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Chapter 6: Problem 23

Find the decimal representation of each quotient. Use a calculator to check each result. \(18.5 \div 5\)

Short Answer

Expert verified
The decimal representation of 18.5 梅 5 is 3.7.

Step by step solution

01

Set Up the Division

To find the decimal representation of the quotient, set it up as a division problem. Here, you need to divide 18.5 by 5.
02

Simplify the Division

Convert the division to a form that's easier to work with by interpreting it as fraction form: \[ \frac{18.5}{5} \] We read it as "18.5 divided by 5." Let's solve this using long division.
03

Perform Long Division

If we perform long division, we note that 5 goes into 18 three times (since 5 x 3 = 15), leaving a remainder of 3. Bring down the 5 making the next number to consider 35. Then, 5 goes into 35 seven times exactly (since 5 x 7 = 35) with no remainder.
04

Calculate using a Calculator

To ensure accuracy, use a calculator to divide 18.5 by 5. Enter the numbers into the calculator as "18.5 divided by 5" or "18.5 梅 5." The result should be 3.7.

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Key Concepts

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

Decimal Representation
The decimal representation of a number is simply how we express numbers in terms of base 10. When dealing with division, converting the result into a decimal form provides a clearer and often easier-to-understand result. For example, in the exercise, we are asked to divide 18.5 by 5. The result of this division, calculated by long division or a calculator, gives us a decimal: 3.7.
Decimals are particularly useful when dealing with non-integer numbers as they precisely indicate the parts of a whole. This allows for a straightforward understanding without needing to interpret complex fractions.
  • Example: Decimal representation of 18.5 divided by 5 is 3.7.
  • Benefits: Easy to read and often more intuitive.
Quotient
In division, the quotient is the result you get when you divide one number by another. Consider it the answer to a division problem. In our example, 18.5 divided by 5 results in a quotient of 3.7.
Understanding quotients is fundamental as they represent the division's outcome, which can be a whole number or a decimal.
  • Whole Number Quotient: Like 15 divided by 5 equals 3.
  • Decimal Quotient: Like 18.5 divided by 5 equals 3.7.
Regardless of the form, the quotient tells us how many times the divisor fits into the dividend or the exact division amount. This makes divisor and dividend identification crucial, ensuring you divide correctly and achieve the right quotient.
Long Division
Long division is a method used to divide large numbers or decimals systematically. In our exercise, we use long division to find how many times 5 fits into 18.5. Here's how it works:
  • Write the dividend (18.5) under the long division symbol and the divisor (5) outside.
  • Determine how many times the divisor fits into the first part of your dividend (it goes into 18 three times; place 3 above the division line).
  • Multiply the divisor by this number and subtract the result from the current dividend portion.
  • Bring down the next number (5), continuing the process until complete.
This approach unfolds step by step, making complex division problems manageable. Long division also helps verify decimals, proving essential when calculators aren't available or if you need to ensure accuracy before technological checks. Using long division,
  • can solve fractional challenges,
  • helps understand step-wise calculations,
  • reinforces comprehending place value and remainders.
Overall, mastering long division boosts confidence and enhances problem-solving skills in arithmetic tasks.

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