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Chapter 3: Problem 71

Find the reciprocal of each number. $$ \frac{9}{7} $$

Short Answer

Expert verified
The reciprocal of \( \frac{9}{7} \) is \( \frac{7}{9} \).

Step by step solution

01

- Understanding Reciprocals

The reciprocal of a number is found by flipping the numerator and the denominator. For a fraction \( \frac{a}{b} \), the reciprocal is \( \frac{b}{a} \).
02

- Apply the Definition

For the given fraction \( \frac{9}{7} \), identify the numerator and the denominator. Here, the numerator is 9, and the denominator is 7.
03

- Find the Reciprocal

Flip the numerator and denominator to find the reciprocal. Thus, the reciprocal of \( \frac{9}{7} \) is \( \frac{7}{9} \).

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Key Concepts

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

numerator and denominator
Let's begin by breaking down the basic terms numerator and denominator. These terms are essential to understanding fractions and their reciprocals.

A numerator is the top number in a fraction, representing how many parts of the whole are being considered. For example, in the fraction \(\frac{9}{7}\), 9 is the numerator.

The denominator is the bottom number in the fraction, indicating the total number of equal parts the whole is divided into. For the fraction \(\frac{9}{7}\), 7 is the denominator.

In simpler terms:
  • Numerator: Tells how many parts we have.
  • Denominator: Tells into how many parts the whole is divided.
Understanding these terms makes it easier to find reciprocals and work with fractions effectively.
fraction
A fraction represents a part of a whole. It consists of a numerator and a denominator, with a line separating them.

We can write fractions in several ways, but the most common form is a simple division of two integers. In the fraction \(\frac{9}{7}\), we have 9 parts out of 7.

Fractions can be:
  • Proper (numerator is less than denominator, e.g., \(\frac{1}{3}\))
  • Improper (numerator is equal to or greater than denominator, e.g., \(\frac{5}{4}\))
  • Mixed numbers (a whole number plus a fraction, e.g., 1\(\frac{1}{2}\))
The given fraction \(\frac{9}{7}\) is an improper fraction, since 9 is greater than 7.
basic mathematics
Understanding basic mathematics concepts like fractions and reciprocals is crucial for everyday problem-solving.

Let's tie these concepts together by looking at how to find a reciprocal.
The reciprocal of a number is simply flipping the numerator and denominator of a fraction. For example, to find the reciprocal of \(\frac{9}{7}\):
  • Identify the numerator (9) and the denominator (7).
  • Flip them to form \(\frac{7}{9}\).
So, the reciprocal of \(\frac{9}{7}\) is \(\frac{7}{9}\). This is a straightforward process if you understand numerators and denominators well!

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Most popular questions from this chapter

Estimate each of the following by estimating each mixed numeral as a whole number or as a mixed numeral where the fraction part is \(\frac{1}{2}\) and by estimating each fraction as \(0, \frac{1}{2},\) or 1 . $$ 96 \frac{2}{13} \div 5 \frac{19}{20}+3 \frac{1}{7} \cdot 5 \frac{18}{21} $$

Estimate each of the following by estimating each mixed numeral as a whole number or as a mixed numeral where the fraction part is \(\frac{1}{2}\) and by estimating each fraction as \(0, \frac{1}{2},\) or 1 . $$ 1 \frac{5}{8}+1 \frac{27}{28} \cdot 6 \frac{35}{74} $$

A triathlete runs \(\frac{7}{8} \mathrm{mi}\), canoes \(\frac{1}{3} \mathrm{mi},\) and swims \(\frac{1}{6}\) mi. How many miles does the triathlete cover?

A baker used \(\frac{1}{2}\) lb of flour for rolls, \(\frac{1}{4}\) lb for donuts, and \(\frac{1}{3} \mathrm{lb}\) for cookies. How much flour was used?

Estimate each of the following by estimating each mixed numeral as a whole number or as a mixed numeral where the fraction part is \(\frac{1}{2}\) and by estimating each fraction as \(0, \frac{1}{2},\) or 1 . $$ 7 \frac{29}{60}+10 \frac{12}{13} \cdot 24 \frac{2}{17} $$
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