Calculate One-Third of 45: Daily Chocolate Cake Production Problem

Q: Why do I multiply 45 by 1/3 instead of dividing by 3?

Great question! Multiplying by $ \frac{1}{3} $ and dividing by 3 give the same result. Both methods work: $ 45 \times \frac{1}{3} = \frac{45}{3} = 15 $.

Q: How do I know if 1/3 means chocolate, vanilla, or strawberry?

The problem states "$ \frac{1}{3} $ of the cakes are chocolate" - this tells you exactly which type! Always read carefully to match the fraction with the correct cake type.

Q: What if the fractions don't add up to 1 whole?

Check your work! In this problem: $ \frac{1}{3} + \frac{1}{3} + \frac{1}{3} = 1 $ whole. If fractions don't equal 1, reread the problem to find the missing information.

Q: Can I convert 1/3 to a decimal first?

Yes! $ \frac{1}{3} = 0.333... $, so $ 45 \times 0.333... = 15 $. However, working with fractions often gives cleaner, exact answers.

Q: How many strawberry cakes are there?

Since $ \frac{1}{3} $ are chocolate and $ \frac{1}{3} $ are vanilla, the remaining $ \frac{1}{3} $ must be strawberry. So there are also 15 strawberry cakes!

Fraction Operations with Word Problems

45 cakes are baked each morning in a bakery.

$\frac{1}{3}$ of the cakes are chocolate, $\frac{1}{3}$ are vanilla, while the rest are strawberry.

How many chocolate cakes are baked each day?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:12 How many chocolate cakes are being baked?

00:15 We'll multiply the ratio of chocolate cakes, by the total number of cakes.

00:20 The answer goes in the numerator.

00:23 Now, let's simplify the fraction, by dividing both the numerator and the denominator.

00:32 Remember, any number divided by one is always equal to itself.

00:39 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

45 cakes are baked each morning in a bakery.

$\frac{1}{3}$ of the cakes are chocolate, $\frac{1}{3}$ are vanilla, while the rest are strawberry.

How many chocolate cakes are baked each day?

Step-by-step solution

Let's begin by multiplying the total number of cakes by the fraction representing the number of chocolate cakes:

$45\times\frac{1}{3}=\frac{45\times1}{3}=\frac{45}{3}$

We then proceed to divide both the numerator and denominator by 3 as follows:

$\frac{45:3}{3:3}=\frac{15}{1}=15$

Final Answer

$15$

Key Points to Remember

Essential concepts to master this topic

Rule: Multiply the total by the fraction to find the part
Technique: Calculate $45 \times \frac{1}{3} = \frac{45}{3} = 15$
Check: Add all parts: 15 + 15 + 15 = 45 total cakes ✓

Common Mistakes

Avoid these frequent errors

Adding the fraction to the total instead of multiplying
Don't calculate 45 + 1/3 = wrong answer! This gives you more than the original total, which is impossible. Always multiply the total by the fraction to find how many items that fraction represents.

Practice Quiz

Test your knowledge with interactive questions

Write the fraction shown in the picture, in words:

FAQ

Everything you need to know about this question

Why do I multiply 45 by 1/3 instead of dividing by 3?

Great question! Multiplying by $\frac{1}{3}$ and dividing by 3 give the same result. Both methods work: $45 \times \frac{1}{3} = \frac{45}{3} = 15$ .

How do I know if 1/3 means chocolate, vanilla, or strawberry?

The problem states " $\frac{1}{3}$ of the cakes are chocolate" - this tells you exactly which type! Always read carefully to match the fraction with the correct cake type.

What if the fractions don't add up to 1 whole?

Check your work! In this problem: $\frac{1}{3} + \frac{1}{3} + \frac{1}{3} = 1$ whole. If fractions don't equal 1, reread the problem to find the missing information.

Can I convert 1/3 to a decimal first?

Yes! $\frac{1}{3} = 0.333...$ , so $45 \times 0.333... = 15$ . However, working with fractions often gives cleaner, exact answers.

How many strawberry cakes are there?

Since $\frac{1}{3}$ are chocolate and $\frac{1}{3}$ are vanilla, the remaining $\frac{1}{3}$ must be strawberry. So there are also 15 strawberry cakes!

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