Question

A client is receiving \(240 \mathrm{~mL}\) of Ensure by mouth as a supplement. The client consumes \(200 \mathrm{~mL}\). What portion of the Ensure remains? (Express your answer as a fraction reduced to lowest terms.) ______

Short answer

The portion of Ensure remaining is \(\frac{1}{6}\).

Step-by-step solution

Determine Total Volume

First, identify the total initial volume of Ensure given to the client, which is stated as 240 mL in the problem.

Determine Volume Consumed

Next, identify how much of the Ensure the client actually consumed, which is given as 200 mL.

Calculate Remaining Volume

Subtract the volume consumed from the initial total volume to determine how much Ensure remains. \[ 240 \text{ mL} - 200 \text{ mL} = 40 \text{ mL} \]

Express as a Fraction

You need to express the remaining Ensure as a fraction of the original volume. Use the remaining volume as the numerator and the initial total volume as the denominator. \[ \frac{40}{240} \]

Reduce the Fraction

Reduce the fraction \(\frac{40}{240}\) to its lowest terms by finding the greatest common divisor (GCD) of 40 and 240, which is 40. Divide both the numerator and the denominator by 40.\[ \frac{40 \div 40}{240 \div 40} = \frac{1}{6} \]

Key concepts

Understanding Fractions

Fractions are a way to represent parts of a whole. They consist of two numbers: the numerator and the denominator. The numerator is the top number, representing how many parts we are considering. The denominator is the bottom number, showing the total number of equal parts the whole is divided into. In our exercise, we started with 240 mL of Ensure, and the client consumed 200 mL. To find out what portion remains as a fraction, we consider the 40 mL left over as our numerator. The original 240 makes up our denominator. Thus, our initial fraction is \( \frac{40}{240} \). Often, it's essential to simplify fractions to their simplest form. To do this, find the greatest common divisor (GCD) of the numerator and denominator. In this case, the GCD of 40 and 240 is 40. Dividing both by 40 gives us the simplified fraction \( \frac{1}{6} \). This means one-sixth of the Ensure remains.

Problem-Solving Approach

Problem solving involves a sequence of steps to reach a solution. Here, we tackled the problem of determining the fraction of Ensure remaining.

• First, identify the total volume initially given, which sets a basis for further calculations. In the exercise, this was 240 mL.
• Next, determine the volume consumed. Here, the client drank 200 mL.
• Then, subtract the consumed volume from the initial total to find the remaining amount. This was \( 240 - 200 = 40 \) mL.
• Convert the leftover amount into a fraction of the original volume.
• Finally, simplify the fraction, if possible, to its lowest terms.

Through clear steps, you can break down complex problems into manageable parts. This makes understanding and solving them much easier.

Building Numerical Reasoning Skills

Numerical reasoning is pivotal in math, as it helps us make sense of numbers and their relationships. In this exercise, we used numerical reasoning to represent a real-world scenario mathematically. Understanding how to interpret fractions and perform basic operations like subtraction helps develop this skill. When you calculate the remaining Ensure by subtracting the consumed portion (\( 40 \mathrm{~mL} \)), and then express it as a fraction \( \frac{40}{240} \), you deploy vital numerical strategies. Furthermore, recognizing when a fraction can be reduced — and knowing how to do it — reflects solid numerical reasoning. By simplifying \( \frac{40}{240} \) to \( \frac{1}{6} \), we show not just arithmetic ability, but also logical thinking. These skills are beneficial beyond the classroom, in everyday decision making and understanding of practical situations.