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Chapter 2: Problem 34

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

Short Answer

Expert verified
-3

Step by step solution

01

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.
02

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
03

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
04

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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Most popular questions from this chapter

The height of Mount Everest is \(29,029 \mathrm{ft}\). The lowest point on the surface of the Earth is \(-35,798 \mathrm{ft}\) (that is, 35,798 ft below sea level) occurring at the Mariana Trench on the Pacific Ocean floor. What is the difference in altitude between the height of Mt. Everest and the Mariana Trench?

simplify. $$.6-33$$

Multiply. $$(-1)(-1)(-1)(-1)(-1)(-1)$$

One of the most famous blizzards in the United States was the blizzard of \(1888 .\) In one part of Nebraska, the temperature plunged from \(40^{\circ} \mathrm{F}\) to \(-25^{\circ} \mathrm{F}\) in \(5 \mathrm{hr}\). What was the average change in temperature during this time?

Place the correct symbol \((>,<, \text { or }=)\) between the two numbers. $$0 \square-6$$
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