Problem 34 Simplify using the order of oper... [FREE SOLUTION]

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Prealgebra

Julie Miller, Molly O鈥橬eill, Nancy Hyde

$Math Studyset 91影视 Explanations$ Math

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Chapter 2: Problem 34

Simplify using the order of operations. $$-7+(1-5)^{2} \div 4$$

Short Answer

Expert verified

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Step by step solution

Perform the operation inside the parentheses

Calculate the value inside the parentheses first. -7 + (1 - 5)^2 The expression inside the parentheses is (1 - 5), which simplifies to -4.

Apply the exponent

Next, apply the exponent to the simplified value inside the parentheses. -7 + (-4)^2 -4 squared is 16, so now we have: -7 + 16

Perform the division

Continue by performing the division operation. According to the original equation: -7 + (16 / 4) 16 divided by 4 is 4, so: -7 + 4

Perform the addition/subtraction

Finally, perform the addition/subtraction operation: -7 + 4 -7 plus 4 equals -3.

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Key Concepts

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

simplifying expressions

Simplifying expressions in mathematics involves reducing complex equations to their simplest form. This process makes it easier to understand and solve problems. Simplifying typically requires you to:
- Evaluate operations inside parentheses first
- Apply exponents
- Perform multiplications and divisions from left to right
- Finally, execute additions and subtractions from left to right
By following these steps, you can break down complicated expressions into manageable smaller parts.

parentheses in mathematics

Parentheses are used in mathematics to group parts of an expression, showing which operations should be performed first. They ensure the correct order of operations, also known as PEMDAS or BIDMAS. For example, in the expression $1-5$, parentheses indicate that subtraction needs to be completed before moving on to other operations. Ignoring parentheses can lead to incorrect results.

exponents in algebra

Exponents in algebra are used to denote repeated multiplication of a number by itself. For instance, $ (-4)^2 $, which means $-4 \times -4$, results in 16.
In any expression, you should:

Evaluate expressions inside parentheses containing exponents first
Apply exponent rules accurately

It's crucial to square the value inside the parentheses after simplifying it.

division and addition in algebra

When simplifying expressions involving division and addition, follow the order of operations:

Complete any division operations before addition or subtraction
Move from left to right through the expression

In the given exercise, after squaring $ -4 $ to get 16, you divide it by 4 to acquire 4. Only then do you add this value to \-7 \ to get the final result of \-3.\
Remember to always follow this methodical order for accurate results.

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91影视

Simplify using the order of operations. $$-7+(1-5)^{2} \div 4$$

Short Answer

Step by step solution

Perform the operation inside the parentheses

Apply the exponent

Perform the division

Perform the addition/subtraction

Key Concepts

simplifying expressions

parentheses in mathematics

exponents in algebra

division and addition in algebra

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