Problem 53 Reduce the given fraction to low... [FREE SOLUTION]

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Prealgebra

David Arnold

$Math Studyset 91影视 Explanations$ Math

2020 Edition

Chapter 4: Problem 53

Reduce the given fraction to lowest terms. $$\frac{94}{-6}$$

Short Answer

Expert verified

The reduced fraction is $ -\frac{47}{3} $.

Step by step solution

Identify the Greatest Common Divisor (GCD)

To reduce the fraction $ \frac{94}{-6} $ to its lowest terms, we first need to find the greatest common divisor (GCD) of the numerator 94 and the denominator 6. Let's list the factors of each number:- Factors of 94: 1, 2, 47, 94- Factors of 6: 1, 2, 3, 6The common factor between them is 2. Therefore, the GCD is 2.

Divide the Numerator and Denominator by the GCD

Now, divide both the numerator and the denominator by the GCD, which is 2:\[ \frac{94}{-6} = \frac{94 \div 2}{-6 \div 2} = \frac{47}{-3} \]

Simplify the Negative Sign

We typically write fractions with the negative sign only in the numerator or in front of the fraction. Here, $ \frac{47}{-3} $ can be rewritten as $ -\frac{47}{3} $ for standard representation.

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Key Concepts

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

Greatest Common Divisor

The Greatest Common Divisor, commonly abbreviated as GCD, is a key concept in simplifying fractions. It refers to the largest number that can evenly divide both the numerator and the denominator of a fraction.
Finding the GCD is essential because it helps us simplify fractions by reducing both the numerator and denominator to their lowest terms.
Here's how you can find the GCD:

List all the factors of the numerator and the denominator.
Identify the largest factor that both numbers share鈥攖his is the GCD.

For example, in the fraction $\frac{94}{-6}$, the factors of 94 are 1, 2, 47, and 94. The factors for 6 are 1, 2, 3, and 6. Their common factor is 2, making the GCD equal to 2. By dividing both terms by the GCD, the fraction can be reduced.

Factors

Factors are the numbers you multiply together to get another number. Understanding factors is crucial when simplifying fractions.
To find factors, start by testing numbers beginning from 1 up to the number itself. If a number divides evenly, without leaving a remainder, it is a factor.
For example, the factors of 94 are:

1, since 1 x 94 = 94
2, since 2 x 47 = 94
47, since 47 x 2 = 94
94, since 94 x 1 = 94

For 6, the factors are:

1, since 1 x 6 = 6
2, since 2 x 3 = 6
3, since 3 x 2 = 6
6, since 6 x 1 = 6

By identifying the common factor, which in this case is 2, you can simplify the fraction $\frac{94}{-6}$ by dividing both numbers by this greatest factor.

Simplifying Fractions

Simplifying fractions means reducing them to their simplest or lowest terms. This process makes fractions easier to work with and understand.
The first step is to find the GCD of the numerator and denominator. Once it's found, you divide both by the GCD.
Let's consider $\frac{94}{-6}$ as an example.
After determining that the GCD is 2, you'll divide both 94 and -6 by 2:

94 divided by 2 equals 47
-6 divided by 2 equals -3

This gives us the simplified fraction $\frac{47}{-3}$.
Typically, we write the negative sign of fractions in front of the entire fraction, yielding $-\frac{47}{3}$. Thus, the fraction is now in its simplest form, making it easier to read and interpret.

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91影视

Reduce the given fraction to lowest terms. $$\frac{94}{-6}$$

Short Answer

Step by step solution

Identify the Greatest Common Divisor (GCD)

Divide the Numerator and Denominator by the GCD

Simplify the Negative Sign

Key Concepts

Greatest Common Divisor

Factors

Simplifying Fractions

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