Problem 55 - BIG IDEAS MATH Algebra 2: Common Core Student Edition 2015

Question

12 pints to gallons

Step-by-Step Solution

Answer

12 Pints is equivalent to 1.5 Gallons.

Step 1: Understand the Conversion Rate

Understand that 1 Gallon is equal to 8 Pints. Furthermore, this exercise requires to convert 12 Pints to Gallons.

Step 2: Set up the Conversion Equation

The conversion equation is \[ Gallons = \frac{Pints}{8} \]. Plug in the given number of Pints, which is 12.

Step 3: Calculate the Conversion

Perform the division to get the result. \[ Gallons = \frac{12}{8} \]

Key Concepts

Pints to Gallons

When you're working with liquids in the US measurement system, you often switch between different units like pints and gallons. To convert from pints to gallons, it's crucial to know the conversion rate, which states how many pints make up a gallon.

The standard conversion is that 1 gallon is equal to 8 pints. This means if you have 8 pints of any liquid, it fills exactly 1 gallon. Remembering this simple relationship can make your conversion tasks fast and accurate every time.

• 1 Gallon = 8 Pints
• Pints are smaller than gallons
• Converting involves division

Conversion Equation

To convert pints into gallons efficiently, you will use a conversion equation. This equation provides a clear mathematical representation of the relationship between the two units.

The conversion equation for converting pints to gallons is expressed as:
\[ Gallons = \frac{Pints}{8} \]

In this formula, you divide the number of pints by 8, since there are 8 pints in a gallon. This transforms the pint measurement into its equivalent in gallons.

• Equation helps simplify conversion
• Use division as the main operation

Gallons Calculation

Once you have set up your conversion equation, it's time for the calculation step. This is where the mathematical magic happens. We'll take our specific number of pints and use the equation to find out how many gallons it equals.

Let's use the example given: converting 12 pints to gallons using the conversion equation. Plugging into the equation \[ Gallons = \frac{12}{8} \] Do the math, and you'll find out how many gallons 12 pints are equivalent to.

• Perform division with the given numbers
• Direct application of the conversion equation

Mathematical Division

Division is an arithmetic operation that helps in splitting a quantity into equal parts, and it's the key technique used in this conversion problem. When converting pints to gallons, you are dividing the total number of pints by 8.

For the question of converting 12 pints into gallons, the division calculation performed is \[ \frac{12}{8} = 1.5 \] This process shows you how many whole gallons and parts of a gallon there are. Therefore, 12 pints are equal to 1.5 gallons.

• Division explains how units relate
• Gives precise measurement conversion
• Helps understand the concept of fractional parts