Math / Data & Statistics

QuestionHere are some facts about units of volume. \begin{tabular}{|c|c|c|} \hline Unit & Symbol & Fact \\ \hline fluid ounce & fl oz & \\ \hline cup & c & $1 \mathrm{c}=8 \mathrm{fl} \mathrm{oz}$ \\ \hline pint & pt & $1 \mathrm{pt}=2 \mathrm{c}$ \\ \hline quart & qt & $1 \mathrm{qt}=2 \mathrm{pt}$ \\ \hline gallon & gal & $1 \mathrm{gal}=4 \mathrm{qt}$ \\ \hline \end{tabular}
Fill in the blanks. $\begin{aligned} 3 \mathrm{pt} & =6 \mathrm{c} \\ 32 \mathrm{qt} & =8[\mathrm{gal} \end{aligned}$

Studdy Solution

STEP 1

What is this asking? We're given a table of volume conversions and need to figure out how many cups are in 3 pints and how many gallons are in 32 quarts. Watch out! It's easy to mix up the conversion factors, so let's be super careful with our units!

STEP 2

1. Convert pints to cups
2. Convert quarts to gallons

STEP 3

We're given that $3$ pints needs to be converted to cups.
From the table, we know that $1 \mathrm{pt} = 2 \mathrm{c}$ .
This is our key to unlocking the problem!

STEP 4

So, to convert $3$ pints to cups, we multiply by $2$ because there are $2$ cups in every pint: $3 \mathrm{pt} \cdot \frac{2 \mathrm{c}}{1 \mathrm{pt}}$

STEP 5

Notice how the units of $\mathrm{pt}$ divide to one, leaving us with just $\mathrm{c}$ , which is exactly what we want! $3 \cdot 2 \mathrm{c} = 6 \mathrm{c}$ So, $3 \mathrm{pt} = 6 \mathrm{c}$ .
Awesome!

STEP 6

Now, we need to convert $32$ quarts to gallons.
The table tells us that $1 \mathrm{gal} = 4 \mathrm{qt}$ .
This is our next key!

STEP 7

Since there are $4$ quarts in every gallon, we can figure out how many gallons are in $32$ quarts by dividing $32$ by $4$ : $32 \mathrm{qt} \cdot \frac{1 \mathrm{gal}}{4 \mathrm{qt}}$

STEP 8

Again, the units of $\mathrm{qt}$ divide to one, leaving us with $\mathrm{gal}$ : $\frac{32}{4} \mathrm{gal} = 8 \mathrm{gal}$ Therefore, $32 \mathrm{qt} = 8 \mathrm{gal}$ .
Fantastic!

STEP 9

$3 \mathrm{pt} = 6 \mathrm{c}$ and $32 \mathrm{qt} = 8 \mathrm{gal}$ .

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Studdy Solution

STEP 1

What is this asking? We're given a table of volume conversions and need to figure out how many cups are in 3 pints and how many gallons are in 32 quarts. Watch out! It's easy to mix up the conversion factors, so let's be super careful with our units!

STEP 2

1. Convert pints to cups
2. Convert quarts to gallons

STEP 3

We're given that $3$ pints needs to be converted to cups.
From the table, we know that $1 \mathrm{pt} = 2 \mathrm{c}$ .
This is our key to unlocking the problem!

STEP 4

So, to convert $3$ pints to cups, we multiply by $2$ because there are $2$ cups in every pint: $3 \mathrm{pt} \cdot \frac{2 \mathrm{c}}{1 \mathrm{pt}}$

STEP 5

Notice how the units of $\mathrm{pt}$ divide to one, leaving us with just $\mathrm{c}$ , which is exactly what we want! $3 \cdot 2 \mathrm{c} = 6 \mathrm{c}$ So, $3 \mathrm{pt} = 6 \mathrm{c}$ .
Awesome!

STEP 6

Now, we need to convert $32$ quarts to gallons.
The table tells us that $1 \mathrm{gal} = 4 \mathrm{qt}$ .
This is our next key!

STEP 7

Since there are $4$ quarts in every gallon, we can figure out how many gallons are in $32$ quarts by dividing $32$ by $4$ : $32 \mathrm{qt} \cdot \frac{1 \mathrm{gal}}{4 \mathrm{qt}}$

STEP 8

Again, the units of $\mathrm{qt}$ divide to one, leaving us with $\mathrm{gal}$ : $\frac{32}{4} \mathrm{gal} = 8 \mathrm{gal}$ Therefore, $32 \mathrm{qt} = 8 \mathrm{gal}$ .
Fantastic!

