/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 456 In the following exercises, find... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 4: Problem 456

In the following exercises, find the difference. $$2 \frac{5}{8}-1 \frac{7}{8}$$

Short Answer

Expert verified
\(\frac{3}{4}\)

Step by step solution

01

- Convert Mixed Numbers to Improper Fractions

First, convert each mixed number to an improper fraction.For \(2 \frac{5}{8}\): Multiply the whole number 2 by the denominator 8, and then add the numerator 5.\[2 \frac{5}{8} = \frac{2 \times 8 + 5}{8} = \frac{16 + 5}{8} = \frac{21}{8} \]For \(1 \frac{7}{8}\): Multiply the whole number 1 by the denominator 8, and then add the numerator 7.\[1 \frac{7}{8} = \frac{1 \times 8 + 7}{8} = \frac{8 + 7}{8} = \frac{15}{8} \]
02

- Subtract the Improper Fractions

Subtract the fractions: \[\frac{21}{8} - \frac{15}{8} \] Since the denominators are the same, subtract the numerators: \[\frac{21 - 15}{8} = \frac{6}{8} \]
03

- Simplify the Fraction

Simplify the fraction \(\frac{6}{8}\):Find the greatest common divisor (GCD) of 6 and 8, which is 2. Divide both the numerator and the denominator by the GCD:\[\frac{6 \div 2}{8 \div 2} = \frac{3}{4} \]

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

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

Mixed Numbers
Mixed numbers combine a whole number and a fraction. For example, in the mixed number 2 \(\frac{5}{8}\), 2 is the whole number and \(\frac{5}{8}\) is the fraction part. Mixed numbers are useful for representing values that are more than a whole but not quite the next whole number.
To work with them in operations like subtraction, it's often easier to convert mixed numbers into improper fractions first.
An improper fraction has a numerator (top number) larger than its denominator (bottom number), making it easier to subtract or add.
Improper Fractions
An improper fraction is where the numerator is greater than or equal to the denominator. For instance, \(\frac{21}{8}\) and \(\frac{15}{8}\) in our exercise are improper fractions.
To convert a mixed number to an improper fraction, follow these steps:
  • Multiply the whole number by the denominator.
  • Add this product to the numerator.
  • Place this sum over the original denominator.
    • For example, to convert \(2\frac{5}{8}\) into an improper fraction: Multiply 2 by 8, add 5, and place the result over 8:
    \[ 2\frac{5}{8} = \frac{2 \times 8 + 5}{8} = \frac{21}{8} \]
    This makes operations like subtraction straightforward since you only need to handle the numerators.
Simplifying Fractions
Simplifying fractions means making them as simple as possible. A fraction is simplified when the numerator and denominator are as small as possible.
For instance, in the final step of the example, we simplify \(\frac{6}{8}\) by finding the greatest common divisor (GCD) of 6 and 8, which is 2.
  • Divide both the numerator and the denominator by their GCD.

The simplified form of \(\frac{6}{8}\) is:
\[ \frac{6 \div 2}{8 \div 2} = \frac{3}{4} \]
Simplifying fractions makes them easier to understand and work with.
It's an essential skill for cleaning up answers and ensuring clarity in both math homework and exams.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

In the following exercises, simplify. $$ \frac{2^{3}-2^{2}}{\left(\frac{3}{4}\right)^{2}} $$

In the following exercises, simplify. $$ -\frac{22}{25}+\frac{9}{40} $$

In the following exercises, subtract. $$\frac{11}{12}-\frac{5}{12}$$

In the following exercises, evaluate the given expression. Express your answers in simplified form, using improper fractions if necessary. 8\(u^{2} v^{3}\) when \(u=-\frac{3}{4}\) and \(v=-\frac{1}{2}\)

In the following exercises, perform the indicated operation. $$ 5 \frac{8}{11}+2 \frac{4}{11} $$
See all solutions

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Read Explanation

Probability and Statistics

Read Explanation

Geometry

Read Explanation

Mechanics Maths

Read Explanation

Statistics

Read Explanation

Applied Mathematics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.