Problem 52 - Prealgebra

Question

Complete. ? ounces \(=\frac{3}{8}\) pound (Hint: 1 pound \(=16\) ounces)

Step-by-Step Solution

Answer

6 ounces.

Step 1: Understand the Relationship

We are given that 1 pound is equal to 16 ounces. We need to find out how many ounces make up \( \frac{3}{8} \) of a pound.

Step 2: Convert Fraction to Multiplication

To determine how many ounces \( \frac{3}{8} \) of a pound equals, we need to multiply \( \frac{3}{8} \) by the number of ounces in a whole pound.

Step 3: Calculate Ounces

Multiply the fraction \( \frac{3}{8} \) by the number of ounces in a pound: \[ \frac{3}{8} \times 16 \text{ ounces} = \frac{3 \times 16}{8} \text{ ounces} \]

Step 4: Simplify the Calculation

Simplify the expression: \[ \frac{3 \times 16}{8} = \frac{48}{8} = 6 \text{ ounces} \] Therefore, \( \frac{3}{8} \) of a pound is equal to 6 ounces.

Key Concepts

Unit Conversion

Unit conversion is the process of changing a measurement from one unit to another unit. In weight measurement, units like pounds and ounces are commonly converted. Particularly in this exercise, we need to change a fractional part of a pound into ounces. We know 1 pound equals 16 ounces. Therefore, to find out how much \( \frac{3}{8} \) of a pound is in ounces, we need to use this relationship. By multiplying \( \frac{3}{8} \) by 16, we convert the unit from pounds to ounces. Each part in this conversion is crucial to correctly transform the measurements from one unit to the expected result.

Multiplication

In this context, multiplication is used to find the equivalent number of ounces in a fraction of a pound. When faced with \( \frac{3}{8} \) pound, the task is to multiply this fraction by the total number of ounces in one pound. That's where multiplication comes in—allowing us to scale a smaller amount to its proportion in a larger unit. For this, you would set up the multiplication like this:

• Multiply the numerator (3) of the fraction by the total number of ounces in a pound (16).
• This gives you \( 3 \times 16 \).
• Continue the operation by focusing on how fractions multiply with whole numbers, which involves adjusting the result by dividing at a later step (in simplification).

Breaking the problem into a multiplication step like this helps to manage and simplify what might initially appear complex.

Simplification

Simplification is a mathematical technique to make calculations easier to handle. After multiplying \( \frac{3}{8} \) by 16, you get the resultant fraction \( \frac{48}{8} \). Simplification involves reducing the fraction by dividing the numerator and the denominator by their greatest common divisor. In this case:

• The multiplication results in \( 48 \) ounces on the numerator and \( 8 \) on the denominator.
• Divide both \( 48 \) and \( 8 \) by \( 8 \), as it is the greatest common divisor.
• After division, you are left with \( 6 \).

Therefore, simplification transforms a complex expression into an easier, more manageable form, making calculations quicker and less error-prone.

Weight Measurement

Weight measurement involves quantifying how heavy an object is, using units such as ounces and pounds. Understanding these measurements and how they relate is essential. Pounds and ounces are common weight units in the United States. 1 pound equals 16 ounces, which often requires conversion when dealing with fractions of a pound, like in this exercise. Relating these two units consistently allows for more accurate and understandable results, especially when transitioning between fractional portions of weight such as \( \frac{3}{8} \) pound and its equivalent in ounces. Knowing the connection and conversion helps facilitate accurate and meaningful assessments of weight. Make sure to always verify what specific measurements pertain to in calculations, ensuring clarity and correctness in these kinds of problems.