Problem 34 - Prealgebra

Question

Complete each sentence. 78 inches \(=\quad\) feet

Step-by-Step Solution

Answer

78 inches is equal to 6.5 feet.

Step 1: Understand the conversion factor

To convert inches to feet, you need to know the conversion factor. There are 12 inches in 1 foot.

Step 2: Set up the conversion equation

We want to convert 78 inches to feet. Using the conversion factor from Step 1, we can describe this as dividing the number of inches by 12. So, the equation will be: \[\text{Feet} = \frac{\text{Inches}}{12} = \frac{78}{12}\]

Step 3: Perform the division

Calculating \(\frac{78}{12}\), we perform the division to find the number of feet:\[\frac{78}{12} = 6.5\]

Step 4: Write the final answer

Now that we have performed the calculation, we can conclude that 78 inches is equal to 6.5 feet.

Key Concepts

Understanding Inches to Feet Conversion

When you need to convert a measurement in inches to feet, knowing the simple relationship between these two units is crucial. There are 12 inches in a single foot.
So, every time you need to translate inches into feet, you'll break down the total number of inches into groups of twelve.
This process allows you to determine how many whole feet, plus any remaining fraction of a foot, an amount of inches represents.

The Importance of the Conversion Factor

The conversion factor is the bridge between two different units, letting us translate values from one system of measurement to another.
In the case of inches to feet, our conversion factor is 12, meaning every foot has 12 inches in it.
When you apply this conversion factor, you equate a unit of inches to a fraction of a foot, thereby simplifying the calculations needed for accurate measurement conversion.

Applying Division in Math

Division in math is the operation of determining how many times one number is contained in another.
In our context, dividing the total number of inches by the conversion factor tells us how many feet are present.
So, when you have 78 inches and need to know how many feet that equals, you simply divide 78 by 12. Performing the mathematics results in 6.5, or six full feet and half a foot remaining.

Measuring Units in Math

Units of measurement allow us to describe physical quantities consistently. In math, different measurements let us account for length, volume, weight, and more.

• Inches are commonly used for smaller distances or lengths, especially in the United States.
• Feet are preferred for measuring more substantial lengths.

When converting between these or other units, it's essential to use multiplication or division with the appropriate conversion factor. This kind of conversion helps maintain precision across various fields of study and application.