Problem 29 $(16-5) \div(3-5)$... [FREE SOLUTION]

91影视

Elementary Algebra Within Reach

Ron Larson, Kimberly Nolting

$Math Studyset 91影视 Explanations$ Math

6 Edition

Chapter 1: Problem 29

$(16-5) \div(3-5)$

Short Answer

Expert verified

-5.5

Step by step solution

Simplify Parentheses

First, simplify the expressions within the parentheses: $16-5$ equals 11 and $3-5$ equals -2.

Division

Now we do the division step: $11 \div -2$ equals -5.5.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Order of Operations

Understanding the order of operations is crucial in simplifying algebraic expressions because it tells us which calculations to perform first to get the correct answer. The standard order is Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right), often remembered by the acronym PEMDAS.

In our exercise $ (16-5) \div (3-5) $, we handle the parentheses first. This means we calculate $ 16-5 $ and $ 3-5 $ before addressing the division sign. If we were to ignore the parentheses and perform division first, we would end up with an incorrect result.

Arithmetic Operations

Arithmetic operations include addition, subtraction, multiplication, and division. They are the building blocks of algebra and are used to manipulate numbers and variables.

In our example, subtraction is used inside the parentheses: $ 16-5 $ gives us 11 and $ 3-5 $ gives us -2. Each of these operations simplifies the parts of the expression so that they can be further operated on, adhering to the order of operations.

Negative Numbers in Algebra

Negative numbers often confuse students, but they follow the same rules as positive numbers. In algebra, when you have a negative sign in front of a parenthesis, it means you should multiply the contents by -1.

In this case, for the expression $ 3-5 $, we get -2. It鈥檚 important to treat this result just like any other number. So for the division in our exercise, we divide 11 by -2. Remember that a positive number divided by a negative number results in a negative answer, hence $ -5.5 $.

Division in Algebra

In algebra, division can seem intimidating, but it operates under straightforward principles. When dividing two numbers, you're essentially determining how many times the divisor fits into the dividend.

In classic arithmetic, we are used to seeing positive numbers, but division with negative numbers works under the same principle. In our problem, we're dividing 11 by -2. It鈥檚 the same as asking, 'How many times does -2 go into 11?' The answer is -5.5 times, reflecting the fact that dividing a positive number by a negative one yields a negative result.

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91影视

\((16-5) \div(3-5)\)

Short Answer

Step by step solution

Simplify Parentheses

Division

Key Concepts

Order of Operations

Arithmetic Operations

Negative Numbers in Algebra

Division in Algebra

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