STEP 9

$3 \mathrm{pt} = 6 \mathrm{c}$ and $32 \mathrm{qt} = 8 \mathrm{gal}$ .

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Studdy Solution

STEP 1

What is this asking? We're given a table of volume conversions and need to figure out how many cups are in 3 pints and how many gallons are in 32 quarts. Watch out! It's easy to mix up the conversion factors, so let's be super careful with our units!

STEP 2

1. Convert pints to cups2. Convert quarts to gallons

STEP 3

We're given that 333 **pints** needs to be converted to **cups**.From the table, we know that 1pt=2c1 \mathrm{pt} = 2 \mathrm{c}1pt=2c.This is our **key** to unlocking the problem!

STEP 4

So, to convert 333 pints to cups, we **multiply** by 222 because there are 222 cups in every pint: 3pt⋅2c1pt3 \mathrm{pt} \cdot \frac{2 \mathrm{c}}{1 \mathrm{pt}}3pt⋅1pt2c​

STEP 5

Notice how the units of pt\mathrm{pt}pt divide to one, leaving us with just c\mathrm{c}c, which is exactly what we want! 3⋅2c=6c3 \cdot 2 \mathrm{c} = 6 \mathrm{c}3⋅2c=6c So, 3pt=6c3 \mathrm{pt} = 6 \mathrm{c}3pt=6c.Awesome!

STEP 6

Now, we need to convert 323232 **quarts** to **gallons**.The table tells us that 1gal=4qt1 \mathrm{gal} = 4 \mathrm{qt}1gal=4qt.This is our **next key**!

STEP 7

Since there are 444 quarts in every gallon, we can figure out how many gallons are in 323232 quarts by **dividing** 323232 by 444: 32qt⋅1gal4qt32 \mathrm{qt} \cdot \frac{1 \mathrm{gal}}{4 \mathrm{qt}}32qt⋅4qt1gal​

STEP 8

Again, the units of qt\mathrm{qt}qt divide to one, leaving us with gal\mathrm{gal}gal: 324gal=8gal\frac{32}{4} \mathrm{gal} = 8 \mathrm{gal}432​gal=8gal Therefore, 32qt=8gal32 \mathrm{qt} = 8 \mathrm{gal}32qt=8gal.Fantastic!

STEP 9

3pt=6c3 \mathrm{pt} = 6 \mathrm{c}3pt=6c and 32qt=8gal32 \mathrm{qt} = 8 \mathrm{gal}32qt=8gal.

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Start learning now

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1. Convert pints to cups
2. Convert quarts to gallons

We're given that $3$ pints needs to be converted to cups.
From the table, we know that $1 \mathrm{pt} = 2 \mathrm{c}$ .
This is our key to unlocking the problem!

So, to convert $3$ pints to cups, we multiply by $2$ because there are $2$ cups in every pint: $3 \mathrm{pt} \cdot \frac{2 \mathrm{c}}{1 \mathrm{pt}}$

Notice how the units of $\mathrm{pt}$ divide to one, leaving us with just $\mathrm{c}$ , which is exactly what we want! $3 \cdot 2 \mathrm{c} = 6 \mathrm{c}$ So, $3 \mathrm{pt} = 6 \mathrm{c}$ .
Awesome!

Now, we need to convert $32$ quarts to gallons.
The table tells us that $1 \mathrm{gal} = 4 \mathrm{qt}$ .
This is our next key!

Since there are $4$ quarts in every gallon, we can figure out how many gallons are in $32$ quarts by dividing $32$ by $4$ : $32 \mathrm{qt} \cdot \frac{1 \mathrm{gal}}{4 \mathrm{qt}}$

Again, the units of $\mathrm{qt}$ divide to one, leaving us with $\mathrm{gal}$ : $\frac{32}{4} \mathrm{gal} = 8 \mathrm{gal}$ Therefore, $32 \mathrm{qt} = 8 \mathrm{gal}$ .
Fantastic!

$3 \mathrm{pt} = 6 \mathrm{c}$ and $32 \mathrm{qt} = 8 \mathrm{gal}$ .