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Chapter 1: Problem 23

Simplify each numerical expression. (Objective 2) $$7 \cdot 4 \cdot 2 \div 8+14$$

Short Answer

Expert verified
The simplified expression is 21.

Step by step solution

01

Perform Multiplication

First, multiply the numbers from left to right as indicated by the order of operations (PEMDAS/BODMAS). Calculate \(7 \cdot 4 \cdot 2\). Multiply 7 and 4 first:\[ 7 \times 4 = 28 \]Then multiply the result by 2:\[ 28 \times 2 = 56 \]
02

Perform Division

Next, divide the result from the multiplication by 8.\[ 56 \div 8 = 7 \]
03

Perform Addition

Finally, add 14 to the result of the division.\[ 7 + 14 = 21 \]

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Key Concepts

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

Arithmetic Operations
Arithmetic operations are basic calculations that involve numbers. These operations include addition, subtraction, multiplication, and division. Understanding these operations is essential for tackling more complex math problems effectively. For example, in the expression given, you have a combination of these operations that you must simplify according to a specific order.
  • Addition combines two or more numbers to get a total sum.
  • Subtraction finds the difference between two numbers.
  • Multiplication finds the total of one number taken repeatedly.
  • Division splits a whole into equal parts.
Understanding these basic operations and knowing how to apply them according to order conventions ensures accurate and efficient problem solving.
Multiplication and Division
Multiplication and division are closely related and involve understanding how numbers scale or distribute evenly.
It's important to know that both operations should be performed from left to right as per the standard order of operations.
When handling expressions such as in our exercise, you must first deal with all multiplication and division operations before moving to addition or subtraction.
For instance, in the expression\[7 \cdot 4 \cdot 2 \div 8\]First, solve the multiplication:\[7 \times 4 = 28\]Continue with:\[28 \times 2 = 56\]Then, perform the division:\[56 \div 8 = 7\]This discipline ensures we don't make mistakes that could affect the final outcome.
Addition and Subtraction
Addition and subtraction are straightforward operations, yet they require careful attention to ensure they are executed correctly. These operations are often performed after multiplication and division when simplifying expressions.
When working through such problems, always remember the addition and subtraction step comes last, following any multiplication or division.
In the current example, after working out the multiplication and division
  • The multiplication gave us 56,
  • The division gave us 7,
and finally, we add 14 to 7:\[7 + 14 = 21\]Breaking these steps into manageable parts can simplify even complex-looking problems. Always make sure to write down each step clearly to avoid any mix-up, ensuring accuracy in your final answer.

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Most popular questions from this chapter

State the property that justifies each statement. For example, \(3+(-4)=(-4)+3\) because of the commutative property for addition. $$5+(-12)=-12+5$$

Simplify each algebraic expression and then evaluate the resulting expression for the given values of the variables. \(4 x y-5-8 x y+9\) for \(x=-3\) and \(y=-3\)

Simplify each algebraic expression and then evaluate the resulting expression for the given values of the variables. \(5 x-9 x y+3 x+2 x y\) for \(x=12\) and \(y=-1\)

State in your own words the associative property for addition of integers.

Simplify each numerical expression. Don't forget to take advantage of the properties if they can be used to simplify the computation. $$-46(-73-27)$$
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