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Chapter 6: Problem 1

Simplify. $$0.64+2.5(0.8)$$

Short Answer

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Question: Simplify the expression $$0.64 + 2.5(0.8)$$. Answer: $$2.64$$

Step by step solution

01

Perform the multiplication

We start by performing the multiplication: $$2.5 \times 0.8$$. To do this, multiply 2.5 by 0.8: $$2.5 \times 0.8 = 2$$
02

Perform the addition

Now we need to perform the addition: $$0.64 + 2$$. To do this, simply add the two numbers: $$0.64 + 2 = 2.64$$
03

Final answer

The simplified expression is: $$0.64 + 2.5(0.8) = 2.64$$

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Key Concepts

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

Understanding Arithmetic Operations
Arithmetic operations form the basic foundation of mathematics that we use in everyday life. They include four operations: addition, subtraction, multiplication, and division. In the given exercise, we work with addition and multiplication. Each operation follows specific rules.

  • Addition: This involves calculating the total of two numbers or expressions. For example, when adding $0.64$ to $2$, you combine them to get $2.64$.
  • Multiplication: This is like repeated addition. Multiplying $2.5$ by $0.8$ means adding $2.5$ to itself $0.8$ times, which gives us the result $2.0$.
Making sure that you understand how to perform each operation correctly is essential for tackling more complex problems later.
Order of Operations Simplified
To solve math expressions correctly, we must follow the order of operations. It's sometimes remembered by the acronym PEMDAS:
  • Parentheses
  • Exponents
  • Multiplication and Division (from left to right)
  • Addition and Subtraction (from left to right)
In the problem \(0.64 + 2.5(0.8)\), the order of operations tells us to do the multiplication first. That's why the first step is to calculate \(2.5 \times 0.8 = 2\). Only after this, should you proceed with the addition \(0.64 + 2\). This ensures that all calculations are done in the correct sequence.
Mastering Decimal Multiplication
Decimal multiplication is an extension of basic multiplication but involves numbers with values less than one. Here's how you handle it:

  • First, ignore the decimal points and multiply the numbers as if they are whole numbers. For instance, \(2.5\) and \(0.8\) become \(25\) and \(8\) respectively.
  • Next, count the total number of decimal places in the original numbers. \(2.5\) has one decimal place and \(0.8\) has one, totaling two decimal places.
  • After multiplying the whole numbers, adjust the decimal point in the result to reflect these two decimal places. Thus, \(25 \times 8 = 200\). Shift the decimal to get \(2.00\), which simplifies further to \(2.0\).
Being proficient with decimal multiplication simplifies many math problems and ensures accuracy in calculations.

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