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Chapter 3: Problem 176

In the following exercises, simplify each expression. $$5 \cdot 7-8 \cdot 2-4 \cdot 9$$

Short Answer

Expert verified
-17

Step by step solution

01

- Perform the multiplication operations

First, perform the multiplications in the expression. The expression is: i) Calculate \(5 \times 7\)ii) Calculate \(8 \times 2\)iii) Calculate \(4 \times 9\) The updated expression will be:\[35 - 16 - 36\]
02

- Perform the subtraction operations

Next, perform the subtractions from left to right:\(35 - 16\) gives 19Then subtract 36 from 19:\[19 - 36 = -17\]

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Key Concepts

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

Multiplication and Subtraction
Understanding multiplication and subtraction is crucial when simplifying expressions. Multiplication means adding a number to itself a certain number of times. For example, with 5 multiplied by 7, you are adding 5 together 7 times: \(5 \times 7 = 35\).
Subtraction is taking one number away from another. If you have 35 and subtract 16, you are left with 19: \(35 - 16 = 19\).
These operations are the basic building blocks for solving more complicated problems. Checking your calculations at each step can help catch errors early and make understanding easier.
Step-by-Step Solutions
Breaking a problem down into smaller steps can make solving it much simpler. Let's consider the example expression step by step. The initial problem is: \(5 \times 7 - 8 \times 2 - 4 \times 9\).
First, we handle the multiplication:
  • \(5 \times 7 = 35\)
  • \(8 \times 2 = 16\)
  • \(4 \times 9 = 36\)
This transforms our original expression into: \[35 - 16 - 36\]
Next, we perform the subtractions sequentially:
  • \(35 - 16 = 19\)
  • Then \(19 - 36 = -17\)
By breaking it down step-by-step, each part of the process becomes manageable. Follow each step carefully and confirm your results before moving forward.
Order of Operations
When simplifying expressions, the order in which you perform operations is very important. This is known as the Order of Operations, often remembered by the acronym PEMDAS: Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right).
In our example, \(5 \times 7 - 8 \times 2 - 4 \times 9\), we only have multiplication and subtraction. According to the order of operations, we handle multiplication before subtraction. Here are the steps again:
  • First, multiply:
  • \(5 \times 7 = 35\)
  • \(8 \times 2 = 16\)
  • \(4 \times 9 = 36\)
  • Then, subtract from left to right:
  • \(35 - 16 = 19\)
  • Then \(19 - 36 = -17\)
By carefully following these steps in the correct order, we ensure that we reach the right solution: -17.

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