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Chapter 1: Problem 101

Divide. $$ \frac{0}{-7} $$

Short Answer

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Step by step solution

01

Identify the Dividend and Divisor

In the expression \(\frac{0}{-7}\), 0 is the dividend and -7 is the divisor.
02

Know the Division Rule for Zero

Any number divided by a non-zero number is zero. This includes both positive and negative divisors.
03

Apply the Rule

Applying the rule, \(\frac{0}{-7} = 0\). This is because dividing zero by any non-zero number results in zero.

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Key Concepts

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

dividend
In any division problem, the dividend is the number that is being divided. It is the number on the top of the division fraction or the numerator in a fraction. For example, in the division problem \(\frac{0}{-7}\), the dividend is 0.
Knowing the dividend is crucial because it determines the nature of the division equation.
  • If the dividend is 0, certain special rules apply which make the division process easier.
  • The dividend can be a positive number, a negative number, or zero itself.
Understand this term well as it will help you to solve division problems effectively and correctly.
divisor
The divisor is the number by which the dividend is being divided. It is the number on the bottom of the division fraction or the denominator. In \(\frac{0}{-7}\), the divisor is -7.
The divisor plays a crucial role in determining the result of the division.
  • A non-zero divisor means the division is possible.
  • If the divisor is zero, the division is undefined and cannot be performed.
Always check your divisor to ensure proper operations in your calculations.
division rule for zero
The division rule for zero is fairly simple but extremely important in mathematics. Here鈥檚 what you need to know:
  • When the dividend is zero (0), and the divisor is any non-zero number (positive or negative), the result of the division is always zero. For example, \(\frac{0}{-7} = 0\).
  • If the divisor is zero, the division operation is undefined. This means you cannot divide any number by zero because it does not result in a meaningful number.
Using these rules helps avoid common mistakes in division problems involving zero.
fraction
Fractions represent a part of a whole and consist of two parts: the numerator (top number) and the denominator (bottom number). In division, fractions can represent the dividend and divisor.
  • The numerator is the dividend.
  • The denominator is the divisor.
In the problem \(\frac{0}{-7}\), this fraction tells us to divide 0 by -7. Knowing how to read and interpret fractions is essential for solving division problems efficiently.

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Most popular questions from this chapter

To the student and the instructor: Writing exercises, denoted by \([\%,\) are meant to be answered using sentences. Because answers to many writing exercises will vary, solutions are not listed at the back of the book. Charlie insists that \(15-4+1 \div 2 \cdot 3\) is \(2 .\) What error is he making?

Calculate using the rules for order of operations. If an expression is undefined, state this. $$ \frac{7 \cdot 3-5^{2}}{9+4 \cdot 2} $$

Find an equivalent expression by factoring. $$ 5 x+50 $$

Calculate using the rules for order of operations. $$ 15-1+\sqrt{5^{2}-(3+1)^{2}}(-1) $$

Calculate using the rules for order of operations. If an expression is undefined, state this. $$ 2^{2}-5^{2} $$
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