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Chapter 1: Problem 28

Divide and then check by multiplying. $$\frac{0}{30}$$

Short Answer

Expert verified
The result of \( \frac{0}{30} \) is 0, verified by multiplication.

Step by step solution

01

Understand the Division Operation

When dividing \(0\) by any non-zero number, the result is always \(0\). In this exercise, you need to divide \(0\) by \(30\). The division can be written as \( \frac{0}{30} \).
02

Perform the Division

To find \( \frac{0}{30} \), we recognize that \(0\) divided by any number is \(0\). Therefore, the result of the division \( \frac{0}{30} \) is \(0\).
03

Check by Multiplying

To verify the answer, multiply the result of the division back by \(30\). If \(0 \times 30 = 0\), then our division result is correct. Since \(0 \times 30 = 0\), the division is verified.

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Key Concepts

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

Multiplication for Verification
Once we have completed a division problem, such as dividing 0 by 30, we can use multiplication to verify our answer. This step ensures accuracy in our calculations.
To verify the division, simply multiply the quotient by the divisor, which in this case are 0 and 30 respectively. When you multiply 0 (the result of \( \frac{0}{30} = 0 \)) by 30, you perform the calculation \( 0 \times 30 \).
  • Understand that multiplying any number by 0 will always result in 0.
  • Through this multiplication check, we see: \( 0 \times 30 = 0 \).
  • Since the multiplication returns to the original numerator (0), our division result is confirmed correct.
This method of verification is very helpful, especially as problems become more complex.
Zero Property of Division
The zero property of division tells us about division involving 0. When 0 is divided by any non-zero number, the result is always 0.
  • This is because there are no parts or segments of zero that can be spread among a non-zero number.
  • The expression \( \frac{0}{b} = 0 \) demonstrates this property, where b is any non-zero divisor.
Let's try it with \( \frac{0}{30} \):
  • You start with zero things and wish to divide them into 30 groups, but still, each group gets nothing, so the result remains 0.
Understanding this property is key to grasping more advanced mathematical concepts.
Division of Zero
To perform the division of zero by a number means you start with zero and attempt to distribute it evenly. But, what does this really mean?
Consider \( \frac{0}{30} \):
  • You are trying to see how many times 30 can go into 0, which naturally is none.
  • No matter the non-zero divisor, the quotient will always be 0 because zero can't be divided further.
The main takeaway is that dividing zero by a non-zero number keeps the quotient simplified to just zero.

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