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Chapter 1: Problem 380

Divide. Then check by multiplying. $$0 \div 8$$

Short Answer

Expert verified
0 梅 8 = 0.

Step by step solution

01

Understand the Division Operation

In this step, understand that dividing any number by 8 means finding how many times 8 fits into that number. Here, the problem is to divide 0 by 8.
02

Perform the Division

Divide 0 by 8. Since dividing 0 by any number always results in 0: \[ 0 \div 8 = 0 \]
03

Check by Multiplying

To check the division, multiply the quotient by the divisor and ensure it equals the original dividend. Here, multiply 0 by 8: \[ 0 \times 8 = 0 \] Since the result is 0 (the original dividend), the division is correct.

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Key Concepts

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

Division by Zero
It's important to understand what happens when you try to divide by zero because it鈥檚 a common source of confusion. Essentially, division by zero is undefined. This means there is no number that can result from dividing a number by zero. Imagine you have zero cookies and you want to share them among your friends. No matter how many friends you have, you simply can鈥檛 divide zero cookies in a way that makes sense! Therefore, in mathematics, when you see an equation like \[ \frac{a}{0} \] where 鈥榓鈥� can be any number, it is considered undefined. Trying to compute it will not give you a valid result and is not allowed in mathematics.
Quotient
The quotient is the result you get when you divide one number by another. For example, in the equation \[ 8 \div 4 = 2 \], the number 2 is the quotient. It tells you how many times the divisor fits into the dividend.
Here are some key points about quotients:
  • The quotient can be either an integer (whole number) or a decimal.
  • The quotient of any number divided by 1 is the number itself.
  • Any number divided by itself (except zero) has a quotient of 1.

In the given problem, 0 divided by 8 results in a quotient of 0. This is because 8 goes into 0, zero times.
Remainder
Remainder is what is left over after performing a division. For instance, when you divide 7 by 3, you get a quotient of 2 and a remainder of 1, because 3 fits into 7 two times, with 1 left over.
Here are the essentials about remainders:
  • If the remainder is zero, then the dividend is exactly divisible by the divisor.
  • The remainder is always less than the divisor.
  • In long division, the remainder helps to check the accuracy of the division process.

In our problem, when you perform the division \[ 0 \div 8 = 0 \], the remainder is 0. That's because 8 perfectly fits into 0, zero times, leaving nothing left over.
Understanding remainders is very useful in many areas of math and helps you to comprehend both simple and complex division problems.

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