Problem 265 Simplify. Give the answer as a d... [FREE SOLUTION]

91影视

Prealgebra

Lynn Marecek, MaryAnne Anthony-Smith

$Math Studyset 91影视 Explanations$ Math

2016 Edition

Chapter 5: Problem 265

Simplify. Give the answer as a decimal. 3.6$\left(\frac{9}{8}-2.72\right)$

Short Answer

Expert verified

-5.742

Step by step solution

- Simplify the Expression Inside the Parentheses

First, calculate the value of the expression inside the parentheses $\frac{9}{8} - 2.72$. Convert $\frac{9}{8}$ to a decimal: \[ \frac{9}{8} = 1.125 \]. Then subtract 2.72 from 1.125: \[ 1.125 - 2.72 = -1.595 \].

- Multiply by 3.6

Next, multiply -1.595 by 3.6: \[ 3.6 \times (-1.595) = -5.742 \].

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 to Decimals

Converting fractions to decimals is a crucial skill. To change a fraction into a decimal, divide the numerator (the top number) by the denominator (the bottom number).

In our exercise, we needed to convert $\frac{9}{8}$ into a decimal. We did this by performing the division:

\[ \frac{9}{8} = 1.125 \]

This gives us 1.125 as the decimal form of $\frac{9}{8} $. Practicing this process with other fractions can help build your understanding. For example, $\frac{1}{4} $ becomes 0.25 and $\frac{3}{5} $ becomes 0.6.

Subtraction of Decimals

Once you have two decimal numbers, subtraction is straightforward. Line up the decimal points and subtract as you would with whole numbers.

In our exercise, we subtracted 2.72 from 1.125:

1.125 鈥� 2.72 = -1.595

Remember, subtracting a larger number from a smaller one yields a negative result. It's just like borrowing in regular subtraction but with more attention to the decimal points.

Practicing with many examples helps with gaining confidence in handling decimal subtraction.

Multiplication of Decimals

Multiplying decimals is a bit different from whole numbers. First, ignore the decimal points and multiply the numbers as if they were whole numbers.

In our exercise, we multiplied 3.6 and -1.595:

Step 1: Multiply 36 and 1595 which equals 57420.

Step 2: Count the total number of decimal places in both original numbers (one in 3.6 and three in 1.595, making a total of four decimal places).

Step 3: Place the decimal point in the product, four places from the right, resulting in a final value of -5.742.

Thus:

\[ 3.6 \times (-1.595) = -5.742 \]

This method assures accuracy when doing decimal multiplication.

One App. One Place for Learning.

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

Get started for free

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

91影视

Simplify. Give the answer as a decimal. 3.6\(\left(\frac{9}{8}-2.72\right)\)

Short Answer

Step by step solution

- Simplify the Expression Inside the Parentheses

- Multiply by 3.6

Key Concepts

Fractions to Decimals

Subtraction of Decimals

Multiplication of Decimals

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Logic and Functions

Geometry

Pure Maths

Decision Maths

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.