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Chapter 1: Problem 68

Write a fraction with denominator 24 that is equivalent to \(\frac{5}{8}\)

Short Answer

Expert verified
The fraction is \(\frac{15}{24}\).

Step by step solution

01

- Understand the problem

The problem asks to find a fraction with denominator 24 that is equivalent to the given fraction \(\frac{5}{8}\).
02

- Set up the equation

An equivalent fraction can be found by multiplying the numerator and the denominator of \(\frac{5}{8}\) by the same number. Here, the target denominator is 24.
03

- Determine the multiplication factor

To change the denominator from 8 to 24, find the number that when multiplied by 8 equals 24. This number is 3, because \(8 \times 3 = 24\).
04

- Multiply numerator and denominator by the same factor

Multiply both the numerator and denominator of \(\frac{5}{8}\) by 3 to get the equivalent fraction. \[\frac{5 \times 3}{8 \times 3} = \frac{15}{24}\]
05

- Write the equivalent fraction

The fraction equivalent to \(\frac{5}{8}\) with a denominator of 24 is \(\frac{15}{24}\).

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Key Concepts

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

Fractions
A fraction represents a part of a whole. It is written with two numbers separated by a slash.
The number above the slash is called the 'numerator,' and the number below it is the 'denominator.'
Fractions can be simplified or turned into equivalent fractions by multiplying or dividing both the numerator and the denominator by the same number.
Understanding this allows us to express the same part of a whole in different ways.
Numerator and Denominator
The numerator and denominator are essential parts of a fraction.
The numerator tells us how many parts we have, and the denominator tells us how many equal parts make up a whole.
For example, in the fraction \(\frac{5}{8}\), 5 is the numerator, and 8 is the denominator. This means we have 5 parts out of a total of 8 equal parts.
Understanding the relationship between the numerator and the denominator helps in operations like finding equivalent fractions.
Multiplication
In fractions, multiplication is used to find equivalent fractions.
This involves multiplying both the numerator and the denominator of a fraction by the same number without changing its value.
In our example, we wanted to change the denominator of \(\frac{5}{8}\) to 24. We determined that multiplying 8 by 3 gives us 24.
\(8 \times 3 = 24\)
To find the new numerator, we also multiply the original numerator by 3:
\(5 \times 3 = 15\)
This gives us the equivalent fraction \(\frac{15}{24}\), which represents the same value as the original fraction.

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Most popular questions from this chapter

The operation of division is used in divisibility tests. A divisibility test allows us to determine whether a given number is divisible (without remainder) by another number. An integer is divisible by 3 if the sum of its digits is divisible by \(3,\) and not otherwise. Show that (a) \(4,799,232\) is divisible by 3 and (b) \(2,443,871\) is not divisible by 3

Write each sentence as an equation, using \(x\) as the variable. Then find the solution from the set of integers between \(-12\) and \(12,\) inclusive. When 5 is added to a number, the result is \(-5\)

Write each sentence as an equation, using \(x\) as the variable. Then find the solution from the set of integers between \(-12\) and \(12,\) inclusive. The quotient of a number and 4 is \(-1\)

Translate each phrase into a mathematical expression. Use \(x\) as the variable. Combine like terms when possible. Nine times a number added to \(6,\) subtracted from triple the sum of 12 and 8 times the number (Hint: Triple means three times.)

The operation of division is used in divisibility tests. A divisibility test allows us to determine whether a given number is divisible (without remainder) by another number. An integer is divisible by 12 if it is divisible by both 3 and \(4,\) and not otherwise. Show that (a) \(4,249,474\) is not divisible by 12 (b) \(4,253,520\) is divisible by 12 and
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