}{3}x = 130$
$x = 130 \times 3$
$x = 390$ .

Therefore, the total number of storks observed is $390$ .

Final Answer

390

Key Points to Remember

Essential concepts to master this topic

Complementary Rule: If 2/3 have spots, then 1/3 don't have spots
Technique: Set up equation: if 1/3x = 130, then x = 130 × 3
Check: Verify 2/3(390) = 260 with spots, 130 without spots ✓

Common Mistakes

Avoid these frequent errors

Adding fractions instead of using complementary parts
Don't add 2/3 + 130 = wrong answer! This treats a fraction and whole number as the same units. Always recognize that 2/3 and 1/3 are complementary parts of the whole, then solve 1/3x = 130.

Practice Quiz

Test your knowledge with interactive questions

Solve for X:

$$ 5x=25 $$

FAQ

Everything you need to know about this question

Why does 2/3 having spots mean 1/3 don't have spots?

Because all storks must add up to the whole group! If 2/3 have a certain trait, the remaining portion is $1 - \frac{2}{3} = \frac{1}{3}$ that don't have that trait.

Can I solve this by working with the 2/3 that have spots instead?

You could, but it's much harder because you don't know how many have spots! Since you know the exact number without spots (130), always work with the known quantity first.

What if the problem said 3/4 have spots and 65 don't?

Same method! If $\frac{3}{4}$ have spots, then $\frac{1}{4}$ don't have spots. Set up: $\frac{1}{4}x = 65$ , so x = 65 × 4 = 260.

How do I check if 390 is really correct?

Test both parts: $\frac{2}{3} \times 390 = 260$ storks with spots, and $\frac{1}{3} \times 390 = 130$ storks without spots. Since 260 + 130 = 390, it works perfectly!

Why do I multiply by 3 instead of dividing by 1/3?

Both give the same answer! Dividing by $\frac{1}{3}$ is the same as multiplying by 3. Most students find multiplying easier, so use whichever method feels more comfortable.

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