Problem 4 Simplify. $$(-1.6+0.4)^{2}$$... [FREE SOLUTION]

91影视

Prealgebra

Julie Miller, Molly O鈥橬eill, Nancy Hyde

$Math Studyset 91影视 Explanations$ Math

1 Edition

Chapter 5: Problem 4

Simplify. $$(-1.6+0.4)^{2}$$

Short Answer

Expert verified

1.44

Step by step solution

Simplify the Expression Inside the Parentheses

Start by simplifying the expression inside the parentheses: (-1.6 + 0.4)

Perform the Addition

Add -1.6 and 0.4: -1.6 + 0.4 = -1.2

Square the Result

Now take the result from step 2 and square it: (-1.2)^2 = 1.44

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.

Basic Arithmetic

Basic arithmetic involves fundamental mathematical operations like addition, subtraction, multiplication, and division. In the exercise given, the key operation is addition.
When we add two numbers, we combine their values to produce a sum. For example, adding -1.6 and 0.4 means we are combining a negative number with a positive one.
Here's the breakdown:

-1.6 is a negative number (moving to the left on a number line)
0.4 is a positive number (moving to the right on a number line)

When we add these together, we get closer to zero. Their sum is -1.2 because the positive number reduces the negative number's magnitude.
Remember:

Negative + Positive = depends on which number has a larger magnitude
Negative + Negative = more negative

Parentheses Evaluation

When dealing with mathematical expressions, evaluating what's inside the parentheses first is crucial. Parentheses tell us which part of the expression to solve before addressing others.
In our exercise, we start with $(-1.6 + 0.4)$.
Parentheses help in:

Grouping terms
Simplifying expressions in a clear order
Avoiding confusion with operations

According to the order of operations (PEMDAS/BODMAS), parentheses come first. This means:

Evaluate inside the parentheses: $-1.6 + 0.4 = -1.2$

By simplifying within the parentheses first, we ensure our calculations are accurate.

Squaring Numbers

Squaring a number means multiplying the number by itself. It's represented by an exponent of 2.
For instance, in our exercise, we need to square -1.2:
$(-1.2)^2$
Here's the process:

Multiply -1.2 by -1.2
Since both numbers are negative, their product is positive

This results in:
$-1.2 \times -1.2 = 1.44$
Squaring always gives a positive result when squaring negative or positive numbers.

Positive $\times$ Positive = Positive
Negative $\times$ Negative = Positive

Squaring numbers can be used to area calculations, expanding polynomials, and solving geometric problems.

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. $$(-1.6+0.4)^{2}$$

Short Answer

Step by step solution

Simplify the Expression Inside the Parentheses

Perform the Addition

Square the Result

Key Concepts

Basic Arithmetic

Parentheses Evaluation

Squaring Numbers

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Mechanics Maths

Discrete Mathematics

Statistics

Decision Maths

Geometry

Study anywhere. Anytime. Across all devices.