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Chapter 1: Problem 42

Find each quotient. $$ \frac{38}{-19} $$

Short Answer

Expert verified
The quotient is -2.

Step by step solution

01

Identify the Numerator and Denominator

The given fraction is \(\frac{38}{-19}\). Here, 38 is the numerator and -19 is the denominator.
02

Divide the Numerator by the Denominator

Divide 38 by -19. This can be calculated as \(38 \div (-19) = -2\).
03

Determine the Sign

Since one number is positive and the other is negative, the result is negative. Therefore, the quotient is -2.
04

Write the Final Answer

The quotient of \(\frac{38}{-19}\) is -2.

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Key Concepts

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

Fraction Division
When we need to divide fractions or numbers that are written in fraction form, we follow certain steps. Let's say we have a fraction of the form \(\frac{a}{b}\), where \(a\) is the numerator and \(b\) is the denominator. To divide the numerator by the denominator, we simply perform the division operation like in any division problem. For example, in the problem \(\frac{38}{-19}\), we divide 38 by -19. This operation can be written and calculated as 38 梅 -19. Furthermore, we need to pay attention to the signs (positive or negative) to find the correct quotient.
Positive and Negative Numbers
It's crucial to understand how positive and negative numbers interact, especially during division. There are a few rules to keep in mind:
  • If both numbers have the same sign (both positive or both negative), the quotient is positive.
  • If the numbers have different signs (one positive and the other negative), the quotient is negative.
In our given example, 38 is a positive number, and -19 is a negative number. Following the rule above, a positive number divided by a negative number results in a negative quotient. Hence, 38 梅 -19 = -2.
Numerator and Denominator
Fractions consist of two parts: the numerator and the denominator. The numerator is the top number, and the denominator is the bottom number. For instance, in the fraction \(\frac{38}{-19}\), 38 is the numerator, and -19 is the denominator. The numerator represents how many parts are being considered, and the denominator represents how many parts make up a whole. Properly identifying these components is essential when performing operations like division. By understanding the roles of the numerator and denominator, you can better analyze and solve fraction problems accurately.

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Most popular questions from this chapter

Simplify each expression. $$ -10+x+4 x-7-4 x $$

Translate each phrase into a mathematical expression. Use \(x\) as the variable. Combine like terms when possible. A number multiplied by \(-7,\) subtracted from the sum of 13 and six times the number

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