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Chapter 4: Problem 219

In the following exercises, simplify. $$\frac{9+3}{7}$$

Short Answer

Expert verified
The simplified form is \(\frac{12}{7}\).

Step by step solution

01

Identify the Numerator and Denominator

The given expression is a fraction. Here, the numerator is the expression within the top part of the fraction: \(9 + 3\). The denominator is the number on the bottom: \(7\).
02

Simplify the Numerator

Simplify the numerator by performing the addition: \(9 + 3 = 12\). Now the fraction is \(\frac{12}{7}\).
03

Result

The fractional expression \(\frac{12}{7}\) is already in its simplest form since 12 and 7 have no common factors other than 1. Therefore, the simplified form of \(\frac{9 + 3}{7}\) is \(\frac{12}{7}\).

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Key Concepts

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

Numerator and Denominator
In a fraction, the top number is called the numerator, and the bottom number is the denominator. The fraction is written as \(\frac{numerator}{denominator}\).
The numerator represents the number of parts we have, while the denominator indicates the number of equal parts into which the whole is divided.
For example, in the fraction \(\frac{9+3}{7}\), 9 + 3 is the numerator, and 7 is the denominator.
Understanding these two components is crucial when working with fractions since it helps us visualize and process what the fraction is representing.
Simplifying Fractions
Simplifying fractions means to make the fraction as simple as possible. Here, simple means that the numerator and denominator have no common factors other than 1.
For instance, if we work with the given expression \(\frac{9+3}{7}\), we first simplify the numerator by performing the addition: \(9+3=12\).
So, the fraction becomes \(\frac{12}{7}\). Next, we check if both the numerator (12) and the denominator (7) have any common factors.
In this case, they do not, so \(\frac{12}{7}\) is already in its simplest form.
Basic Arithmetic
Basic arithmetic operations include addition, subtraction, multiplication, and division.
These operations are essential for solving and simplifying fractions. In the given exercise, addition is used to simplify the numerator: \(9+3=12\).
With this simplified numerator, the fraction becomes \(\frac{12}{7}\).
Understanding basic arithmetic is fundamental because it allows us to break down complex problems into simpler steps, making it easier to solve or simplify fractions.
Practice with these operations will enhance your ability to handle more intricate mathematical problems in a clear and efficient manner.

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Most popular questions from this chapter

In the following exercises, perform the indicated operations and simplify. $$\left(\frac{11}{12}+\frac{3}{8}\right) \div\left(\frac{5}{6}-\frac{1}{10}\right)$$

In the following exercises, determine whether the each number is a solution of the given equation. $$ y+\frac{3}{5}=\frac{5}{9} $$ $$ (a)y=\frac{1}{2} $$ $$ (b)y=\frac{52}{45} $$ $$ (c)y=-\frac{2}{45} $$

In the following exercises, evaluate the given expression. Express your answers in simplified form, using improper fractions if necessary. \(x-\frac{1}{3}\) when (a) \(x=\frac{2}{3} \quad\) (b) \(x=-\frac{2}{3}\)

In the following exercises, simplify. $$ -\frac{3}{10}+\left(-\frac{5}{8}\right) $$

In the following exercises, evaluate the given expression. Express your answers in simplified form, using improper fractions if necessary. 2\(x^{2} y^{3}\) when \(x=-\frac{2}{3}\) and \(y=-\frac{1}{2}\)
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