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Chapter 1: Problem 404

Simplify. $$ \frac{9 \cdot 6-4 \cdot 7}{22+3} $$

Short Answer

Expert verified
.The simplified fraction is

Step by step solution

01

Simplify the Numerator

First, simplify the expression in the numerator: The numerator is given by: The numerator is: : : - - . Simplify each part separately: : result is 54.Next, the term : The result is 28.Subtract these results: 54 - 28 = 26.
02

Simplify the Denominator

Simplify the denominator: . The sum is 25.
03

Form the Simplified Fraction

Combine the simplified numerator and denominator: . We have established that the numerator is 26 and the denominator is 25. So, the simplified fraction is

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Key Concepts

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

Fraction Simplification
Fraction simplification is a fundamental skill in algebra. It involves reducing a fraction to its simplest form. This means ensuring the numerator (top number) and denominator (bottom number) have no common factors other than 1. Proper simplification can make fractions easier to understand and work with.
Here鈥檚 a breakdown of the process:
  • Simplify the numerator by performing any arithmetic operations.
  • Simplify the denominator by performing any arithmetic operations.
  • Combine the simplified numerator and denominator to form a new fraction.
  • Check for any common factors and reduce if possible.
Remember, simplifying fractions often relies on basic arithmetic operations such as addition, subtraction, multiplication, and division.
Numerator and Denominator
Understanding the terms numerator and denominator is key to working with fractions. In a fraction represented as \(\frac{a}{b}\),
  • The numerator 'a' represents the number of parts being considered.
  • The denominator 'b' represents the total number of equal parts in a whole.
In our example, the fraction is \(\frac{9 \times 6 - 4 \times 7}{22 + 3}\).
First, we calculate the numerator: \9 \times 6 - 4 \times 7\
This simplifies to:
54 - 28 = 26.
Next, we calculate the denominator:
22 + 3 = 25.
So, the simplified fraction becomes \(\frac{26}{25}\).
Basic Arithmetic Operations
Basic arithmetic operations are the building blocks of algebra and are crucial for simplifying fractions.
These operations include:
  • Addition (+)
  • Subtraction (-)
  • Multiplication (脳)
  • Division (梅)
In our given problem, we use multiplication, addition, and subtraction to simplify the fraction.
Starting with the numerator, we perform the following steps:
Multiply 9 by 6, which equals 54.
Multiply 4 by 7, which equals 28.
Subtract 28 from 54 to get 26.
For the denominator, we simply add 22 and 3 to get 25.
These steps showcase the importance of basic arithmetic in solving algebraic expressions and simplifying fractions.

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