Calculate 1/9 of 36: Finding White Flowers in a Garden

Q: Why do I multiply the fraction by 36 instead of dividing?

When finding "a fraction OF something", the word "of" means multiply! Think: $ \frac{1}{9} $ of 36 flowers means one-ninth times 36, not 36 divided by one-ninth.

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

Check if your answer is smaller than the total! Since $ \frac{1}{9} $ is less than 1, you should get fewer than 36 white flowers. Our answer of 4 is much less than 36, so it makes sense!

Q: What's the easiest way to multiply a fraction by a whole number?

Multiply the numerator by the whole number, keep the denominator the same: $ \frac{1 \times 36}{9} = \frac{36}{9} $, then simplify by dividing!

Q: Why does the problem mention red flowers if we don't need to find them?

The context helps you understand what the fraction represents! Knowing there are only two types of flowers helps you visualize that $ \frac{1}{9} $ are white and $ \frac{8}{9} $ must be red.

Fraction Operations with Real-World Applications

In a garden there are 36 flowers, $\frac{1}{9}$ of which are white, while the rest are red.

How many white flowers are there in the garden?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 How many white flowers are in the garden?

00:03 The given ratio of white flowers

00:07 Multiply this ratio by the total flowers to find the number of white flowers

00:10 Move the product to the numerator

00:15 Reduce the fraction, make sure to divide both numerator and denominator

00:28 Any number divided by 1 is always equal to itself

00:32 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

In a garden there are 36 flowers, $\frac{1}{9}$ of which are white, while the rest are red.

How many white flowers are there in the garden?

Step-by-step solution

First multiply the fraction by the number of flowers:

$\frac{1}{9}\times36$

Then multiply the numerator by 36:

$\frac{1\times36}{9}=\frac{36}{9}$

Next, divide both the numerator and denominator by 9:

$\frac{36:9}{9:9}$

Therefore:

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

Final Answer

$4$

Key Points to Remember

Essential concepts to master this topic

Rule: To find a fraction of a number, multiply fraction times number
Technique: Multiply numerator by whole number: $\frac{1}{9} \times 36 = \frac{36}{9}$
Check: Verify 4 white + 32 red = 36 total flowers ✓

Common Mistakes

Avoid these frequent errors

Dividing instead of multiplying the fraction
Don't divide 36 by 1/9 (which gives 324) = way too many flowers! This confuses 'finding a fraction OF a number' with division. Always multiply the fraction by the whole number to find the part.

Practice Quiz

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Write the fraction shown in the picture, in words:

FAQ

Everything you need to know about this question

Why do I multiply the fraction by 36 instead of dividing?

When finding "a fraction OF something", the word "of" means multiply! Think: $\frac{1}{9}$ of 36 flowers means one-ninth times 36, not 36 divided by one-ninth.

How do I know if my answer makes sense?

Check if your answer is smaller than the total! Since $\frac{1}{9}$ is less than 1, you should get fewer than 36 white flowers. Our answer of 4 is much less than 36, so it makes sense!

What's the easiest way to multiply a fraction by a whole number?

Multiply the numerator by the whole number, keep the denominator the same: $\frac{1 \times 36}{9} = \frac{36}{9}$ , then simplify by dividing!

How can I check my work without doing the problem again?

Add your parts together! White flowers (4) + red flowers should equal 36 total. Since 36 - 4 = 32, we have 4 white + 32 red = 36 total ✓

Why does the problem mention red flowers if we don't need to find them?

The context helps you understand what the fraction represents! Knowing there are only two types of flowers helps you visualize that $\frac{1}{9}$ are white and $\frac{8}{9}$ must be red.

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