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Chapter 6: Problem 8

Perform the following operations. \(0.418-\frac{67}{200}\)

Short Answer

Expert verified
The result of the operation is 0.083.

Step by step solution

01

Convert Fraction to Decimal

First, we need to convert the fraction \( \frac{67}{200} \) to a decimal. To do this, divide 67 by 200: \( \frac{67}{200} = 0.335 \).
02

Perform the Subtraction

Next, we perform the subtraction \( 0.418 - 0.335 \). Align the decimal points and subtract: \( 0.418 - 0.335 = 0.083 \).

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Key Concepts

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

Fraction to Decimal Conversion
Converting fractions into decimals is an essential skill in mathematics. It helps simplify calculations and make them more intuitive. The process involves division鈥攖he numerator is divided by the denominator. For instance, converting the fraction \( \frac{67}{200} \) to a decimal involves dividing 67 by 200, which gives us 0.335.

Here's a simple roadmap to convert any fraction to a decimal:
  • Identify the numerator (the top number of the fraction).
  • Identify the denominator (the bottom number of the fraction).
  • Perform division: numerator 梅 denominator.
This conversion is particularly useful when you are required to perform arithmetic operations involving both fractions and decimals, ensuring consistency and accuracy in your calculations.
Subtraction of Decimals
Subtracting decimals is a straightforward process, but it requires careful alignment of the decimal points. Incorrect alignment could lead to inaccurate results. To subtract decimals correctly, follow these steps:
  • Align both numbers vertically, ensuring the decimal points are in a straight line.
  • If necessary, add zeros to the right of one of the numbers to match the number of decimal places.
  • Subtract as you would with whole numbers, from right to left.
For example, when subtracting 0.418 and 0.335, aligning the decimal points and performing the subtraction gives us 0.083. Practicing this will help reinforce your skills in dealing with decimal numbers in various mathematical problems.
Mathematics Problem Solving
Problem-solving in mathematics is a process that involves understanding the problem, devising a plan, carrying out the plan, and then evaluating the solution. It is crucial to have a clear strategy and approach before tackling any problem. When dealing with operations involving decimals and fractions, such as \( 0.418 - \frac{67}{200} \), it's important to:
  • Carefully read and understand the problem.
  • Convert any fractions to decimals if necessary, to maintain a uniform approach to calculations.
  • Follow the correct order of operations, especially in complex scenarios.
Approaching problems with a systematic strategy not only makes solving them easier but also builds confidence and reinforces mathematical understanding. By practicing these strategies, students can improve their problem-solving abilities and better tackle more complex mathematical challenges.

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Most popular questions from this chapter

Perform each operation and simplify. $$ 150.79 \div 100 $$

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