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Chapter 5: Problem 698

In the following exercises, simplify each expression. $$ 4(10.3-5.8) $$

Short Answer

Expert verified
18

Step by step solution

01

Identify the Expression Inside the Parentheses

Look at the expression inside the parentheses: \(10.3 - 5.8\)
02

Subtract the Numbers Inside the Parentheses

Perform the subtraction inside the parentheses: \(10.3 - 5.8 = 4.5\)
03

Multiply by the Number Outside the Parentheses

Now multiply the result by the number outside the parentheses: \(4 \times 4.5\)
04

Calculate the Final Product

Perform the multiplication: \(4 \times 4.5 = 18\)

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Key Concepts

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

Basic Arithmetic
Arithmetic is the branch of mathematics that deals with numbers and the basic operations: addition, subtraction, multiplication, and division. Understanding arithmetic is crucial as it forms the foundation for more advanced math concepts.
Here, let's look at a simple subtraction within parentheses:
  • Identify the Numbers: You have 10.3 and 5.8.
  • Perform the Subtraction: Subtract 5.8 from 10.3 to get 4.5.
    This subtraction gives us the number needed for the next step.
Knowing how to execute basic arithmetic operations is essential for simplifying expressions and solving more complex problems in mathematics.
Parentheses in Math
Parentheses are symbols used in math to group parts of an expression that should be considered as one unit. They help in determining the order of operations, making sure that calculations inside the parentheses are performed first.
For example, in the expression 4(10.3 - 5.8):
  • Focus Inside Parentheses First: Calculate the value inside the parentheses: 10.3 - 5.8 = 4.5.
  • Simplify Step by Step: Perform operations inside the parentheses before moving to those outside.
By simplifying what鈥檚 inside the parentheses first, you follow the correct order of operations (PEMDAS/BODMAS), ensuring accurate results.
Multiplication
Multiplication is one of the basic operations of arithmetic. It involves calculating the total of one number added repeatedly. In the expression 4(10.3 - 5.8), multiplication is straightforward once you've dealt with what's inside the parentheses.
Here鈥檚 how you handle multiplication in our example:
  • Identify the Values to Multiply: You have 4 and 4.5.
  • Perform the Multiplication: Multiply them: 4 times 4.5 equals 18.
Multiplication helps in quickly scaling numbers, transforming simpler, repeated addition into a single calculation.
It鈥檚 vital in both everyday math and more complex mathematical contexts.

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