Math / Numbers & Operations

QuestionMr. Harris owns a bubble machine that he uses for different school events. The bubble solution contains $\frac{3}{4}$ cup of corn starch for every 2 cups of water.
What is the rate in cups of corn starch per cup of water?
The rate is of water. \begin{tabular}{|l|} \hline $?$ \\ \hline $\frac{3}{8}$ \\ \hline $\frac{2}{3}$ \\ \hline $1 \frac{1}{2}$ \\ \hline $2 \frac{2}{3}$ \\ \hline \end{tabular}

Studdy Solution

STEP 1

What is this asking? How much corn starch is needed for each cup of water in Mr.
Harris' awesome bubble solution? Watch out! Don't mix up corn starch and water!
We want corn starch per cup of water.

STEP 2

1. Set up the ratio.
2. Divide to find the rate.

STEP 3

We're given that the bubble solution has $\frac{3}{4}$ cup of corn starch for every $2$ cups of water.
We can write this as a ratio: $\frac{3/4 \text{ cup corn starch}}{2 \text{ cups water}}$ .
Remember, we want to find out how much corn starch is needed per cup of water.

STEP 4

To get the rate of corn starch per cup of water, we need to make the denominator $1$ .
So, we'll divide both the numerator (corn starch) and the denominator (water) by $2$ .
This keeps the ratio balanced, just like multiplying by $\frac{1/2}{1/2}$ which is $1$ .

STEP 5

Let's do the division!
We have $\frac{3/4}{2}$ .
Remember dividing by $2$ is the same as multiplying by $\frac{1}{2}$ , so we have $\frac{3}{4} \cdot \frac{1}{2} = \frac{3 \cdot 1}{4 \cdot 2} = \frac{3}{8}$ .
This means we need $\frac{3}{8}$ cups of corn starch.

STEP 6

Now, let's look at the water.
We have $\frac{2}{2} = 1$ .
So, we have $1$ cup of water.

STEP 7

Putting it all together, our rate is $\frac{3/8 \text{ cup corn starch}}{1 \text{ cup water}}$ , or simply $\frac{3}{8}$ cups of corn starch per cup of water.

STEP 8

The rate is $\frac{3}{8}$ cups of corn starch per cup of water.

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Studdy Solution

STEP 1

What is this asking? How much corn starch is needed for each cup of water in Mr.
Harris' awesome bubble solution? Watch out! Don't mix up corn starch and water!
We want corn starch per cup of water.

STEP 2

1. Set up the ratio.
2. Divide to find the rate.

STEP 3

We're given that the bubble solution has $\frac{3}{4}$ cup of corn starch for every $2$ cups of water.
We can write this as a ratio: $\frac{3/4 \text{ cup corn starch}}{2 \text{ cups water}}$ .
Remember, we want to find out how much corn starch is needed per cup of water.

STEP 4

To get the rate of corn starch per cup of water, we need to make the denominator $1$ .
So, we'll divide both the numerator (corn starch) and the denominator (water) by $2$ .
This keeps the ratio balanced, just like multiplying by $\frac{1/2}{1/2}$ which is $1$ .

STEP 5

Let's do the division!
We have $\frac{3/4}{2}$ .
Remember dividing by $2$ is the same as multiplying by $\frac{1}{2}$ , so we have $\frac{3}{4} \cdot \frac{1}{2} = \frac{3 \cdot 1}{4 \cdot 2} = \frac{3}{8}$ .
This means we need $\frac{3}{8}$ cups of corn starch.

STEP 6

Now, let's look at the water.
We have $\frac{2}{2} = 1$ .
So, we have $1$ cup of water.

STEP 7

Putting it all together, our rate is $\frac{3/8 \text{ cup corn starch}}{1 \text{ cup water}}$ , or simply $\frac{3}{8}$ cups of corn starch per cup of water.

STEP 8

The rate is $\frac{3}{8}$ cups of corn starch per cup of water.

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Studdy Solution

STEP 1

What is this asking? How much corn starch is needed for each cup of water in Mr.Harris' awesome bubble solution? Watch out! Don't mix up corn starch and water!We want corn starch *per* cup of water.

STEP 2

1. Set up the ratio.2. Divide to find the rate.

STEP 3

STEP 4

To get the rate of corn starch *per* cup of water, we need to make the denominator 111.So, we'll divide both the numerator (corn starch) and the denominator (water) by 222.This keeps the ratio balanced, just like multiplying by 1/21/2\frac{1/2}{1/2}1/21/2​ which is 111.

STEP 5

STEP 6

Now, let's look at the water.We have 22=1\frac{2}{2} = 122​=1.So, we have 111 cup of water.

STEP 7

Putting it all together, our rate is 3/8 cup corn starch1 cup water\frac{3/8 \text{ cup corn starch}}{1 \text{ cup water}}1 cup water3/8 cup corn starch​, or simply 38\frac{3}{8}83​ cups of corn starch per cup of water.

STEP 8

The rate is 38\frac{3}{8}83​ cups of corn starch per cup of water.

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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? How much corn starch is needed for each cup of water in Mr.
Harris' awesome bubble solution? Watch out! Don't mix up corn starch and water!
We want corn starch per cup of water.

1. Set up the ratio.
2. Divide to find the rate.

To get the rate of corn starch per cup of water, we need to make the denominator $1$ .
So, we'll divide both the numerator (corn starch) and the denominator (water) by $2$ .
This keeps the ratio balanced, just like multiplying by $\frac{1/2}{1/2}$ which is $1$ .

Now, let's look at the water.
We have $\frac{2}{2} = 1$ .
So, we have $1$ cup of water.

Putting it all together, our rate is $\frac{3/8 \text{ cup corn starch}}{1 \text{ cup water}}$ , or simply $\frac{3}{8}$ cups of corn starch per cup of water.

The rate is $\frac{3}{8}$ cups of corn starch per cup of water.