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Chapter 1: Problem 42

Simplify. $$ \frac{132}{11} $$

Short Answer

Expert verified
The simplified fraction is 12.

Step by step solution

01

Identify Numerator and Denominator

The given fraction is \(\frac{132}{11}\). Here, 132 is the numerator and 11 is the denominator.
02

Divide the Numerator by the Denominator

To simplify the fraction, divide the numerator (132) by the denominator (11). \(\frac{132}{11} = 12\).

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Key Concepts

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

Introduction to Numerator
In fractions, the numerator is the top number. It shows how many parts of the whole are being considered. For example, in the fraction \(\frac{132}{11}\), 132 is the numerator. It tells us that there are 132 parts we are looking at. Always remember that numerators can be any number, both positive and negative, whole or fractions themselves. This is crucial when simplifying fractions. The numerator is divided by the denominator to find the simplified form of the fraction.
Understanding the Denominator
The denominator is the bottom number of a fraction. It tells us how many parts make up a whole. For example, in \(\frac{132}{11}\), the number 11 is the denominator. This means that the whole is divided into 11 equal parts. The denominator helps to understand the size of each part that the whole is divided into. When simplifying fractions, the denominator is used to divide the numerator. If both the numerator and the denominator share a common factor, it can make the simplification process easier.
Simplifying Fractions through Division
Simplifying fractions often involves division. Division helps to reduce the fraction to its simplest form. For instance, in \(\frac{132}{11}\), we divide 132 (numerator) by 11 (denominator). The result is 12. This means the fraction simplifies to 12. When dividing, make sure to divide both the numerator and the denominator by their greatest common divisor (GCD) when possible. This ensures that the fraction is in simplest form. Division is key in fraction simplification as it transforms complex fractions into easier, more understandable forms.

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Most popular questions from this chapter

Simplify. Match the algebraic expression with the equivalent rewritten expression below. Check your answer by calculating the expression by hand and by using a calculator. A) \((5(3-7)+4 \wedge 3) /(-2-3)^{2}\) B) \((5(3-7)+4 \wedge 3) /\left(-2-3^{2}\right)\) C)\((5(3-7)+4) \wedge 3 /-2-3^{2}\) D) \(5(3-7)+4 \wedge 3 /(-2-3)^{2}\) $$ \frac{5(3-7)+4^{3}}{(-2-3)^{2}} $$

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