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Chapter 1: Problem 275

Divide. $$ -52 \div(-4) $$

Short Answer

Expert verified
The answer is 13.

Step by step solution

01

Identify the Numbers

Identify the numbers in the division problem. The numbers given are -52 and -4.
02

Divide the Absolute Values

Divide the absolute values of the numbers. The absolute value of -52 is 52, and the absolute value of -4 is 4. So, divide 52 by 4, which equals 13.
03

Determine the Sign of the Quotient

The rule for division involving negative numbers states that if you divide two numbers with the same sign, the quotient is positive. Since both numbers are negative, the quotient is positive.
04

State the Final Answer

Combine the results from the previous steps: The quotient is 13.

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Key Concepts

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

absolute value
The absolute value of a number represents its distance from zero on the number line. It is always a non-negative number.
For example, the absolute value of -5 is 5, written as \(|-5| = 5\) and the absolute value of 3 is 3, written as \(|3| = 3\).
Understanding absolute values helps simplify calculations, especially when dealing with negative numbers.
For instance, in the exercise, we have the numbers -52 and -4. Their absolute values are 52 and 4 respectively.
This lets us perform the division more easily by working with positive numbers first.
negative numbers
Negative numbers are numbers less than zero, and they are represented with a minus sign (-).
When working with negative numbers, there are a few rules to remember:
  • Adding a negative number is like subtracting a positive number.
  • Subtracting a negative number is like adding a positive number.
  • Multiplying or dividing two negative numbers results in a positive number.
  • Multiplying or dividing a negative number by a positive number results in a negative number.
In the exercise, we are dividing -52 by -4. Both numbers are negative, so according to the rules, the result will be positive.
division rules
When dividing numbers, there are some important rules to follow:
  • Dividing two positive numbers gives a positive result.
  • Dividing a positive number by a negative number, or vice versa, gives a negative result.
  • Dividing two negative numbers gives a positive result because the negatives cancel each other out.
In our exercise, we divide \(-52 \div -4\).

First, we find the absolute values, which are 52 and 4.
Dividing 52 by 4 gives us 13. Since we divided two negative numbers, our final answer is positive 13.

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