Fraction Problem: Finding Combined 1/5 and 1/3 of 15 Balls

Q: Why can't I just add 1/5 + 1/3 first?

Adding the fractions first assumes all balls are either red or blue, but the problem doesn't say that! Some balls could be other colors. Always find each part separately: $ \frac{1}{5} \times 15 = 3 $ blue and $ \frac{1}{3} \times 15 = 5 $ red.

Q: What if the fractions don't give whole numbers?

If $ \frac{1}{5} \times 15 $ or $ \frac{1}{3} \times 15 $ gives a decimal, check your work! In real problems about counting objects, you should get whole numbers. The problem likely has nice numbers that work out evenly.

Q: Can the red and blue balls overlap?

No! Each ball is one color only. When the problem says some balls are red and some are blue, these are separate groups. That's why we add the counts: 3 blue + 5 red = 8 total.

Q: How do I check if my answer makes sense?

Ask yourself: Does my answer seem reasonable? Here, 8 colored balls out of 15 total means about half are colored and half are other colors. That seems realistic!

Fraction Operations with Part-to-Whole Problems

There are a total of 15 balls in a jar.

$\frac{1}{5}$ of the balls are blue and $\frac{1}{3}$ of the balls are red.

How many balls in the jar are either red or blue?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:09 Let's find out how many blue and red balls are in the jar.

00:13 First, look at the number of balls related to the total amount. Here's how.

00:18 Multiply the total balls by the portion that's red to get the number of red balls.

00:25 Now, you've found the number of red balls in the jar.

00:31 Use the same method to figure out the number of blue balls. Let's do it!

00:37 Great! This gives us the number of blue balls.

00:50 Finally, add both numbers together to find the total sum.

00:55 And there you have it! That's how we solve the problem.

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

There are a total of 15 balls in a jar.

$\frac{1}{5}$ of the balls are blue and $\frac{1}{3}$ of the balls are red.

How many balls in the jar are either red or blue?

Step-by-step solution

Let's solve the problem step-by-step:

Step 1: Calculate the number of blue balls.

We know that $\frac{1}{5}$ of the 15 balls are blue. Thus, the number of blue balls is calculated as:

$\text{Number of blue balls} = \frac{1}{5} \times 15 = 3$

Step 2: Calculate the number of red balls.

Similarly, $\frac{1}{3}$ of the 15 balls are red. So, the number of red balls is:

$\text{Number of red balls} = \frac{1}{3} \times 15 = 5$

Step 3: Find the total number of balls that are either red or blue.

Sum the number of blue balls and the number of red balls:

$\text{Total number of red or blue balls} = 3 + 5 = 8$

Therefore, there are a total of 8 balls in the jar that are either red or blue.

Final Answer

Key Points to Remember

Essential concepts to master this topic

Rule: Calculate each fraction of the total separately first
Technique: Multiply fraction by total: $\frac{1}{5} \times 15 = 3$
Check: Add parts together and verify they don't exceed total: 3 + 5 = 8 ≤ 15 ✓

Common Mistakes

Avoid these frequent errors

Adding fractions first before multiplying by total
Don't add $\frac{1}{5} + \frac{1}{3} = \frac{8}{15}$ then multiply by 15 = 8! This assumes all balls are colored, but some might be other colors. Always calculate each part separately, then add the results.

Practice Quiz

Test your knowledge with interactive questions

$\frac{2}{4}+\frac{1}{4}=$ $$

FAQ

Everything you need to know about this question

Why can't I just add 1/5 + 1/3 first?

Adding the fractions first assumes all balls are either red or blue, but the problem doesn't say that! Some balls could be other colors. Always find each part separately: $\frac{1}{5} \times 15 = 3$ blue and $\frac{1}{3} \times 15 = 5$ red.

How do I know if there are other colored balls?

Calculate the total colored balls and compare to the total. Here: 3 + 5 = 8 colored balls out of 15 total means 7 balls are other colors (like green, yellow, etc.).

What if the fractions don't give whole numbers?

If $\frac{1}{5} \times 15$ or $\frac{1}{3} \times 15$ gives a decimal, check your work! In real problems about counting objects, you should get whole numbers. The problem likely has nice numbers that work out evenly.

Can the red and blue balls overlap?

No! Each ball is one color only. When the problem says some balls are red and some are blue, these are separate groups. That's why we add the counts: 3 blue + 5 red = 8 total.

How do I check if my answer makes sense?

Ask yourself: Does my answer seem reasonable? Here, 8 colored balls out of 15 total means about half are colored and half are other colors. That seems realistic!

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