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Chapter 1: Problem 11

Evaluate each of the following expressions, if possible. $$\frac{30}{-6}$$

Short Answer

Expert verified
-5

Step by step solution

01

Identify the Numerator and Denominator

The given expression is \(\frac{30}{-6}\). Here, 30 is the numerator and -6 is the denominator.
02

Understand the Division of a Positive by a Negative Number

When dividing a positive number by a negative number, the result will be negative.
03

Perform the Division

Divide the absolute values of the numerator and the denominator: \(\frac{30}{6} = 5\). Since we are dividing a positive number by a negative number, the result will be negative. Thus, \(\frac{30}{-6} = -5\).

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Key Concepts

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

Numerator and Denominator
To understand division, it's crucial to grasp what numerators and denominators are. In any fraction, like \(\frac{30}{-6}\), the number on top is the numerator, and the number on the bottom is the denominator. The numerator represents how many parts or units we have, while the denominator indicates how many of those parts make up a whole. In our example, 30 is the numerator, meaning we have 30 parts. The denominator is -6, showing each group has 6 parts, but it's also negative. This simple division setup plays a significant role in understanding more complex algebraic expressions.
Positive and Negative Numbers
Positive and negative numbers are the backbone of algebra. Positive numbers are greater than zero and are found to the right of zero on a number line. Negative numbers are less than zero and lie to the left of zero. In division, understanding the signs of numbers is vital. When you divide a positive number by a negative number, the result is always negative. This rule comes from the fundamental properties of numbers. For example, in \(\frac{30}{-6}\), since 30 is positive and -6 is negative, the answer will be negative. The same applies to dividing negative by positive, but dividing two numbers with the same sign will always result in a positive number.
Division
Division in algebra involves splitting a number into equal parts. Think of it as finding out how many times a number (denominator) fits into another number (numerator). Here are the steps to follow:
  • First, identify the numerator and denominator.
  • Next, apply the division rules for positive and negative numbers. If the signs are different, the quotient will be negative.
  • Finally, perform the division using absolute values (ignore the signs temporarily), then apply the appropriate sign to the result.

In our example, \(\frac{30}{-6}\), we divide 30 by 6 to get 5. Since the numerator and denominator have different signs, the result is negative, giving us -5. This systematic approach makes solving such division problems straightforward.

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Most popular questions from this chapter

Evaluate the given expression. Remember to follow the order of operations. $$\frac{24-4 \cdot 5+8}{2+3 \cdot 6-4 \cdot 2}$$

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