Problem 74 - Prealgebra

Question

Perform each of the following divisions. $$90,902 \div 5$$

Step-by-Step Solution

Answer

The result of the division is 18,180 with a remainder of 2.

Step 1: Set Up the Division

Write the number 90,902 inside the division bracket and 5 outside. We will divide 90,902 by 5.

Step 2: Divide the Thousands

Look at the thousands digit, which is 9. Divide 9 by 5 to get 1 with a remainder of 4. Write 1 above the division bar.

Step 3: Divide the Hundreds

Bring down the next digit, 0, making the number 40. Divide 40 by 5 to get 8 with no remainder. Write 8 next to the 1 above the division bar.

Step 4: Divide the Tens

Bring down the next digit, which is 9, making the new number 9. Divide 9 by 5 to get 1 with a remainder of 4. Write 1 next to 18 above the division bar.

Step 5: Divide the Ones (First Cycle)

Bring down the next digit, which is 0, making the new number 40. Divide 40 by 5 to reach 8. Write 8 next to the 181 above the division bar.

Step 6: Divide the Units

Bring down the last digit, which is 2, making the new number 2. Divide 2 by 5, resulting in 0 with a remainder of 2. Write 0 next to 1818 above the division bar.

Step 7: Write the Remainder

The remainder is 2 because 2 cannot be divided by 5. Write the remainder as part of the answer to reflect this.

Key Concepts

Division Problems

Division problems involve splitting a larger number, known as the dividend, into equal parts determined by a smaller number called the divisor. In the exercise of dividing 90,902 by 5, the aim is to see how many times 5 fits into 90,902. This process reveals the quotient, which represents the number of full pieces created. To understand division problems better:

• Identify the dividend (the number to be divided) and the divisor (the number used to divide). Here, our dividend is 90,902, and the divisor is 5.
• The result of dividing these numbers is called the quotient, and it answers how many full groups or parts we can create.
• If there are any leftover numbers that cannot be divided further by the divisor, they form a remainder.

Understanding these terms makes tackling division problems easier and more manageable.

Step-by-Step Solution

Breaking down division into simple, individual steps is key to solving any division problem. Let’s recap the steps used for dividing 90,902 by 5: Step 1 focuses on setting up the division problem by organizing the numbers in a division bracket.

• Place the dividend (90,902) inside the bracket and the divisor (5) outside.

In Step 2, begin with the largest place value: the thousands.

• Divide the thousandth digit, which is 9, by 5 to obtain 1 as the part of the quotient (rest is the remainder).

Continuing to place value processing in Step 3, handle the hundreds.

• Add the next digit to the remainder from Step 2, making it 40, which is then divided by 5.

This detailed approach means dividing each place value individually until we reach the units, finishing with writing any remainders. These steps ensure no details are missed and strengthen understanding with each movement.

Remainder in Division

Understanding the remainder in division is essential when the dividend is not perfectly divisible by the divisor. In this division exercise, a remainder was encountered at the last step. Here's why remainders appear:

• Division results in whole parts of the dividend fitting into the divisor completely, but sometimes there's still an unallocated part left over.
• This part is called the remainder, which cannot be further divided by the divisor without fractionating.

For example, when dividing 90,902 by 5, most digits align perfectly until the last step. The result is 18,180 R2, where 'R2' denotes the remainder. A remainder indicates that the division process cannot continue completely and serves as an adjustment of sorts in the division outcome.

Division by Single-Digit Numbers

Dividing by single-digit numbers, like 5 in our exercise, simplifies the division process. Using smaller numbers often makes calculations straightforward and faster, which is especially approachable for those new to division. Here's why single-digit division is beneficial:

• Each division step is manageable and doesn't involve overly complex arithmetic.
• Smaller divisors result in fewer potential steps, as seen by quickly resolving place values one-by-one in 90,902.

Though single-digit division can seem simple, it offers vital practice for understanding more complex math concepts. Mastery here forms the foundation for handling larger, multi-digit divisions later. Utilizing single-digit numbers as divisors is a practical start to building confidence in mathematics.