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Chapter 1: Problem 3

Find each quotient. $$36 \div 3$$

Short Answer

Expert verified
The quotient is 12.

Step by step solution

01

Understand the Problem

We need to find the result of dividing 36 by 3. This means we want to know how many times the number 3 can fit into the number 36 without exceeding it.
02

Set Up the Division

Write the division problem as a fraction: \( \frac{36}{3} \). This represents dividing 36 into 3 equal parts.
03

Perform the Division

Divide 36 by 3. Start by determining how many times 3 goes into 36. You can do this by multiplying 3 by numbers until you reach or exceed 36. 3 times 12 equals exactly 36.
04

Verify the Solution

Multiply the quotient by the divisor to ensure it equals the dividend. So, \( 3 \times 12 = 36 \), which matches the original number. The solution is verified.

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Key Concepts

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

Quotient
The quotient is the result you get when you divide one number, called the dividend, by another number, known as the divisor. In our example of dividing 36 by 3, the quotient is 12. This means that 3 fits into 36 exactly 12 times.
  • Quotient = Dividend 梅 Divisor
  • For 36 梅 3, the quotient is 12
Understanding the quotient is essential since it tells you how much of one unit fits into another without exceeding it. If the quotient is not a whole number, it means there is a remainder or, in some cases, you might need to express the quotient as a fraction or decimal.
Divisor
A divisor is the number by which another number is divided. In the division equation, it is the number that 'does the dividing.' For instance, in our division problem 36 梅 3, the divisor is 3. The divisor determines how many times it can evenly divide the dividend.
  • Divisor and Dividend Relationship: Used to find the quotient
  • Example: Divisor of 36 梅 3 is 3
When dividing, the divisor should not be zero, as division by zero is undefined in mathematics. The concept of the divisor is crucial for solving division problems correctly.
Dividend
The dividend is the number that you want to divide. In our example of dividing 36 by 3, the dividend is 36. It's the amount you're splitting into equal parts determined by the divisor.
  • Dividend = Total that鈥檚 being divided
  • Example: In 36 梅 3, the dividend is 36
Recognizing the dividend is important because it represents the initial quantity or value you begin with in a division problem. Without a dividend, there'd be nothing to divide.
Verification of Division
Verification of division is an essential step to ensure your division result is correct. You can verify a division calculation by multiplying the quotient by the divisor. If the product equals the dividend, then your division is accurate.
  • Verification Formula: Quotient 脳 Divisor = Dividend
  • For our example: 12 脳 3 = 36
This verification step helps to confirm that no errors were made during division, like miscalculating the quotient or misinterpreting the problem. Always perform this check to be confident in your results.

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Most popular questions from this chapter

In Example 12 in this section, we found that the average of \(75,96,81,\) and 88 is \(85 .\) If the number 96 is removed from the list of numbers, does the average increase or decrease? Explain why.

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