Question

A client weighed \(1601 / 2 \mathrm{lb}\) at the previous visit to the doctor. At this visit, the client weighs \(2^{3} / 4\) lb more. How many lb does the client weigh? ______

Short answer

The client weighs 802.5 pounds.

Step-by-step solution

Understand the problem

The client initially weighed \(1601 / 2\) pounds. At the current visit, the client weighs an additional \(2^3 / 4\) pounds.

Simplify the initial weight

The initial weight of the client is given as \(1601 / 2\). To find the actual weight in pounds, we divide 1601 by 2. \[ 1601 / 2 = 800.5 \] So, the initial weight is 800.5 pounds.

Simplify the additional weight

The additional weight is given as \(2^3 / 4\). First, simplify \(2^3\) which is \(8\). Then divide by 4 to find the additional pounds: \[ 8 / 4 = 2 \] So, the additional weight is 2 pounds.

Calculate the total weight

Add the simplified initial weight and the additional weight to find the total weight of the client. The initial weight is 800.5 pounds and the additional weight is 2 pounds. \[ 800.5 + 2 = 802.5 \] Thus, the total weight is 802.5 pounds.

Key concepts

Understanding Fractions

Fractions represent a part of a whole. In math, fractions are written as two numbers separated by a line. The top number is called the numerator, and it shows how many parts we have. The bottom number is the denominator, which tells us into how many parts the whole is divided. For example, in the fraction \( \frac{1601}{2} \), 1601 is the numerator, and 2 is the denominator.

When solving weight problems, it's important to simplify fractions to make calculations easier. This means finding an equivalent fraction where the numerator and denominator cannot be reduced further, or finding the decimal form of the fraction if it simplifies the problem.

Calculating Weight in Math Problems

Calculating weight often involves adding or subtracting fractions, especially when tracking changes over time like weight gain or loss. Understanding how to manipulate fractions is key. Here's how you approach weight calculation using an example:

• Start with the initial weight presented as a fraction, such as \( \frac{1601}{2} \), and simplify it to find the initial weight in pounds.
• Then, look at the change in weight, expressed here as an additional \(\frac{8}{4}\) pounds, and simplify that fraction as well.

This kind of calculation helps determine the total weight or changeover from one period to another.

The Process of Simplification in Fractions

Simplification makes fractions much easier to work with, especially in calculations. The aim is to turn complex fractions into simpler forms or decimals that are easier to manage.

Here's how you simplify a fraction:

• Divide the numerator and the denominator by their greatest common divisor (GCD) or find the decimal representation if appropriate.
• For example, the fraction \( \frac{8}{4} \) is simplified by dividing both numbers by 4, resulting in \(2\).
• Similarly, for \( \frac{1601}{2} \), dividing gives us the simplified result of 800.5.

Simplification helps avoid errors by reducing complexity during the addition or subtraction of fractions.

Addition of Simplified Weights

After simplifying both the initial and additional weights, the next step is to combine them. This step involves the basic arithmetic operation of addition to reach the final weight.

For instance, once the initial weight \(1601/2\) is simplified to 800.5 pounds, and the additional weight \(2^3/4\) is simplified to 2 pounds, we add these two together:

• The calculation is straightforward: \(800.5 + 2 = 802.5\).
• This operation yields the client's total current weight.

Addition of simplified values ensures accurate and easy-to-verify results, minimizing the likelihood of mistakes in weight calculations.