Question

Express the following notations in words: \(8 \frac{1}{4} \mathrm{oz}\)

Short answer

Eight and one fourth ounces.

Step-by-step solution

Understand Mixed Numbers

A mixed number is a whole number and a proper fraction combined, in this case, 8 and \(\frac{1}{4}\). The whole number part here is 8.

Describe the Fraction

The fraction part \(\frac{1}{4}\) is read as 'one fourth' or 'a quarter,' which describes the portion less than one whole.

Include Unit of Measurement

The entire expression is measured in ounces (\(\mathrm{oz}\)), so we will include this unit in our verbal expression.

Combine Elements

Combine all components: read \(8\frac{1}{4} \mathrm{oz}\) as 'eight and one fourth ounces' or 'eight and a quarter ounces.'

Key concepts

Mixed Numbers

Mixed numbers can be a little puzzling at first because they combine two different forms of numbers: whole numbers and fractions.
Basically, a mixed number consists of a whole number plus a fraction. For instance, in the mixed number \(8 \frac{1}{4}\), the number 8 is the whole number, while the fraction \(\frac{1}{4}\) represents the part of a whole.
Mixed numbers are often used in real-life scenarios, such as in measuring ingredients in cooking or to describe distances, where both whole units and parts of units are relevant.

Fractions

Fractions represent parts of a whole and are essential in understanding numbers that are not whole.
They have two parts: a numerator and a denominator. In the fraction \(\frac{1}{4}\), 1 is the numerator and 4 is the denominator.
The denominator indicates into how many equal parts the whole is divided, and the numerator tells how many of these parts are considered.

• A fraction like \(\frac{1}{4}\) is read as 'one fourth' or 'a quarter'
• The role of fractions in mixed numbers is to show the part of a whole that is added to the whole numbers

This is how fractions are seamlessly incorporated into mixed numbers and are used in various calculations and measurements.

Measurement Units

Measurement units are essential in quantifying objects, substances, or phenomena.
In the context of our exercise, the unit of measurement is ounces (\text{oz}). Ounces are a common unit of weight in the imperial system, often used in the United States.

• Understanding the unit of measurement is critical when interpreting numbers combined with units, especially with mixed numbers or fractions
• It ensures clarity, such as in our example '8 and \(\frac{1}{4}\) ounces,' which tells us not just a value, but a specific quantity of weight

Using measurement units correctly helps convey clear and precise information in mathematics, science, and everyday life.

Word Notation

Word notation involves writing numbers and mathematical expressions in words rather than symbols.
This is particularly useful in communication, ensuring the meaning is clear even without visual representation of numbers.

• For example, the expression \(8 \frac{1}{4}\) ounces can be written in words as 'eight and one fourth ounces' or 'eight and a quarter ounces'
• Using word notation can help diverse audiences understand numerical information, regardless of their familiarity with number symbols

This practice is especially helpful in verbal communication where visual aids are absent, making word notation a vital skill in various educational and professional contexts.