/*! 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 5 Change each mixed number to an i... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 3: Problem 5

Change each mixed number to an improper fraction. $$1 \frac{5}{8}$$

Short Answer

Expert verified
\(1 \frac{5}{8} = \frac{13}{8}\)

Step by step solution

01

Understand the Mixed Number

The mixed number is given as \(1 \frac{5}{8}\). This means there is 1 whole and \(\frac{5}{8}\) as the fractional part.
02

Expression of Whole Number as Fraction

Convert the whole number part (1) into a fraction with the same denominator as the fractional part. This is \(\frac{8}{8}\).
03

Add Fractions Together

Add the fraction representation of the whole number (\(\frac{8}{8}\)) to the fractional part (\(\frac{5}{8}\)). The equation becomes: \[\frac{8}{8} + \frac{5}{8}\]
04

Calculate the Numerator Sum

Since the denominators are the same, add the numerators: \(8 + 5 = 13\).
05

Write Final Improper Fraction

The result of adding the fractions is \(\frac{13}{8}\), which is the improper fraction equivalent to the mixed number.

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
A mixed number is a combination of a whole number and a fraction. Think of it as a hybrid of the two, where it represents parts of a whole beyond just whole numbers.
This is useful when you deal with situations that aren't perfectly divisible by one whole unit but have a remainder.
  • For example, in daily life, you might say you have one and a half pizzas, which in mixed numbers is written as \(1 \frac{1}{2}\).
  • In our exercise, the mixed number \(1 \frac{5}{8}\) means there is 1 whole pizza and \(\frac{5}{8}\) of another.
Mixed numbers help us see clearly both the number of wholes and the remaining fractional part.
Conversion
Converting between mixed numbers and improper fractions is a key skill in mathematics. An improper fraction is one where the numerator, the number on top, is larger than the denominator, or the bottom number.
  • To convert a mixed number to an improper fraction, you need to turn the whole number into a fraction with the same denominator.
  • For instance, with \(1 \frac{5}{8}\), the whole number 1 is expressed as \(\frac{8}{8}\).
  • This makes it easy to add to the fractional part \(\frac{5}{8}\) to get \(\frac{13}{8}\).
Through conversion, you can perform mathematical operations more easily, such as addition or multiplication.
Adding Fractions
Adding fractions, especially with like denominators, is straightforward once you understand the process.
  • The key is to keep the denominator the same, allowing you to simply add the numerators together.
  • In our example, adding \(\frac{8}{8}\) and \(\frac{5}{8}\) is simplified to adding the numerators: 8 and 5.
  • This addition gives us \(\frac{13}{8}\), a simple yet effective way to convert and sum fractions.
Remember, this only works when the denominators are the same. Otherwise, you'd have to find a common denominator first.
Numerator and Denominator
Understanding numerators and denominators is crucial in working with fractions.
  • The numerator, the top number, represents how many parts we are considering.
  • The denominator, the bottom number, tells us into how many parts the whole is divided.
  • In an exercise like \(\frac{13}{8}\), 13 is the numerator indicating how many parts \(\text{(of size }\frac{1}{8}\text{ each)}\) we have, while 8 is the denominator.
This foundational knowledge helps in actions like converting mixed numbers, or adding and subtracting fractions. Recognizing their roles lets you manipulate fractions with confidence.

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

Write 1 as a fraction with denominator \(8 .\)

Simplify. $$4 \cdot 6+3$$

Find the area of the triangle with base 13 inches and height 8 inches.

Multiply or divide as indicated. $$\frac{9}{10}+\frac{7}{10}$$

The following problems all involve the concept of borrowing. Subtract in case. \(9 \frac{2}{3}-5 \frac{3}{4}\)
See all solutions

Recommended explanations on Math Textbooks

Discrete Mathematics

Read Explanation

Statistics

Read Explanation

Mechanics Maths

Read Explanation

Logic and Functions

Read Explanation

Probability and Statistics

Read Explanation

Theoretical and Mathematical Physics

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.