/*! 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 45 Give the result as a fraction in... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 8: Problem 45

Give the result as a fraction in simplest form. $$ (0.5)\left(-\frac{1}{8}\right) $$

Short Answer

Expert verified
\( \frac{-1}{16} \)

Step by step solution

01

Convert Decimal to Fraction

Convert the decimal number to a fraction. The number 0.5 is equal to the fraction \( \frac{1}{2} \).
02

Multiply the Fractions

Next, multiply the two fractions: \( \frac{1}{2} \) and \( -\frac{1}{8} \). Use the rule for multiplying fractions: multiply the numerators together and then the denominators together.\[ \frac{1}{2} \times -\frac{1}{8} = \frac{1 \times -1}{2 \times 8} = \frac{-1}{16} \]
03

Simplify the Fraction

Check if the fraction \( \frac{-1}{16} \) can be simplified. Since both the numerator and the denominator are already in their simplest form, the fraction \( \frac{-1}{16} \) is the simplest form.

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.

Decimals to Fractions
Decimals are numbers that represent fractions in base ten. Converting a decimal to a fraction involves writing the decimal number as a fraction of two whole numbers. For example, the decimal 0.5 can be written as \( \frac{1}{2} \). This is because 0.5 means 5 tenths or \( \frac{5}{10} \), which simplifies to \( \frac{1}{2} \).
To convert a decimal to a fraction:
  • Write down the decimal divided by 1 (e.g., 0.5/1)
  • Multiply the numerator and denominator by 10 for every number after the decimal point (e.g., for 0.5, multiply by 10 to get \( \frac{5}{10} \))
  • Simplify the fraction, if possible, by dividing both the numerator and denominator by their greatest common divisor
Converting decimals to fractions helps in performing arithmetic operations like multiplication and division as fractions make these operations straightforward.
Multiplying Fractions
Multiplying fractions involves a simple rule: multiply the numerators together and then multiply the denominators together. Let鈥檚 look at an example.
The multiplication of \( \frac{1}{2} \) and \( -\frac{1}{8} \) is calculated as follows:
  • Multiply the numerators: \( 1 \times -1 = -1 \)
  • Multiply the denominators: \( 2 \times 8 = 16 \)
  • Combine these results to get the product: \( \frac{-1}{16} \)
The multiplication of fractions is easy because you only need to follow the standard procedure of multiplying the numerators to get the new numerator and the denominators to get the new denominator. Always remember to check your final answer to see if it can be simplified further, although, in this case, \( \frac{-1}{16} \) is already at its simplest form.
Simplifying Fractions
Simplifying a fraction means reducing it to its simplest form where the numerator and denominator share no common factors other than 1. A fraction is in its simplest form when it cannot be reduced any further. Let's see how this works:
For example, if you have a fraction such as \( \frac{8}{16} \):
  • Find the greatest common divisor (GCD) of the numerator and the denominator, which is 8 in this case
  • Divide both the numerator and the denominator by this GCD: \( \frac{8}{8} = 1 \) and \( \frac{16}{8} = 2 \)
  • So, \( \frac{8}{16} \) simplifies to \( \frac{1}{2} \)
In the original exercise, the fraction \( \frac{-1}{16} \) is already in its simplest form because 1 and 16 have no common divisors other than 1. Simplifying fractions makes them easier to understand and work with in calculations.

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

Fill in each table. Round to the nearest degree. Then draw a circle graph to represent the information given in each table. $$ \begin{array}{|l|c|c|} \hline {\text { Color Distribution of M\&M's Milk Chocolate }} \\ \hline \text { Color } & \text { Percent } & \text { Degrees in Sector } \\ \hline \text { Blue } & 24 \% & \\ \hline \text { Orange } & 20 \% & \\ \hline \text { Green } & 16 \% & \\ \hline \text { Yellow } & 14 \% & \\ \hline \text { Red } & 13 \% & \\ \hline \text { Brown } & 13 \% & \\ \hline \end{array} $$

Find each percent. See Sections 7.2 or 7.3. $$ 30 \% \text { of } 12 $$

Two dice are tossed. Find the probability of each sum of the dice. (Hint: Draw a tree diagram of the possibilities of two tosses of a die, and then find the sum of the numbers on each branch.) A sum of 6

Graph each equation. $$ 5 x-2 y=10 $$

Twenty-five people in a survey were asked to give their current checking account balances. Use the balances shown in the following list to complete the frequency distribution table to the right. See Example 6. $$\begin{array}{rrrrr}\$ 53 & \$ 105 & \$ 162 & \$ 443 & \$ 109 \\\\\$ 468 & \$ 47 & \$ 259 & \$ 316 & \$228 \\\\\$ 207 & \$ 357 & \$ 15 & \$ 301 & \$ 75 \\\\\$ 86 & \$ 77 & \$ 512 & \$ 219 & \$ 100 \\\\\$ 192 & \$288 & \$ 352 & \$ 166 & \$ 292\end{array}$$ $$\begin{array}{|c|c|c|}\hline \begin{array}{c}\text { Class Intervals } \\\\\text { (Account Balances) }\end{array} & \text { Tally } & \begin{array}{c}\text { Class Frequency } \\\\\text { (Number of People) }\end{array} \\\\\hline \$ 100-\$ 199 & & \\\\\hline\end{array}$$
See all solutions

Recommended explanations on Math Textbooks

Probability and Statistics

Read Explanation

Calculus

Read Explanation

Mechanics Maths

Read Explanation

Pure Maths

Read Explanation

Applied Mathematics

Read Explanation

Statistics

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.