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Chapter 1: Problem 1

Simplify each numerical expression. (Objective 2) $$9+14-7$$

Short Answer

Expert verified
The simplified expression is 16.

Step by step solution

01

Add the First Two Numbers

Take the first two numbers in the expression, which are 9 and 14, and add them together. \[ 9 + 14 = 23 \]
02

Subtract the Next Number

Take the result from Step 1 and subtract the next number in the expression, which is 7. \[ 23 - 7 = 16 \]

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Key Concepts

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

Understanding Addition
Addition is one of the basic operations in arithmetic that helps us combine numbers. When we perform addition, we start with a set of numbers and find their sum. It鈥檚 like putting amounts together into a larger amount. In the expression you鈥檙e working with, addition is the first operation: you add 9 and 14.

To understand this step more deeply:
  • Identify the numbers to be added. In this case, it's 9 and 14.
  • Add the numbers together: 9 + 14.
  • Write down the result, which is 23.
Addition is commutative, which means the order doesn't change the sum (e.g., 9 + 14 is the same as 14 + 9). However, since the expression has both addition and subtraction, it鈥檚 important to follow the given order to correctly simplify it.
Exploring Subtraction
Subtraction is another fundamental operation that helps us find the difference between numbers. It鈥檚 like taking away one number from another to see what remains. In the original expression, subtraction follows the addition step, taking the result 23 and subtracting 7 from it.

Here's a deeper dive into subtraction:
  • Start with the result from the addition step, which is 23.
  • Subtract the next number in the sequence, 7, from 23.
  • Write down the final result, which is 16.
Like addition, subtraction is not commutative; changing the order changes the result. Therefore, it鈥檚 crucial to always follow the correct sequence when simplifying numerical expressions.
The Step-by-Step Solution
The step-by-step solution is a systematic approach to simplifying numerical expressions. It's like following a recipe in a cookbook: each step builds on the previous one to achieve the final result. For the expression 9 + 14 - 7, the solution was broken down as follows:

Firstly, perform addition:
  • Add the first two numbers, 9 and 14, to get 23.
Secondly, perform subtraction:
  • Take the result from the addition, which is 23, and subtract 7 to obtain 16.
This approach ensures clarity and precision, allowing students to follow each arithmetic operation logically and systematically. Step-by-step solutions are not only vital for enhancing understanding but also for catching mistakes along the way by checking each intermediate result.

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Most popular questions from this chapter

Simplify each algebraic expression and then evaluate the resulting expression for the given values of the variables. \(5 x-6 x+x-7 x-x-2 x\) for \(x=-15\)

State whether the expressions in each problem are equivalent and explain why or why not. \(a+5(x+y)\) and \((a+5) x+y\)

State whether the expressions in each problem are equivalent and explain why or why not. \(7 x+6(y-2 z)\) and \(6(2 z-y)+7 x\)

State the property that justifies each statement. For example, \(3+(-4)=(-4)+3\) because of the commutative property for addition. $$143(-7)=-7(143)$$

Simplify each numerical expression. Don't forget to take advantage of the properties if they can be used to simplify the computation. $$-16-14+18+21+14-17$$
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