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Chapter 2: Problem 7

Find the reciprocal of each number. \(\frac{10}{3}\)

Short Answer

Expert verified
\(\frac{3}{10}\)

Step by step solution

01

Understand the Reciprocal

The reciprocal of a number is found by exchanging the numerator and the denominator of a fraction.
02

Reciprocal of a Fraction

Given the fraction \(\frac{10}{3}\), the reciprocal would be \(\frac{3}{10}\).
03

Simplify if Necessary

Check if the reciprocal fraction \(\frac{3}{10}\) can be simplified. In this case, it is already in its simplest form.

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Key Concepts

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

Fraction Basics
A fraction represents a part of a whole. It is written as one number over another, separated by a line. The top number is called the numerator, and the bottom number is called the denominator. For example, in the fraction \(\frac{10}{3}\), 10 is the numerator and 3 is the denominator.

Fractions have many applications in everyday life, from splitting a pizza to dividing up time. Understanding fractions is fundamental to grasping more complex mathematical concepts.
Simplifying Fractions
Simplifying a fraction means reducing it to its simplest form. This involves dividing the numerator and the denominator by their greatest common divisor (GCD). For instance, if a fraction is \(\frac{4}{8}\), both 4 and 8 can be divided by 4. So, \(\frac{4}{8}\) simplifies to \(\frac{1}{2}\).

Here are steps to simplify fractions:
  • Find the GCD of the numerator and the denominator.
  • Divide both the numerator and the denominator by the GCD.
  • Write down the simplified fraction.
In our exercise, the reciprocal \(\frac{3}{10}\) cannot be simplified further as 3 and 10 do not have any common divisors other than 1.
Numerator and Denominator
The numerator and denominator are crucial parts of a fraction.

Numerator: This is the number above the line in a fraction. It represents how many parts of the whole are being considered. In \(\frac{10}{3}\), the numerator is 10.

Denominator: This is the number below the line in a fraction. It shows the total number of equal parts the whole is divided into. In \(\frac{10}{3}\), the denominator is 3.

When finding a reciprocal, the roles of the numerator and the denominator switch places. So the reciprocal of \(\frac{10}{3}\) becomes \(\frac{3}{10}\). It's important to understand these terms to avoid mistakes in mathematical operations.

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Most popular questions from this chapter

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