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Chapter 5: Problem 221

Simplify the expression. \(9.73+\frac{17}{20}\)

Short Answer

Expert verified
10.58

Step by step solution

01

- Convert the Fraction to a Decimal

Convert the fraction \( \frac{17}{20} \) to a decimal. Divide the numerator by the denominator: \( \frac{17}{20} = 0.85 \).
02

- Add the Decimal to the Given Number

Now add the decimal 0.85 to the given number 9.73. \( 9.73 + 0.85 = 10.58 \).
03

- Write the Final Answer

The simplified expression is 10.58.

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Key Concepts

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

fractions to decimals conversion
Understanding how to convert fractions to decimals is an essential skill in mathematics. A fraction consists of a numerator (top number) and a denominator (bottom number). To convert a fraction to a decimal, divide the numerator by the denominator. For example, to convert \( \frac{17}{20} \) to a decimal, divide 17 by 20. This operation yields:
\[ \frac{17}{20} = 0.85 \]
Practice converting different fractions to decimals to become more comfortable with this process. It will make problems involving fractions much easier!
decimal addition
Adding decimals involves straightforward steps. Begin by aligning the numbers by their decimal points. This helps in ensuring that digits of the same place value are in the correct column. For our problem, we need to add 9.73 and 0.85 together:
- 9.73
+ 0.85
First, add the digits in the rightmost column (hundredths). Next, add the tenths and then the ones. Carry over any extra value just like in whole number addition:
\[ 9.73 + 0.85 = 10.58 \]
This step-by-step approach will assist you in performing decimal addition with ease.
prealgebra arithmetic
Prealgebra arithmetic covers fundamental math concepts that lay the groundwork for higher-level math. This includes operations with whole numbers, decimals, and fractions.

**Key Concepts in Pre-Algebra:**
  • Understanding and performing arithmetic operations: addition, subtraction, multiplication, and division.
  • Working with fractions: simplifying, converting between improper fractions and mixed numbers, and performing operations.
  • Handling decimals: understanding place value, converting between fractions and decimals, and performing arithmetic operations.

Building a strong foundation in these core areas is crucial for success in algebra and beyond. Practice solving problems that combine these elements, like the simplification exercise, to build confidence and proficiency.

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