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Chapter 5: Problem 222

Simplify the expression. \(6.29+\frac{21}{40}\)

Short Answer

Expert verified
6.815

Step by step solution

01

Convert the fraction to a decimal

First, convert \(\frac{21}{40}\) into a decimal. Divide 21 by 40 which equals 0.525.
02

Add the decimal to the whole number

Add 6.29 and 0.525. This results in 6.815.

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Key Concepts

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

Converting Fractions to Decimals
To simplify an expression involving both fractions and decimals, it is useful to convert the fractions to decimals first. This makes addition or other operations straightforward and consistent. To convert a fraction to a decimal, you simply divide the numerator (top number) by the denominator (bottom number).
For example, let's look at the fraction \(\frac{21}{40}\). Here, 21 is the numerator and 40 is the denominator.
To convert \(\frac{21}{40}\) to a decimal, divide 21 by 40.
\[ \frac{21}{40} = 0.525 \]
Now, you have successfully converted \(\frac{21}{40}\) to 0.525! It鈥檚 that simple.
Addition of Decimals
Once you have all numbers in decimal form, the addition process becomes easier. Adding decimals is very much like adding whole numbers, but you must pay extra attention to the decimal points.
Always align the decimal points vertically when adding.
In this example, we have two numbers: 6.29 and 0.525.
Align them as follows:
\[ \begin{array}{r} 6.290\ + 0.525\ \hline 6.815\ \end{array} \] Adding these vertically, starting from the rightmost digit and moving to the left, ensures you get the sum accurately. As you can see from our example, the sum of 6.29 and 0.525 is 6.815.
Basic Arithmetic Operations
Understanding basic arithmetic operations, such as addition, subtraction, multiplication, and division, is crucial for simplifying expressions effectively. Each operation has specific rules. Here, we focus on addition and division.
In the given exercise, two basic operations are used: division to convert the fraction to a decimal and addition to combine all numbers.
Steps to follow:
  • First, division was used to convert the fraction \(\frac{21}{40}\) into the decimal 0.525.
  • Second, we added this decimal to the given whole number 6.29.
For division, remember to divide the numerator by the denominator.
For addition, always line up the decimal points vertically to ensure accuracy. Using these methods, you can simplify expressions efficiently and correctly.

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