Solve for Red Flowers: Finding 8/9 of 36 in a Garden Problem

Q: Why do I subtract from 1 instead of just using the given fraction?

The problem gives you the fraction for white flowers, but asks for red flowers. Since white + red = all flowers (which equals 1), you need to find what's left over.

Q: Can I just multiply 36 by 1/9 and subtract from 36?

Yes! That's another correct method: 36 - (36 × $ \frac{1}{9} $) = 36 - 4 = 32. Both approaches give the same answer, so use whichever feels easier to you.

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

Multiply the whole number by the numerator, then divide by the denominator: $ \frac{8 \times 36}{9} = \frac{288}{9} = 32 $.

Q: What if the denominator doesn't divide evenly into 36?

No problem! You might get a decimal or mixed number answer. For example, if there were 37 flowers, you'd get $ \frac{8 \times 37}{9} = 32\frac{8}{9} $ red flowers.

Fraction Operations with Complementary Parts

In a garden there are 36 flowers. $\frac{1}{9}$ are white and the rest are red.

How many red flowers are there in the garden?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:07 Let's figure out how many red flowers are in the garden.

00:11 We know the number of white flowers.

00:15 Subtract the ratio of white flowers from the total.

00:19 First, convert the whole number to a fraction.

00:23 Make sure to subtract using a common denominator.

00:29 This gives us the fraction for red flowers.

00:37 Now, multiply this fraction by the total number of flowers.

00:44 Raise the product to the numerator.

00:55 Simplify the fraction by dividing both top and bottom.

01:08 Finally, calculate the product.

01:13 And that's how we find the number of red flowers!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

In a garden there are 36 flowers. $\frac{1}{9}$ are white and the rest are red.

How many red flowers are there in the garden?

Step-by-step solution

Let's first split 36 into two fractions:

The one that represents the white flowers will be as follows:

$\frac{1}{9}$

Now let's find the fraction that represents the red flowers:

$1-\frac{1}{9}=\frac{9}{9}-\frac{1}{9}=\frac{8}{9}$

Next, we'll multiply the number of flowers by the fraction that represents the red flowers:

$\frac{8}{9}\times36$

Let's now multiply the numerator by 36:

$\frac{8\times36}{9}$

We'll then divide both the numerator and denominator by 9:

$\frac{8\times36:9}{9:9}=$

Now we can solve the divisions in the numerator and denominator to get:

$\frac{8\times4}{1}=8\times4=32$

Final Answer

$32$

Key Points to Remember

Essential concepts to master this topic

Complementary Fractions: If $\frac{1}{9}$ are white, then $\frac{8}{9}$ are red
Finding the Part: Multiply total by fraction: $\frac{8}{9} \times 36 = 32$
Verification: Check that white + red = total: 4 + 32 = 36 ✓

Common Mistakes

Avoid these frequent errors

Multiplying by the given fraction instead of its complement
Don't multiply 36 by $\frac{1}{9}$ to find red flowers = 4 red flowers! This gives you the white flowers, not the red ones. Always find the complement first: $1 - \frac{1}{9} = \frac{8}{9}$ , then multiply by the total.

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

How do I know what fraction represents the red flowers?

Since all flowers are either white OR red, the fractions must add up to 1 (the whole garden). If $\frac{1}{9}$ are white, then red flowers = $1 - \frac{1}{9} = \frac{8}{9}$ .

Why do I subtract from 1 instead of just using the given fraction?

The problem gives you the fraction for white flowers, but asks for red flowers. Since white + red = all flowers (which equals 1), you need to find what's left over.

Can I just multiply 36 by 1/9 and subtract from 36?

Yes! That's another correct method: 36 - (36 × $\frac{1}{9}$ ) = 36 - 4 = 32. Both approaches give the same answer, so use whichever feels easier to you.

How do I multiply a whole number by a fraction?

Multiply the whole number by the numerator, then divide by the denominator: $\frac{8 \times 36}{9} = \frac{288}{9} = 32$ .

What if the denominator doesn't divide evenly into 36?

No problem! You might get a decimal or mixed number answer. For example, if there were 37 flowers, you'd get $\frac{8 \times 37}{9} = 32\frac{8}{9}$ red flowers.

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