/*! 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 6 Convert each complex decimal to ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 6: Problem 6

Convert each complex decimal to a fraction or mixed number. Be sure to reduce. \(0.12 \frac{2}{5}\)

Short Answer

Expert verified
The complex decimal \(0.12 \frac{2}{5}\) converts to the fraction \(\frac{13}{25}\).

Step by step solution

01

Separate the Mixed Decimal

The given number is a complex decimal: \(0.12 \frac{2}{5}\). Recognize that it can be separated into a decimal part \(0.12\) and a fractional part \(\frac{2}{5}\).
02

Convert Decimal to Fraction

Convert the decimal part \(0.12\) to a fraction. We know that \(0.12 = \frac{12}{100}\). Simplify this fraction by dividing the numerator and denominator by their greatest common divisor, which is 4. This gives us \(\frac{3}{25}\).
03

Add the Fractions

Now we need to combine the fractions \(\frac{3}{25}\) and \(\frac{2}{5}\). First, convert \(\frac{2}{5}\) into a fraction with a denominator of 25 by multiplying both the numerator and the denominator by 5. This gives \(\frac{10}{25}\).
04

Simplify the Result

Add \(\frac{3}{25}\) and \(\frac{10}{25}\) by adding the numerators: \(3 + 10 = 13\). The resultant fraction is \(\frac{13}{25}\).
05

Finalize the Answer

Since \(\frac{13}{25}\) cannot be reduced further (13 is a prime number and does not divide 25), this is the final answer. The complex decimal \(0.12 \frac{2}{5}\) converts to the fraction \(\frac{13}{25}\).

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.

Complex Decimals
Complex decimals are numbers that include both a decimal and a fractional component. They can seem intimidating at first because they blend these two different representations of numbers. However, transforming them into a more uniform expression like a fraction or a mixed number can make things much simpler.When handling a complex decimal such as \(0.12 \frac{2}{5}\), it is important to break it down into manageable parts. This means separating the decimal part (in this case, 0.12) and the fractional part (\(\frac{2}{5}\)), each of which is converted separately before being combined into a single fraction.
Mixed Decimals
Mixed decimals have components that are both decimal parts and fractional parts. Understanding how to work with them is a critical skill as they often appear in real-world problems.Begin by observing each part of the mixed decimal separately. For example, in \(0.12 \frac{2}{5}\), you treat the decimal (0.12) and the fraction (\(\frac{2}{5}\)) as two separate entities that will ultimately combine into one.The process involves converting the decimal to a fraction, followed by adjusting and combining it with the fractional part. This helps in simplifying calculations and helps unify the expression into a single fraction.
Fraction Simplification
Fraction simplification is a crucial step in converting decimals to fractions efficiently. It involves reducing a fraction to its simplest form by dividing both the numerator and the denominator by their greatest common divisor.For instance, when you convert the decimal 0.12 to a fraction, you get \(\frac{12}{100}\). The greatest common divisor of 12 and 100 is 4. By dividing both the numerator and denominator by 4, you simplify the fraction to \(\frac{3}{25}\). This practice not only makes calculations easier but also ensures the results are presented in their simplest form, which is always preferred.
Adding Fractions
Adding fractions requires a common denominator. If fractions have different denominators, it's important to adjust them so they share the same one鈥攖his allows for straightforward addition.Take the example of \(\frac{3}{25}\) and \(\frac{2}{5}\). These fractions have different denominators, 25 and 5 respectively. To add them, convert \(\frac{2}{5}\) into a fraction with a denominator of 25. Multiply both numerator and denominator by 5 to get \(\frac{10}{25}\).Once both fractions share the same denominator, simply add the numerators: \(3 + 10 = 13\). This results in the fraction \(\frac{13}{25}\), which, in this case, is already in its simplest form.

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

Convert each fraction to a decimal. $$ \frac{3}{8} $$

Perform the following operations. \(\frac{15}{16} \cdot\left(\frac{7}{10}-0.5\right)\)

Perform each operation. $$ \text { Convert } 0.5 \frac{9}{16} \text { to a decimal. } $$

Read each decimal by writing it in words. 0.005

Perform each operation. $$ 4 \frac{13}{18} \div\left(5 \frac{3}{14}+3 \frac{5}{21}\right) $$
See all solutions

Recommended explanations on Math Textbooks

Decision Maths

Read Explanation

Probability and Statistics

Read Explanation

Calculus

Read Explanation

Applied Mathematics

Read Explanation

Mechanics Maths

Read Explanation

Geometry

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.