Problem 398 Simplify. $$ \frac{-6+3}{17-... [FREE SOLUTION]

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Chapter 1: Problem 398

Simplify. $$ \frac{-6+3}{17-8} $$

Short Answer

Expert verified

The simplified form is $ \frac{-1}{3} $.

Step by step solution

Simplify the Numerator

Look at the numerator: $ -6 + 3 $. Perform the addition inside the numerator first. $ -6 + 3 = -3 $.

Simplify the Denominator

Next, simplify the denominator: $ 17 - 8 $. Perform the subtraction inside the denominator. $ 17 - 8 = 9 $.

Divide the Simplified Numerator by the Simplified Denominator

Now, divide the simplified numerator by the simplified denominator: $ \frac{-3}{9} $. This simplifies to $ \frac{-1}{3} $ by dividing both the numerator and the denominator by 3.

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Key Concepts

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

Numerator and Denominator

Fractions can seem difficult at first, but they become much simpler once you understand the roles of the numerator and the denominator. In any fraction, the numerator is the top number, representing a part of the whole. The denominator is the bottom number, showing the total number of equal parts that make up the whole.
The exercise begins with the fraction $ \frac{-6+3}{17-8} $. Here, $-6 + 3$ is the numerator, and $17 - 8$ is the denominator. By first addressing the operations in the numerator and denominator separately, you can simplify the fraction step-by-step.
Knowing this, you can double-check your work as you go, ensuring you simplify correctly.

Addition and Subtraction

Simplifying fractions often involves basic arithmetic operations like addition and subtraction within the numerator and denominator. In this particular exercise, we start with the expression $ \frac{-6+3}{17-8} $.
It's crucial to handle the addition and subtraction before doing anything else. First, simplify the numerator by performing the addition: $ -6 + 3 = -3 $. Then, simplify the denominator by performing the subtraction: $ 17 - 8 = 9 $.
These operations turn the original fraction into $ \frac{-3}{9} $. Solving in this way helps you progressively break down the problem, making it easier to manage.

Division and Simplification

The last step in simplifying fractions involves dividing and reducing the fraction to its simplest form. For the fraction $ \frac{-3}{9} $, identify the greatest common factor (GCF) of the numerator and denominator. The GCF of 3 and 9 is 3.
Divide both the numerator and the denominator by this GCF:

Numerator: $ -3 \div 3 = -1 $
Denominator: $ 9 \div 3 = 3 $

After this division, your simplified fraction is $ \frac{-1}{3} $.
This step-by-step approach ensures you simplify complex fractions correctly, and understanding each step clearly helps you build a robust mathematical foundation.

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91影视

Simplify. $$ \frac{-6+3}{17-8} $$

Short Answer

Step by step solution

Simplify the Numerator

Simplify the Denominator

Divide the Simplified Numerator by the Simplified Denominator

Key Concepts

Numerator and Denominator

Addition and Subtraction

Division and Simplification

One App. One Place for Learning.

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