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Chapter 1: Problem 56

Evaluate each of the following expressions, if possible. $$\frac{-28}{-4}-\frac{-32}{-8}$$

Short Answer

Expert verified
The expression evaluates to 3.

Step by step solution

01

- Simplify the First Fraction

Simplify the fraction \(\frac{-28}{-4}\). Since both the numerator and the denominator are negative, the fraction simplifies to a positive value. Compute the division: \(\frac{28}{4} = 7\).
02

- Simplify the Second Fraction

Simplify the fraction \(\frac{-32}{-8}\). Similarly, since both the numerator and the denominator are negative, the fraction simplifies to a positive value. Compute the division: \(\frac{32}{8} = 4\).
03

- Subtract the Simplified Fractions

Now that the fractions have been simplified to 7 and 4, subtract the second simplified fraction from the first: \(7 - 4 = 3\).

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Key Concepts

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

Fractions
Fractions are a way to represent parts of a whole.
They consist of a numerator (the top number) and a denominator (the bottom number).
In algebra, fractions are often encountered and need to be properly understood to solve equations.
  • The numerator indicates how many parts we have.
  • The denominator shows into how many parts the whole is divided.
In the exercise provided, fractions like \(\frac{-28}{-4}\) and \(\frac{-32}{-8}\) are given. Both the numerator and the denominator are negative, leading to a positive result when simplified.
Simplification
Simplification is the process of making an expression easier to work with.
For fractions, it means reducing them to their simplest form. This is done by dividing the numerator and the denominator by their greatest common divisor (GCD).
In the exercise, we simplified the fractions as follows:
  • For \(\frac{-28}{-4}\), we notice that both numbers are negative, so the fraction becomes positive.
  • Next, divide 28 by 4 to get 7.
The same process applies to \(\frac{-32}{-8}\):
  • Both numbers are negative, so the fraction becomes positive.
  • Then, divide 32 by 8 to get 4.
Simplification helps us easily compare, add, or subtract fractions.
Division
Division is one of the basic arithmetic operations and is essential in working with fractions.
It involves determining how many times one number is contained within another.
When dividing negative numbers, remember these key points:
  • A negative divided by a negative gives a positive result.
  • A negative divided by a positive (or vice versa) gives a negative result.
In our exercise, we divided negative numerators by negative denominators.
For instance, \(\frac{-28}{-4}\) results in 7 since the negatives cancel out, leading to a positive quotient.
Similarly, \(\frac{-32}{-8}\) results in 4. Understanding these division rules is crucial for handling fractions correctly in algebra.

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Most popular questions from this chapter

Evaluate the given expression. Remember to follow the order of operations. $$6+(4 \cdot 3+2)$$

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