Problem 10 - Prealgebra

Question

Because there are 3 feet in every yard, the formula \(F=3 \cdot Y\) will convert \(Y\) yards into \(F\) feet. find \(F\). \(Y=8\) yards

Step-by-Step Solution

Answer

8 yards is equal to 24 feet.

Step 1: Understand the Formula

The formula provided is \(F = 3 \cdot Y\), which is used to convert yards into feet. Here, \(F\) represents the number of feet and \(Y\) represents the number of yards.

Step 2: Substitute the Given Value

We are given that \(Y = 8\) yards. Substitute this value into the formula. So, the equation becomes \(F = 3 \cdot 8\).

Step 3: Perform the Multiplication

Calculate the product of 3 and 8. So, \(3 \cdot 8 = 24\).

Step 4: Write the Final Answer

Since \(3 \cdot 8 = 24\), it means that \(F = 24\). Therefore, 8 yards is equal to 24 feet.

Key Concepts

Prealgebra

Prealgebra is an essential foundation in mathematics that prepares students for more advanced concepts. It involves the basic operations and the understanding of number relationships necessary for future mathematical success. One key part of prealgebra is using formulas to solve problems, which often involves substituting known values into an equation.
For example, if you have a formula like \( F = 3 \cdot Y \), understanding that it represents a relationship between two quantities is crucial. Here, the formula tells us how to convert yards (\( Y \)) into feet (\( F \)). By substituting a given value into the formula, we can find the unknown variable. This step-by-step approach is a critical skill in prealgebra and sets the stage for algebraic manipulations later on.

• Learn to recognize variables and constants in formulas.
• Know how to substitute given values into formulas.
• Develop arithmetic skills to compute the results.

Yards to Feet Conversion

Converting yards to feet is a common task and is straightforward once you understand the ratio between the two units. This specific type of conversion is frequently encountered in measurement-related problems.
From the original exercise, we know that there are 3 feet in one yard. Therefore, every time you measure a yard, you can multiply it by 3 to find the equivalent number of feet. So, for the problem where \( Y = 8 \) yards:

• Find the conversion by multiplying 8 by 3.
• Calculate \( 8 \times 3 = 24 \), thus 8 yards equals 24 feet.

Remembering this conversion factor \( (3 \, \text{feet} = 1 \, \text{yard}) \) will help you quickly and accurately switch between these units in different situations.

Multiplication in Mathematics

Multiplication is a foundational operation in mathematics often used to find the total number of items in groups of equal size. In the context of unit conversions or everyday calculations, understanding multiplication is crucial.
For the exercise, you used multiplication to convert yards to feet. By multiplying the number of yards by 3, you found how many feet there are in total. In general, remember these points about multiplication:

• It is a quicker way to add the same number multiple times.
• You can use it to scale quantities up or down efficiently.
• It is an essential arithmetic skill necessary for many areas of math.

So, practicing multiplication helps create fluency in many mathematical tasks, making problems like unit conversions speedy and efficient.