Problem 81 - Prealgebra

Question

Perform each of the following divisions. $$3 8 \longdiv { 3 1 , 3 5 0 }$$

Step-by-Step Solution

Answer

The quotient of the division is 825.

Step 1: Set up the Division Problem

The division problem involves dividing \(31,350\) by \(38\). Begin by writing \(31,350\) under the long division symbol and \(38\) outside the long division bracket.

Step 2: Divide the First Part

Determine how many times \(38\) fits into the leading digits of \(31,350\). Start with \(313\) from \(31,350\). \(38\) goes into \(313\) eight times. Write \(8\) above the division bracket, aligned with \(3\) from \(313\).

Step 3: Multiply and Subtract

Multiply \(8\) by \(38\), which equals \(304\). Subtract \(304\) from \(313\) to get \(9\). Bring down the next digit \(5\) from \(31,350\) to form \(95\).

Step 4: Continue the Division Process

Now determine how many times \(38\) can fit into \(95\). It goes two times. Write \(2\) above the bracket next to \(8\).

Step 5: Multiply and Subtract Again

Multiply \(2\) by \(38\) to get \(76\). Subtract \(76\) from \(95\) to get \(19\). Bring down the last digit \(0\) to make this \(190\).

Step 6: Final Division

Determine how many times \(38\) fits into \(190\). It fits five times. Write \(5\) at the top. Multiply \(5\) by \(38\) to get \(190\), subtract \(190\) from \(190\) to get \(0\), which means no remainder.

Step 7: Conclusion: Write the Final Answer

The quotient of dividing \(31,350\) by \(38\) is \(825\).

Key Concepts

Understanding Division Problems

Division problems can seem tricky, but with practice, they become easier. The purpose of a division problem is to see how many times one number, called the divisor, can be contained within another number, called the dividend. In our exercise, the number 31,350 is the dividend and 38 is the divisor.

To solve division problems efficiently, it's helpful to break them into smaller, more manageable steps using long division. This method allows you to find how many times your divisor fits into different segments of the dividend. It involves division, multiplication, and subtraction, making it a practical way to simplify complex problems.

• Divisor: The number you are dividing by (e.g., 38).
• Dividend: The number you are dividing (e.g., 31,350).
• Quotient: The result of the division (e.g., 825).

Mastering Step by Step Division

Breaking down a division problem into simple steps makes it more approachable. Step by step division allows us to systematically conquer a larger problem by focusing on smaller portions of the dividend.

Consider the given problem of dividing 31,350 by 38:

• Begin by setting up your division: Write 31,350 under the division symbol and 38 outside it.
• Divide the leading digits (e.g., 313 by 38) to get the first number above the division line.
• Multiply the divisor by this number, subtract the result from the relevant segment of the dividend, and bring down the next digit.
• Repeat these steps, methodically moving through each part of the dividend, until you have processed all digits.

By following these practical steps, you ensure that no part of the division problem is overlooked, leading to a comprehensive solution.

Prealgebra and Division Techniques

Prealgebra is an essential phase of learning where foundational mathematical concepts are solidified, including division. This stage helps students build a strong base for more advanced math topics by learning basic operations such as division in a structured manner.

In prealgebra, division is more than just finding how many times one number goes into another. It is about understanding the process, which includes composing and decomposing numbers, understanding remainders, and solving real-world problems.

• Develop a deep understanding of division involving both whole numbers and remainders.
• Use division to solve practical problems and apply these skills in various contexts.
• Build confidence in manipulating numbers and expressions through consistent practice.

By focusing on prealgebra, students gain the tools they need to approach division problems with confidence, laying the groundwork for success in mathematics.