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Chapter 5: Problem 220

Simplify the expression. \(3.9+\frac{9}{20}\)

Short Answer

Expert verified
4.35

Step by step solution

01

Convert Fraction to Decimal

First, convert the fraction \(\frac{9}{20}\) into a decimal. Divide the numerator by the denominator: \(\frac{9}{20} = 0.45\).
02

Add the Decimal to the Whole Number

Now add the decimal form of the fraction to the whole number: \(3.9 + 0.45\).
03

Perform the Addition

Add the decimals together: \(3.9 + 0.45 = 4.35\). This is the simplified form of the expression.

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Key Concepts

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

Convert Fraction to Decimal
In order to simplify expressions that contain both fractions and decimals, it is often useful to convert fractions into decimal form. To convert a fraction into a decimal, you divide the numerator (the top number) by the denominator (the bottom number). For example, to convert \(\frac{9}{20}\) into a decimal, you divide 9 by 20. When you perform this division, 9 divided by 20 equals 0.45. Therefore, \(\frac{9}{20} = 0.45\). This makes it easier to work with the number during calculations.
Addition of Decimals
After converting the fraction to a decimal, the next step is to add it to the other number in the expression. Adding decimals is similar to adding whole numbers but requires aligning the decimal points for accuracy. For example, to add 3.9 and 0.45, align the decimal points like this:
3.90
+0.45
------
4.35
Now, add the digits column by column starting from the rightmost side. The result is 4.35. This is done by ensuring that each digit is placed directly above or below others in the same column.
Numerator and Denominator
Understanding the terms numerator and denominator is foundational in working with fractions. The numerator is the top number in a fraction and represents how many parts we have. The denominator, on the other hand, is the bottom number and indicates how many parts the whole is divided into. In the fraction \(\frac{9}{20}\), 9 is the numerator and 20 is the denominator. This means we have 9 parts out of a whole that is divided into 20 parts. Knowing these terms helps you understand and manipulate fractions more effectively, such as when converting them to decimals.

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Most popular questions from this chapter

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