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Chapter 1: Problem 87

Simplify the given expression. $$ \frac{17+14}{9-8} $$

Short Answer

Expert verified
The simplified expression is 31.

Step by step solution

01

Simplify the Numerator

First, simplify the numerator of the fraction by adding the two numbers together: \( 17 + 14 = 31 \).
02

Simplify the Denominator

Next, simplify the denominator by subtracting the two numbers: \( 9 - 8 = 1 \).
03

Write the Simplified Fraction

Now, write the fraction using the simplified numerator and denominator: \( \frac{31}{1} \).
04

Simplify the Fraction

Since dividing by 1 does not change the value, the fraction simplifies to just \( 31 \).

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Key Concepts

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

Numerator and Denominator
Fractions are composed of two main parts: the numerator and the denominator. The numerator is the number above the fraction bar. It indicates how many parts of a whole we are considering. In our example fraction \( \frac{17+14}{9-8} \), the numerator is \( 17+14 \).
The denominator, on the other hand, is the number below the fraction bar. It tells us into how many parts the whole is divided. In the same fraction, the denominator is \( 9-8 \).
  • The numerator answers "how many" or "how much."
  • The denominator shows "into how many equal parts."
Recognizing these parts will make operations like simplifying fractions more intuitive.
Basic Arithmetic Operations
To simplify a fraction, you often need to perform basic arithmetic operations like addition, subtraction, multiplication, or division. These operations help us break down and reorganize the numbers within a fraction. In our problem, we start with a fraction that requires top and bottom arithmetic.
First, we perform addition in the numerator: \( 17 + 14 \). This calculates to \( 31 \). Next, we execute subtraction in the denominator: \( 9 - 8 \). This is simplified to \( 1 \).
  • Addition helps to sum up or combine different terms.
  • Subtraction assists in finding the difference or reducing terms.
Using these operations appropriately is key to correctly simplifying fractions.
Fraction Simplification Steps
Once you have simplified both the numerator and the denominator through basic arithmetic, it becomes straightforward to simplify the fraction as a whole. Let's go through the fraction simplification steps:
  • Simplify Operations: Start by performing any necessary operations on the numerator and denominator, like addition or subtraction.
  • Form the Fraction: Use these newly calculated numbers to form a new fraction, which in this case becomes \( \frac{31}{1} \).
  • Simplify: Check if the fraction can be simplified further. Here, a denominator of 1 simplifies the fraction to just the numerator, giving us \( 31 \).
By understanding these steps, you can effectively manage fraction simplifications, turning complex expressions into simpler, more readable forms.

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