Problem 51 - Prealgebra

Question

Set up the following conversions as you have been doing. Then perform the calculations on a calculator. Change \(4,982\) yards to inches.

Step-by-Step Solution

Answer

4,982 yards equals 179,352 inches.

Step 1: Understanding the Units

To convert yards to inches, we must understand the relationship between these units of measurement. We know that 1 yard is equivalent to 36 inches. This conversion factor will be important for our calculation.

Step 2: Setting up the Conversion Equation

We start with the value we want to convert, which is 4,982 yards. To convert yards to inches, we can set up our equation by multiplying the number of yards by the conversion factor from Step 1. Mathematically, it is expressed as: \[ 4,982 \text{ yards} \times 36 \text{ inches per yard}. \]

Step 3: Calculating the Conversion

Perform the multiplication to convert yards to inches. Using a calculator, multiply 4,982 by 36. This will give us the total number of inches in 4,982 yards: \[ 4,982 \times 36 = 179,352 \text{ inches}. \]

Key Concepts

yards to inches

When it comes to changing measurements from yards to inches, the key thing to remember is the conversion factor. Every yard is equal to 36 inches.
So, whenever you want to convert any number of yards into inches, you simply multiply by 36. Think of it like having a piece of ribbon: if you cut one yard of ribbon into smaller pieces, you will have 36 pieces, each one inch long. Here's a simple example:

• If you have 2 yards and you want to know how many inches that is, you'd calculate it by multiplying 2 yards by 36 inches per yard.
• So, 2 yards = 2 x 36 = 72 inches.

By knowing this one conversion factor, you can handle any yards-to-inches problem with ease!

measurement conversion

Understanding measurement conversion is like learning a universal language for numbers and quantities. Converting between different units allows us to compare and work with different types of measurements more effectively. Many units can be converted using a simple multiplication factor, which is the key to understanding conversion. In our case, yards to inches has a factor of 36, which represents how many inches fit into one yard. Converting measurements involves:

• Knowing the relationship between the two units.
• Using that relationship to form a ratio or multiplication factor.
• Performing the multiplication to convert your measurement.

Always remember that conversions are not about changing the amount of something; they're about expressing that amount in a different way. Being comfortable with conversions will make solving related problems feel like a breeze!

prealgebra calculations

Prealgebra is like the foundation of a house; it is vital for building a strong base for more advanced math. When dealing with prealgebra, you'll often encounter problems that involve basic arithmetic and simple equation solving. The skill of performing calculations, like converting yards to inches, falls under the umbrella of prealgebra because it involves multiplication with a conversion factor. These calculations help to reinforce basic math skills and arithmetic fluency. Here are some tips for prealgebra calculations:

• Keep your conversion factors handy, like 1 yard = 36 inches.
• Don't rush the process; take your time to set up the problem correctly.
• Check your work by estimating: is your answer reasonable? For instance, if you're converting 2 yards, is getting 72 inches logical?

Mastering prealgebra calculations will help you manage more complex math challenges with confidence!