Question

A juice glass holds \(120 \mathrm{~mL}\). If a client drinks \(2^{1} / 3\) glasses, how many milliliters did the client consume? ______

Short answer

The client consumed 280 milliliters of juice.

Step-by-step solution

Convert Mixed Number to Improper Fraction

First, we need to convert the mixed number \(2^{1}/3\) glasses into an improper fraction. A mixed number consists of a whole number and a fraction. Here, \(2^{1}/3\) is composed of the whole number 2 and the fraction \(1/3\). To convert it:\[2 + \frac{1}{3} = \frac{2 \times 3 + 1}{3} = \frac{7}{3}\]

Calculate Total Milliliters Consumed

Now that we have \(\frac{7}{3}\) glasses as the total amount consumed, we multiply this by the amount each glass holds, which is 120 mL.\[\frac{7}{3} \times 120 = \frac{7 \times 120}{3} = \frac{840}{3} = 280\]

Final Answer

The client consumed 280 milliliters of juice.

Key concepts

Improper Fractions

Improper fractions might sound a little confusing at first, but they're really just a neat way to express both whole numbers and fractions together.

• In an improper fraction, the numerator (the top number) is equal to or larger than the denominator (the bottom number).
• This contrasts with proper fractions where the numerator is smaller than the denominator.

An example is \(\frac{7}{3}\), where 7 is greater than 3.Why do we use improper fractions? They're great for calculations! When you work on combining or multiplying fractions, improper fractions make it easier and faster to go through the math without converting between forms.
In cases where a mixed number is involved, transforming it into an improper fraction is often the first step.You multiply the whole number by the fraction's denominator, add the numerator, and keep the same denominator. For example, with \(2^{1}/3\):\[2 + \frac{1}{3} = \frac{2 \times 3 + 1}{3} = \frac{7}{3}\]

Mixed Numbers

Mixed numbers are a way to express numbers that include both a whole number and a fractional part.

• They are useful in everyday situations where you're working with wholes and parts of wholes.
• An example of a mixed number is \(2^{1}/3\), which represents two whole glasses and one-third of another glass.

When you are performing mathematical operations, such as multiplication or addition, involving mixed numbers, always consider converting them first into improper fractions. This simplifies the calculations by dealing with just one type of fraction instead of juggling whole numbers and fractions separately.To convert a mixed number into an improper fraction, you multiply the whole number by the denominator of the fraction, add the numerator of the fraction, and place that result over the original denominator. Simple as that! Once converted, you can easily proceed with additional calculations.This step ensures you get accurate results, like ensuring the total amount of liquid consumed when drinking fractions of more than one glass.

Unit Conversion

Unit conversion is something we encounter regularly. Whether you're converting miles to kilometers or mL to L, understanding how to shift between units can be very handy.In this context, we're dealing with milliliters. To find how many milliliters a drinker consumed, you multiply the number or fraction of glasses by the volume of one glass.

• Remember, the basic idea behind unit conversion is to multiply by a ratio that represents one.
• Here, that ratio is each glass holding 120 mL.

For instance, if someone drinks \(\frac{7}{3}\) glasses, you calculate:\[\frac{7}{3} \times 120 = \frac{7 \times 120}{3} = 280 \, \text{mL} \]This process allows us to convert the number of glasses directly into milliliters, which is a more tangible way to understand the amount consumed.Converting units accurately ensures that your calculations reflect real-world quantities correctly, allowing you to interpret your results with confidence.