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Chapter 1: Problem 51

Divide, if possible, and check. If a quotient is undefined, state this. $$ 14 \div(-2) $$

Short Answer

Expert verified
The quotient is -7.

Step by step solution

01

Identify the Numbers

In this division problem, identify the dividend and the divisor. The dividend is 14 and the divisor is -2.
02

Divide the Numbers

Divide the numbers as you normally would. Compute \( 14 \div (-2) \).
03

Simplify the Result

When dividing a positive number by a negative number, the result is negative. Hence, \(14 \div (-2) = -7\).
04

Check the Result

To verify, multiply the quotient by the divisor and check if the product equals the dividend. \(-7 \times (-2) = 14\). Since this is true, our division is correct.

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Key Concepts

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

division of integers
Understanding the division of integers is essential for solving many math problems. When dealing with integers, these numbers can be both positive and negative.

Here are the key steps:
  • Identify the dividend (the number being divided) and the divisor (the number you are dividing by).
  • Conduct the division as you would with positive numbers.
  • Consider the sign of both the dividend and the divisor to determine the sign of the quotient.

For example, in the problem \( 14 \div (-2) \), we identify 14 as the dividend and -2 as the divisor. We then conduct the division 14 / 2 as usual to get 7. Because one number is positive and the other negative, the quotient will be negative. Therefore, \( 14 \div (-2) = -7 \).
positive and negative numbers
When dividing integers, it's crucial to understand how positive and negative numbers interact.

General rules include:
  • Positive 梅 Positive = Positive
  • Negative 梅 Negative = Positive
  • Positive 梅 Negative = Negative
  • Negative 梅 Positive = Negative

In our example, 14 is positive, and -2 is negative. Following the rules, a positive divided by a negative equals a negative result. Hence, \( 14 \div (-2) = -7 \).

Having these rules at your fingertips can simplify the process of working with integers.
verifying division results
After computing a division problem, it's essential to verify your result to ensure its accuracy.

Checking the result involves:
  • Multiplying the quotient by the divisor
  • Confirming that the product equals the original dividend

Following our example, we calculated the quotient to be -7. To check this, we multiply -7 by -2: \[ -7 \times (-2) = 14 \]
The product is 14, which matches our original dividend. This shows our division is correct. Verifying results helps avoid mistakes and ensures confidence in your answers.

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Most popular questions from this chapter

Explain the different uses of the symbol "-". Give examples of each use of the symbol.

Simplify. $$ 15 x-y-5(3 x-2 y+5 z) $$

Write an equivalent expression without using grouping symbols. $$ -(9 x+1) $$

Evaluate. $$ \frac{a^{3}-4 a}{a(a-3)}, \text { for } a=-2 $$

Translate to an algebraic expression.[ 1.1] Nine more than twice a number
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