Problem 17 - Prealgebra

Question

Write each number as a fraction. $$60$$

Step-by-Step Solution

Answer

The number 60 as a fraction is \( \frac{60}{1} \).

Step 1: Understand the Problem

We need to express the number 60 as a fraction. Fractions represent a part of a whole and can also express whole numbers.

Step 2: Identify the Fraction Format

To express a whole number as a fraction, we write the number over 1. This is because any number divided by 1 is itself.

Step 3: Write the Number as a Fraction

Write the whole number 60 as a fraction by placing it over 1: \( \frac{60}{1} \). This represents that 60 is the whole, as each whole number can be seen as being divided entirely into one part.

Step 4: Verify the Fraction

Verify that \( \frac{60}{1} \) is correct by simplifying: dividing 60 by 1 gives 60, confirming the fraction is correctly expressing the number 60.

Key Concepts

Understanding Whole Numbers

Whole numbers are the numbers we use for counting and ordering. They include zero and all positive numbers without fractions or decimals.

• Zero is a whole number.
• Whole numbers do not include negative numbers.
• Examples of whole numbers are 0, 1, 2, 3, and so on.

When dealing with whole numbers, you can think of them as complete units or items. Unlike fractions, which represent parts of a unit, whole numbers represent entire units. This distinction is crucial when converting numbers into fractions, where whole numbers can easily be represented by putting them over 1.

The Basics of Division

Division is one of the four basic arithmetic operations. It is essentially the process of splitting a larger number into equal smaller parts.

• In the division process, the larger number is called the "dividend."
• The number you divide by is called the "divisor."
• The result obtained is known as the "quotient."

For instance, in the division equation \(60 \div 1\), 60 is the dividend, 1 is the divisor, and 60 again is the quotient. This illustrates a key property of whole numbers and division: any number divided by one remains unchanged, which simplifies the expression of whole numbers as fractions.

Simplifying Fractions

Simplifying fractions involves reducing the fraction to its simplest form. This means the numbers in the fraction have no common divisors other than 1.

• A fraction like \(\frac{60}{60}\) simplifies to \(1\) because both the numerator and denominator can be divided by 60.
• Similarly, \(\frac{60}{1}\) is already simplified, since there are no other common factors between 60 and 1.

The primary goal of simplifying fractions is to make them easier to understand and work with, especially in calculations. Remember that while simplifying a fraction may not change its value, it makes the fraction cleaner and often more insightful.