Calculate 3/5 of 15: A Fraction Distribution Problem

Q: Why do I multiply the fraction by 15 instead of adding?

The fraction $ \frac{3}{5} $ tells us what part of the 15 apples goes to mom. To find 3/5 of 15, we multiply: $ \frac{3}{5} \times 15 $.

Q: How do I multiply a fraction by a whole number?

Multiply the numerator by the whole number, keep the denominator the same: $ \frac{3}{5} \times 15 = \frac{3 \times 15}{5} = \frac{45}{5} = 9 $

Q: How can I check if 9 apples is correct?

Add up all the parts: Mom gets $ \frac{3}{5} \times 15 = 9 $, sister gets $ \frac{1}{5} \times 15 = 3 $, Graciela keeps $ 15 - 9 - 3 = 3 $. Total: 9 + 3 + 3 = 15 ✓

Q: What does 'of' mean in math problems?

The word 'of' in fraction problems means multiply. So '3/5 of 15' means $ \frac{3}{5} \times 15 $.

Q: Can I convert the fraction to a decimal first?

Yes! $ \frac{3}{5} = 0.6 $, so $ 0.6 \times 15 = 9 $. Both methods work, but fractions often give exact answers without rounding errors.

Fraction Multiplication with Whole Numbers

Graciela bought 15 apples and distributed them to give to her mother $\frac{3}{5}$ , to her sister $\frac{1}{5}$ and the rest for herself.

How many apples did Graciela's mother receive?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:11 How many apples did Dina's mom get?

00:15 First, let's multiply Dina's mom's apple share by the total apples.

00:20 Put this multiplication result at the top, or the numerator.

00:24 Now, let's simplify as much as we can.

00:28 Make sure to divide both the top and bottom, or numerator and denominator.

00:36 Let's multiply the numbers now.

00:42 Remember, any number divided by one stays the same.

00:47 And that's how we solve the problem!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Graciela bought 15 apples and distributed them to give to her mother $\frac{3}{5}$ , to her sister $\frac{1}{5}$ and the rest for herself.

How many apples did Graciela's mother receive?

Step-by-step solution

Let's multiply the number of apples by the fraction representing the number of apples she gave to her mother:

$\frac{3}{5}\times15=$

We'll multiply the numerator by 15:

$\frac{3\times15}{5}=$

We'll divide both the numerator and denominator by 5

$\frac{3\times15:5}{5:5}=$

Let's first solve the division operations in the numerator and denominator, and we'll get:

$\frac{3\times3}{1}=\frac{9}{1}=9$

Final Answer

$9$

Key Points to Remember

Essential concepts to master this topic

Rule: Multiply fraction by whole number using numerator multiplication
Technique: $\frac{3}{5} \times 15 = \frac{3 \times 15}{5} = \frac{45}{5} = 9$
Check: Verify that $\frac{3}{5} + \frac{1}{5} + \frac{1}{5} = \frac{5}{5} = 1$ whole ✓

Common Mistakes

Avoid these frequent errors

Adding instead of multiplying the fraction
Don't add 3/5 + 15 = 3/5 + 75/5 = 78/5! This gives a result larger than the total apples. Always multiply the fraction by the whole number to find the part of the total.

Practice Quiz

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Write the fraction shown in the diagram as a number:

FAQ

Everything you need to know about this question

Why do I multiply the fraction by 15 instead of adding?

The fraction $\frac{3}{5}$ tells us what part of the 15 apples goes to mom. To find 3/5 of 15, we multiply: $\frac{3}{5} \times 15$ .

How do I multiply a fraction by a whole number?

Multiply the numerator by the whole number, keep the denominator the same: $\frac{3}{5} \times 15 = \frac{3 \times 15}{5} = \frac{45}{5} = 9$

How can I check if 9 apples is correct?

Add up all the parts: Mom gets $\frac{3}{5} \times 15 = 9$ , sister gets $\frac{1}{5} \times 15 = 3$ , Graciela keeps $15 - 9 - 3 = 3$ . Total: 9 + 3 + 3 = 15 ✓

What does 'of' mean in math problems?

The word 'of' in fraction problems means multiply. So '3/5 of 15' means $\frac{3}{5} \times 15$ .

Can I convert the fraction to a decimal first?

Yes! $\frac{3}{5} = 0.6$ , so $0.6 \times 15 = 9$ . Both methods work, but fractions often give exact answers without rounding errors.

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