Problem 74 - Prealgebra

Question

Find each quotient. $$102 \div 3$$

Step-by-Step Solution

Answer

The quotient of 102 divided by 3 is 34.

Step 1: Understand Division

Division is the process of determining how many times one number, called the divisor, fits into another number, called the dividend. In this exercise, 102 is the dividend, and 3 is the divisor.

Step 2: Perform Division Using Long Division

Arrange 102 under the long division bracket and 3 outside. Start by seeing how many times 3 can fit into the first digit of 102, which is 1. Since 3 cannot fit into 1, write 0 above the line next to the 1.

Step 3: Bring Down the Next Digit

Since 3 does not go into the first digit 1, bring down the next digit, which is 0. Now we have 10. See how many times 3 can fit into 10.

Step 4: Divide 10 by 3

3 goes into 10 three times because 3 × 3 = 9. Write 3 above the division line next to the 0 on top, and subtract 9 from 10, leaving us with a remainder of 1.

Step 5: Bring Down the Last Digit

Bring down the last digit, 2, making the number 12. Determine how many times 3 fits into 12.

Step 6: Divide 12 by 3

3 fits into 12 four times exactly, since 3 × 4 = 12. Write 4 above the division line.

Step 7: Combine the Quotient

Combine all the numbers written above the division line. The numbers are 34. Hence, 102 divided by 3 is 34.

Key Concepts

Division Process

The division process is like sharing a collection of items into equal parts. Think of it as finding out how many times one number fits into another number. It's all about breaking down a larger number (the dividend) into equal parts defined by a smaller number (the divisor).
In our exercise, when we're dividing 102 by 3, the goal is to figure out how many groups of 3 we can make from 102. You start by working from the highest place value of the dividend and move from left to right, bringing down digits to deal with at each step.

• First, you look at the largest digit or group of digits that the divisor can divide into.
• Then, you determine how many times the divisor fits into that number.
• Finally, you subtract the result from the current number and bring down the next digit from the dividend.

This step-by-step approach continues until you've processed every digit of the dividend, giving you the quotient at the end of the division process.

Divisors and Dividends

In the language of division, two key terms often pop up: divisors and dividends. The dividend is the larger number that you want to divide. It's what you start with. In our example, that's the number 102.
The divisor, on the other hand, is the smaller number that you are dividing by. In the exercise, that number is 3. It's essential to recognize these two parts because understanding them helps you perform division correctly. The dividend is like a pie you want to slice, and the divisor tells you how many slices you need.

• The role of the dividend is to be the total amount you aim to divide.
• The divisor helps determine how big each piece (or group) should be.

Grasping the concept of divisors and dividends is crucial for setting up and solving division problems.

Basic Arithmetic Operations

Basic arithmetic operations form the building blocks of mathematics, and division is one of them. The other core operations include addition, subtraction, and multiplication. Each of these operations helps us solve different types of problems.
When performing division, you often employ these other arithmetic operations to arrive at the solution. For instance, once you've divided part of your dividend with the divisor, you'll use multiplication to check how many times the divisor fits in, then subtraction to manage the remainder.

• Addition is often used to check your subtraction by reversing the process.
• Subtraction helps manage what’s left of the dividend after part of it is divided.
• Multiplication checks how many complete times the divisor fits into the current number.

Each of these operations plays a part in the process, making it important to have a solid grasp of them.

Quotients in Division

Quotients are what you're left with when you finish dividing. It's the answer to "how many times does the divisor fit into the dividend?" In our example of dividing 102 by 3, the quotient is 34.
Every division problem works towards finding this quotient. It represents how much shared equally each part gets from the whole. Calculating it involves the steps of the long division method:

• Recognizing how many full parts a number can be divided into.
• Understanding that any remainder is part of what can't be fully shared equally.

Once the division is complete, the quotient provides a clear and concise answer to the division problem, illustrating how many times the divisor fits, without any remainder left ungrouped.