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Chapter 1: Problem 10

Simplify. $$ 8.2-3 \div 1.2 \cdot 2.1 $$

Short Answer

Expert verified
The simplified expression is 2.95.

Step by step solution

01

Address the Division

First, perform the division operation as it appears before the multiplication, according to the order of operations (PEMDAS/BODMAS). Divide \(3\) by \(1.2\):\[3 \div 1.2 = 2.5\]
02

Address the Multiplication

Next, multiply the result from the division by \(2.1\):\[2.5 \cdot 2.1 = 5.25\]
03

Perform the Subtraction

Finally, subtract the result of the multiplication from \(8.2\):\[8.2 - 5.25 = 2.95\]

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Key Concepts

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

Division
The order of operations tells us to tackle division before addressing multiplication or subtraction in the given expression. In this problem, we begin by dividing 3 by 1.2. To conduct this division smoothly:
  • Recognize that division is essentially finding how many times the divisor fits into the dividend.
  • Convert the division into a simpler problem if needed (here it remains straightforward with division resulting in 2.5).
Understanding division strengthens your foundational math skills and enhances your ability to solve more complex equations efficiently.
Multiplication
Once division has been handled, we proceed with multiplication next per the order of operations. Multiplying the quotient obtained from the division (2.5) by 2.1 involves:
  • Keeping track of the decimal places, which requires multiplying normally and then adjusting the decimal point in the final answer.
  • Arriving at the product, which in this step is 5.25.
Multiplication is about combining groups and managing it in this problem ensures the expression simplifies correctly.
Subtraction
Finally, after handling both division and multiplication, we move to subtraction. The remaining task is to subtract the product from the previous step (5.25) from the original number 8.2. Here's how that looks:
  • Align the decimal points to ensure accuracy.
  • Subtract the smaller number from the larger, which results in a final answer of 2.95.
Subtraction is the process of removing or "taking away." It's crucial to get this step right for the integrity of the problem's solution.

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