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Chapter 1: Problem 38

Find each quotient. $$ \frac{-28}{7} $$

Short Answer

Expert verified
-4

Step by step solution

01

Identify the numerator and denominator

In the given fraction, \(\frac{-28}{7}\), the numerator is \(-28\) and the denominator is \7\.
02

Divide the numerator by the denominator

Divide \(-28\) by \7\. When dividing a negative number by a positive number, the result will be negative. Calculate \-28 \/ 7\ which equals \-4\.

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Key Concepts

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

Numerator and Denominator
In any fraction, the fraction itself has two main components: the numerator and the denominator. Picture them as parts of a whole. The numerator is the top number of the fraction, while the denominator is the bottom number.
For instance, in the fraction \(\frac{-28}{7}\), \-28\ is the numerator and \7\ is the denominator. The numerator tells us how many parts of a whole we have, and the denominator tells us into how many equal parts the whole is divided.
Understanding these two components is the foundation of dealing with fractions, especially when performing operations like division. Always identify the numerator and denominator first before performing any division.
Negative and Positive Numbers
When dealing with negative and positive numbers, it is important to remember the basic rules of multiplication and division involving these numbers. A negative number multiplied or divided by a positive number always results in a negative number. Similarly, a negative number multiplied or divided by another negative number results in a positive number.
In the example given, \(\frac{-28}{7}\), we are dividing a negative number \(-28\) by a positive number \(7\). Hence, according to the rule, the result will be negative. It is critical to understand these sign rules to avoid mistakes. This is especially useful when calculating quotients of integers.
Integer Division
Integer division is a mathematical operation where one integer (the dividend) is divided by another integer (the divisor). The result is also an integer.
When performing integer division, especially with fractions, it is essential first to understand the values of the numerator and the denominator. Next, apply the rules of division for positive and negative numbers. In the exercise \(\frac{-28}{7}\), we performed integer division by dividing \-28\ by \7\. Since the denominator is a positive number, and the numerator is negative, the result of the division will be negative.
The calculation for \-28 \/ 7\ results in \-4\.

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Most popular questions from this chapter

To find the average (mean) of numbers, we add the numbers and then divide the sum by the number of terms added. For example, to find the average of \(14,8,3,9,\) and \(1,\) we add them and then divide by 5. $$ \frac{14+8+3+9+1}{5}=\frac{35}{5}=7 \leftarrow \text { Average } $$ Find the average of each group of numbers. \(23,18,13,-4,\) and \(-8\)

Write each sentence as an equation, using \(x\) as the variable. Then find the solution from the set of integers between \(-12\) and \(12,\) inclusive. The quotient of a number and 4 is \(-1\)

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To find the average (mean) of numbers, we add the numbers and then divide the sum by the number of terms added. For example, to find the average of \(14,8,3,9,\) and \(1,\) we add them and then divide by 5. $$ \frac{14+8+3+9+1}{5}=\frac{35}{5}=7 \leftarrow \text { Average } $$ Find the average of each group of numbers. $$ -15,29,8,-6 $$

Decide whether each statement is an example of the commutative, associative, identity, inverse, or distributive property. See Examples \(1,2,3,5,6,7,\) and \(9 .\) $$2(x+y)=2 x+2 y$$
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