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Questions and Answers
To add decimal numbers, we must line up the ______ points and add the numbers from right to left
decimal
Subtracting decimal numbers requires lining up the decimal points and subtracting the numbers from right to ______
left
Dividing decimal numbers involves moving the decimal point in the dividend and division result so that the digits to the right of the decimal point ______
align
Decimals are an essential component of mathematics, especially when dealing with fractions and ______
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Adding decimals - for example, to add 5.21 and 3.76, the result is ______
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Multiplying decimal numbers is similar to multiplying whole numbers, but we must pay attention to the ______ points.
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For instance, to multiply 0.37 by 9.1: 0.37 × 9.1 = ______
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Given that a bookstore receives 55 books at $12.49 each and sells 40 of them at $15.67 each, calculate the total ______.
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Study Notes
Decimals: A Guide to Working with Fractional Numbers
Decimals are an essential component of mathematics, especially when dealing with fractions and measurements. This article will explore decimals as a means of representing fractional parts of whole numbers, and how we can perform basic operations and solve problems using these numbers.
Representing Decimals
A decimal number consists of an integer part (whole number) and a fractional part (a number to the right of the decimal point). For instance, 3.14 is a decimal number, where 3 is the integer part, and 14 is the fractional part.
Adding Decimals
To add decimal numbers, we must line up the decimal points and add the numbers from right to left, carrying over if necessary. For example, to add 5.21 and 3.76:
5.21
+3.76
-------
9.97
Subtracting Decimals
Subtracting decimal numbers requires lining up the decimal points and subtracting the numbers from right to left, borrowing if necessary. For instance, to subtract 7.82 from 10.36:
10.36
-7.82
-------
2.54
Dividing Decimals
Dividing decimal numbers involves moving the decimal point in the dividend and division result so that the digits to the right of the decimal point align. For example, to divide 1.2 by 0.8:
1.2
÷ 0.8
-------
1.5
To get the final answer, move the decimal point one place to the right: 1.5 → 1.50.
Multiplying Decimals
Multiplying decimal numbers is similar to multiplying whole numbers, but we must pay attention to the decimal points. For instance, to multiply 0.37 by 9.1:
0.37 × 9.1
------- = 3.387
Word Problems
Word problems involving decimals may require converting units or applying rates. For example, given that a bookstore receives 55 books at $12.49 each and sells 40 of them at $15.67 each, calculate the total revenue.
- First, find the initial revenue for selling 55 books at $12.49 each: 55 × 12.49 = 691.75.
- Next, calculate the revenue from selling 40 books at $15.67 each: 40 × 15.67 = 626.80.
- Add the initial revenue and the revenue from selling the remaining books: 691.75 + 626.80 = 1318.55.
Conclusion
Decimals are essential in mathematics and everyday life. Understanding the basic operations and being able to solve word problems involving decimals will equip you with the tools to handle mathematical situations that involve fractional parts of whole numbers. With practice and patience, you will be able to work with decimals confidently.
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Description
Learn about decimals, including representing them, adding, subtracting, multiplying, dividing, and solving word problems. This guide provides step-by-step explanations and examples to help you master working with decimal numbers.
