Math / Numbers & Operations

QuestionEmily made blueberry muffins for her scout troop's bake sale. For her first batch, she used 1 cup of blueberries and 2 cups of oats. She didn't think that would make enough muffins, so she made a larger second batch with 3 cups of blueberries and 6 cups of oats. When she tod the last tray out of the oven, her little brother asked if he could have a muffin with lots of blueberries as a snack. Which batch had a greater ratio of blueberries to oats?
The first batch had the greater ratio.
The second batch had the greater ratio.
Neither. The batches had the same ratio.

Studdy Solution

STEP 1

What is this asking? Which muffin batch has more blueberries compared to oats? Watch out! Don't just compare the amounts of blueberries; we need the ratio of blueberries to oats!

STEP 2

1. Calculate the blueberry-to-oat ratio for the first batch.
2. Calculate the blueberry-to-oat ratio for the second batch.
3. Compare the ratios.

STEP 3

Alright, let's dive into the first batch!
Emily used $1$ cup of blueberries and $2$ cups of oats.
We want the ratio of blueberries to oats.

STEP 4

So, we'll divide the amount of blueberries by the amount of oats.
This gives us $\frac{1}{2}$ .
This means for every cup of oats, there's half a cup of blueberries!

STEP 5

Now, for the second batch, Emily ramped things up!
She used $3$ cups of blueberries and $6$ cups of oats.

STEP 6

Again, we want the ratio of blueberries to oats.
We divide the amount of blueberries by the amount of oats, which gives us $\frac{3}{6}$ .

STEP 7

Let's simplify that fraction!
Both the numerator and denominator are divisible by $3$ .
Dividing both by $3$ gives us $\frac{3 \div 3}{6 \div 3} = \frac{1}{2}$ .
So, for every cup of oats, there's half a cup of blueberries in this batch too!

STEP 8

The first batch's ratio is $\frac{1}{2}$ .
The second batch's ratio is also $\frac{1}{2}$ .

Studdy Solution

STEP 1

What is this asking? Which muffin batch has more blueberries compared to oats? Watch out! Don't just compare the amounts of blueberries; we need the ratio of blueberries to oats!

STEP 2

1. Calculate the blueberry-to-oat ratio for the first batch.
2. Calculate the blueberry-to-oat ratio for the second batch.
3. Compare the ratios.

STEP 3

Alright, let's dive into the first batch!
Emily used $1$ cup of blueberries and $2$ cups of oats.
We want the ratio of blueberries to oats.

STEP 4

So, we'll divide the amount of blueberries by the amount of oats.
This gives us $\frac{1}{2}$ .
This means for every cup of oats, there's half a cup of blueberries!

STEP 5

Now, for the second batch, Emily ramped things up!
She used $3$ cups of blueberries and $6$ cups of oats.

STEP 6

Again, we want the ratio of blueberries to oats.
We divide the amount of blueberries by the amount of oats, which gives us $\frac{3}{6}$ .

STEP 7

Let's simplify that fraction!
Both the numerator and denominator are divisible by $3$ .
Dividing both by $3$ gives us $\frac{3 \div 3}{6 \div 3} = \frac{1}{2}$ .
So, for every cup of oats, there's half a cup of blueberries in this batch too!

STEP 8

The first batch's ratio is $\frac{1}{2}$ .
The second batch's ratio is also $\frac{1}{2}$ .

STEP 9

Are these ratios the same?
Yes! They're exactly the same!

STEP 10

Neither batch has a greater ratio of blueberries to oats.
They are the same!

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Studdy Solution

STEP 1

What is this asking? Which muffin batch has more blueberries compared to oats? Watch out! Don't just compare the *amounts* of blueberries; we need the *ratio* of blueberries to oats!

STEP 2

1. Calculate the blueberry-to-oat ratio for the first batch.2. Calculate the blueberry-to-oat ratio for the second batch.3. Compare the ratios.

STEP 3

Alright, let's dive into the first batch!Emily used 111 cup of blueberries and 222 cups of oats.We want the ratio of blueberries to oats.

STEP 4

So, we'll **divide** the amount of blueberries by the amount of oats.This gives us 12\frac{1}{2}21​.This means for every cup of oats, there's half a cup of blueberries!

STEP 5

Now, for the second batch, Emily ramped things up!She used 333 cups of blueberries and 666 cups of oats.

STEP 6

Again, we want the ratio of blueberries to oats.We **divide** the amount of blueberries by the amount of oats, which gives us 36\frac{3}{6}63​.

STEP 7

Let's **simplify** that fraction!Both the **numerator** and **denominator** are divisible by 333.Dividing both by 333 gives us 3÷36÷3=12\frac{3 \div 3}{6 \div 3} = \frac{1}{2}6÷33÷3​=21​.So, for every cup of oats, there's half a cup of blueberries in this batch too!

STEP 8

The first batch's ratio is 12\frac{1}{2}21​.The second batch's ratio is also 12\frac{1}{2}21​.

STEP 9

Are these ratios the same?Yes! They're **exactly** the same!

STEP 10

Neither batch has a greater ratio of blueberries to oats.They are the same!

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Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

What is this asking? Which muffin batch has more blueberries compared to oats? Watch out! Don't just compare the amounts of blueberries; we need the ratio of blueberries to oats!

1. Calculate the blueberry-to-oat ratio for the first batch.
2. Calculate the blueberry-to-oat ratio for the second batch.
3. Compare the ratios.

Alright, let's dive into the first batch!
Emily used $1$ cup of blueberries and $2$ cups of oats.
We want the ratio of blueberries to oats.

So, we'll divide the amount of blueberries by the amount of oats.
This gives us $\frac{1}{2}$ .
This means for every cup of oats, there's half a cup of blueberries!

Now, for the second batch, Emily ramped things up!
She used $3$ cups of blueberries and $6$ cups of oats.

Again, we want the ratio of blueberries to oats.
We divide the amount of blueberries by the amount of oats, which gives us $\frac{3}{6}$ .

Let's simplify that fraction!
Both the numerator and denominator are divisible by $3$ .
Dividing both by $3$ gives us $\frac{3 \div 3}{6 \div 3} = \frac{1}{2}$ .
So, for every cup of oats, there's half a cup of blueberries in this batch too!

The first batch's ratio is $\frac{1}{2}$ .
The second batch's ratio is also $\frac{1}{2}$ .

Are these ratios the same?
Yes! They're exactly the same!

Neither batch has a greater ratio of blueberries to oats.
They are the same!