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Chapter 4: Problem 4

Identify the numerator and the denominator for each fraction. $$\frac{12 x}{11 y^{2}}$$

Short Answer

Expert verified
Numerator: \(12x\), Denominator: \(11y^2\)

Step by step solution

01

Identify the fraction components

Fractions consist of two main parts: the numerator and the denominator. In a fraction, the numerator is the number above the fraction line, and the denominator is the number below the fraction line.
02

Determine the numerator

Look at the given fraction \(\frac{12x}{11y^2}\). The numerator is the value or expression that is located above the fraction line. Here, the numerator is \(12x\).
03

Determine the denominator

The denominator is the value or expression located below the fraction line in the given fraction \(\frac{12x}{11y^2}\). In this case, the denominator is \(11y^2\).

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Key Concepts

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

Numerator
In fractions, the numerator is a fundamental component. It appears at the top of the fraction line. The primary function of the numerator is to represent the 'part' of the whole. For instance, in the fraction \(\frac{12x}{11y^2}\), the numerator is \(12x\). This tells us how many parts we are considering out of a whole, defined by the denominator.
When dealing with numerators in algebra, they can be numbers, variables, or products of both. For example, if you have \(5a\) as the numerator, it means that there are \(5a\) parts of the whole determined by the denominator.
Denominator
The denominator is another crucial part of a fraction. It is located below the fraction line and denotes the 'whole' or the total number of equal parts the numerator is divided into. For instance, in \( \frac{12x}{11y^2} \), \(11y^2 \) is the denominator.
The denominator informs us about the entire set compared to the parts indicated by the numerator. Like the numerator, the denominator in algebra can consist of numbers, variables, or their products, making the whole concept versatile and essential in algebraic expressions.
Fractions in Algebra
Fractions play a significant role in algebra. They are used to express parts of a whole and ratios between quantities. In algebra, fractions can have complex expressions in both the numerator and the denominator. For example, \( \frac{12x}{11y^2} \) is a typical algebraic fraction.
Here are some key points to remember about fractions in algebra:
  • Both the numerator and denominator can include variables.
  • Algebraic operations (addition, subtraction, multiplication, division) can be performed with fractions, as long as we follow the rules for manipulating expressions.
  • Fractions can also be simplified by finding common factors in the numerator and the denominator.
Remember, understanding fractions in algebra is essential. It allows you to solve equations and make sense of various relationships between quantities.

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