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Chapter 1: Problem 30

Use the properties of division to simplify the expression, if possible. \(13 \div 13\)

Short Answer

Expert verified
The expression simplifies to 1.

Step by step solution

01

Identify the Division

Recognize that the expression involves dividing 13 by 13, which can be interpreted as the fraction \( \frac{13}{13} \).
02

Apply the Identity Property of Division

Use the identity property of division that states any number divided by itself equals 1. Therefore, \( \frac{13}{13} = 1 \).
03

Simplify the Expression

Based on the identity property, simplify the expression \( 13 \div\ 13 = 1 \).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

identity property
The identity property of division is an important and foundational principle in mathematics. This property tells us that any nonzero number divided by itself equals 1. For example, if you have the expression \( \frac{a}{a} \), where \(a\) is any nonzero number, the result will always be 1. This is because dividing a number by itself means you are determining how many times that number fits into itself, which is exactly once. Thus, \( 13 \div 13 \approx 1\). Recognizing and using the identity property can greatly simplify many mathematical tasks and expressions.
simplifying expressions
Simplifying expressions involves reducing them to their most basic and easily understood form. In mathematics, this means performing operations and using properties like the identity property to reduce expressions. For instance, in the problem \( 13 \div 13 \), we used the identity property of division to quickly see that \( \approx 1 \). Simplification is a vital skill because it helps in solving problems more efficiently and with fewer errors. Simplified expressions are easier to work with, understand, and verify.
fractions
Fractions represent parts of a whole and are written as \( \frac{numerator}{denominator} \). In the exercise, we interpret \( 13 \div 13 \) as the fraction \( \frac{13}{13} \), demonstrating that division can be represented as a fraction. When the numerator and denominator of a fraction are the same nonzero number, the fraction simplifies to 1. Understanding fractions is crucial as they appear in varied contexts, from basic arithmetic to complex algebraic equations. Remember, simplifying fractions often involves looking for common factors and applying properties like the identity property.

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