/*! 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 248 Simplify. \(\frac{4}{5}(8.6+3.... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 5: Problem 248

Simplify. \(\frac{4}{5}(8.6+3.9)\)

Short Answer

Expert verified
10

Step by step solution

01

Add the numbers inside the parentheses

First, calculate the sum inside the parentheses: \(8.6 + 3.9\). Combine the decimal numbers to get the result: \(8.6 + 3.9 = 12.5\).
02

Multiply the fraction by the sum

Next, multiply the fraction \(\frac{4}{5}\) by the sum \(12.5\) we found in Step 1. To do this, convert the fraction to a decimal: \(\frac{4}{5} = 0.8\).Now multiply: \(0.8 \times 12.5 = 10\).
03

Provide the simplified result

After performing the multiplication, the simplified result is \(10\).

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.

Fractions
Fractions represent a part of a whole. They consist of a numerator (top number) and a denominator (bottom number). The fraction \( \frac{4}{5} \) means that we have 4 parts out of 5 equal parts.

To simplify expressions with fractions, you can sometimes convert the fraction to a decimal. For example, \( \frac{4}{5} \) can be changed to 0.8 because 4 divided by 5 equals 0.8.

Fraction addition or subtraction requires the denominators to be the same. But for multiplication, you only need to multiply the numerators together and the denominators together. Then, you simplify the result if possible.
Decimal Addition
When adding decimals, it's important to align the decimal points. This ensures that you are adding the correct place values together (like tenths with tenths, hundredths with hundredths, etc.).

For instance, in the given exercise, we add 8.6 and 3.9. To do this, you align the decimal points and add each column of numbers:
  • 8.6
  • + 3.9

When added together, 8.6 + 3.9 equals 12.5.

It is also helpful to note that if the decimal places are different, you can add zeros to make them the same, ensuring accuracy.
Multiplication
Multiplication involves calculating the total of one number taken multiple times. When it involves fractions or decimals, understanding place values and conversions is crucial.

In our exercise, we multiply \( \frac{4}{5} \) (which we converted to 0.8) with 12.5.

Steps to multiply a fraction by a decimal:
  • Convert the fraction to a decimal if necessary (e.g., \( \frac{4}{5} = 0.8 \)).
  • Multiply the decimal numbers (0.8 and 12.5 in this case).

When you multiply 0.8 by 12.5, you get 10.

Tip: Always double-check your conversions and alignments to ensure accuracy in multiplication, whether with whole numbers, fractions, or decimals.

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, round each number to the nearest hundredth. $$5.7932$$

In the following exercises, convert each decimal to a fraction or mixed number. $$12.75$$

In the following exercises, find the unit rate. Round to two decimal places, if necessary. 54 beats in 0.5 minute

In the following exercises, find each unit price and then identify the better buy. Round to three decimal places. Cheese \(\$ 6.49\) for 1 lb. block or \(\$ 3.39\) for \(\frac{1}{2}\) lb. block

In the following exercises, locate each number on a number line. $$0.8$$
See all solutions

Recommended explanations on Math Textbooks

Geometry

Read Explanation

Applied Mathematics

Read Explanation

Probability and Statistics

Read Explanation

Discrete Mathematics

Read Explanation

Calculus

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.