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Chapter 1: Problem 122

\(\frac{18-5+2}{1-4}\)

Short Answer

Expert verified
-5

Step by step solution

01

- Simplify the Numerator

First, we need to simplify the expression in the numerator, which is \(18 - 5 + 2\). Start by performing the subtraction: \(18 - 5 = 13\). Next, add 2 to the result: \(13 + 2 = 15\). So, the simplified numerator is 15.
02

- Simplify the Denominator

Now, simplify the expression in the denominator, which is \(1 - 4\). Perform the subtraction: \(1 - 4 = -3\). So, the simplified denominator is -3.
03

- Divide the Numerator by the Denominator

Finally, divide the simplified numerator by the simplified denominator: \(\frac{15}{-3}\). Perform the division: \(15 \text{ 梅 } -3 = -5\). So, the result of the expression \(\frac{18-5+2}{1-4}\) is -5.

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Key Concepts

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

Simplifying Expressions
Simplifying expressions is all about breaking down complex arithmetic operations into simpler steps. When you see an expression like \(18 - 5 + 2\), focus on the individual operations inside first.

Here's how you can do it:
  • Perform each operation step by step.
  • For example, start with \(18 - 5\). This subtraction gives us 13.
  • Next, add the remaining number, which is 2, to the result.
  • So, \(13 + 2 = 15\).

By simplifying in this manner, you avoid mistakes and make complex expressions easier to handle. This follows the order of operations, which is key to getting the correct answer.
Numerator and Denominator
In any fraction, the numerator is the top part, and the denominator is the bottom part. For instance, in the fraction \(\frac{a}{b}\), 'a' is the numerator, and 'b' is the denominator.

When simplifying an expression like \(\frac{18-5+2}{1-4}\), you first work on each part separately. For the numerator 18 - 5 + 2:
  • First, subtract 5 from 18 to get 13.
  • Next, add 2 to 13 to get 15.

So, the numerator simplifies to 15.
For the denominator, perform the subtraction 1 - 4, which is -3. Always remember to follow the proper steps to simplify both parts before combining them.
Division
Once you have your simplified numerator and denominator, you can perform the division. In our example, we're left with \(\frac{15}{-3}\).

Division is straightforward:
  • Divide the numerator (15) by the denominator (-3).
  • The result of \(15 \div -3\) is -5.

Make sure to keep track of the signs when dividing. A positive divided by a negative is always negative, hence the result is -5. Being careful with signs ensures you get the right answer every time.

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