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Chapter 5: Problem 43

Divide. Simplify, if possible. $$ 80.892 \div 8.4 $$

Short Answer

Expert verified
9.63

Step by step solution

01

Set up the Division

To divide 80.892 by 8.4, place 80.892 as the dividend and 8.4 as the divisor in the division format.
02

Decimal Point Adjustment

Move the decimal point in the divisor (8.4) one place to the right to make it 84. Move the decimal point in the dividend (80.892) the same number of places to the right, making it 808.92.
03

Perform Long Division

Divide 808.92 by 84. Set up the division problem as 80892 divided by 84 and perform the long division.
04

Simplify

Find the quotient from the long division operation. 808.92 divided by 84 equals 9.63.

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Key Concepts

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

Long Division
When tackling a division problem, long division is a methodical process to divide larger numbers. Set up the division by writing the dividend under the division bar and the divisor outside. Start dividing the leftmost digits of the dividend by the divisor. Write the result (quotient) above the division bar. Multiply the quotient by the divisor, write the product below the dividend and subtract. Bring down the next digit of the dividend and repeat until all digits have been used. This step-by-step helps in breaking down the division operation into manageable parts.
Decimal Point Adjustment
To divide numbers with decimals, you first need to adjust the decimal points. Move the decimal point in the divisor to the right to make it a whole number. Do the same with the dividend. For instance, to divide 80.892 by 8.4, move the decimal point one place to the right in both numbers, transforming the problem into 808.92 divided by 84. This simplification makes the division easier to manage and ensures accuracy in the result.
Simplifying Division Problems
Simplifying a division problem involves breaking it down into easier steps. First, adjust decimal points if needed. Next, use long division to find the quotient. Find any common factors between the dividend and divisor to simplify the numbers, if possible. For example, solving 808.92 divided by 84 through long division yields a quotient of 9.63. Always double-check your work to make sure the solution is fully simplified and accurate.
Arithmetic Operations
Division is one of the core arithmetic operations, alongside addition, subtraction, and multiplication. It involves determining how many times a number (divisor) fits into another number (dividend). Accurate division requires careful execution of procedures like long division and decimal adjustment. Understanding and mastering these operations help in solving complex problems and build a strong mathematical foundation.

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Most popular questions from this chapter

Find the unit price of each brand. Then, in each exercise, determine which brand is the better buy based on unit price alone. $$ \begin{array}{|c|c|c|} \hline \text { Brand } & \text { Size } & \text { Price } \\ \hline \mathrm{F} & 14 \mathrm{oz} & \$ 1.29 \\ \mathrm{G} & 19 \mathrm{oz} & \$ 1.99 \\ \mathrm{P} & 20 \mathrm{oz} & \$ 2.49 \\ \hline \end{array} $$

Find the unit price of each brand. Then, in each exercise, determine which brand is the better buy based on unit price alone. $$ \begin{array}{|c|c|c|} \hline \text { Brand } & \text { Size } & \text { Price } \\ \hline \mathrm{M} & 54 \mathrm{oz} & \$ 4.79 \\ \mathrm{~T} & 59 \mathrm{oz} & \$ 5.99 \\ \hline \end{array} $$

Find each unit price Then, in each exercise, determine which size is the better buy based on unit price alone. $$ \begin{array}{|c|c|c|} \hline \text { Size } & \text { Price } & \text { Unit Price } \\ \hline 10.7 \mathrm{oz} & \$ 1.09 & \\ \hline 26 \mathrm{oz} & \$ 2.69 & \\ \hline \end{array} $$

Find the length \(L\) of the lake. Assume that the ratio of \(L\) to 120 yd is the same as the ratio of 720 yd to 30 yd.

Solve. $$ \frac{6}{y}=\frac{18}{15} $$
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