Find Each Sum. Write Your Answer In Simplest Form.15. \[$-\frac{2}{5} + \left(\frac{1}{10}\right)\$\]16. \[$-\frac{1}{3} + \frac{4}{9}\$\]17. \[$-0.21 + (-6.3)\$\]18. \[$-4 \frac{1}{2} + 1 \frac{1}{2}\$\]19.

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Introduction

In mathematics, simplifying complex fractions and decimals is an essential skill that helps us solve problems efficiently and accurately. In this article, we will explore four different problems that involve adding fractions and decimals, and we will provide step-by-step solutions to each problem.

Problem 15: Adding a Negative Fraction and a Positive Fraction

Problem Statement

Find the sum of −25-\frac{2}{5} and 110\frac{1}{10}.

Solution

To add these two fractions, we need to find a common denominator. The least common multiple (LCM) of 5 and 10 is 10. So, we can rewrite −25-\frac{2}{5} as −410-\frac{4}{10}.

-\frac{2}{5} = -\frac{4}{10}

Now, we can add the two fractions:

-\frac{4}{10} + \frac{1}{10} = -\frac{3}{10}

Therefore, the sum of −25-\frac{2}{5} and 110\frac{1}{10} is −310-\frac{3}{10}.

Problem 16: Adding a Negative Fraction and a Positive Fraction

Problem Statement

Find the sum of −13-\frac{1}{3} and 49\frac{4}{9}.

Solution

To add these two fractions, we need to find a common denominator. The least common multiple (LCM) of 3 and 9 is 9. So, we can rewrite −13-\frac{1}{3} as −39-\frac{3}{9}.

-\frac{1}{3} = -\frac{3}{9}

Now, we can add the two fractions:

-\frac{3}{9} + \frac{4}{9} = \frac{1}{9}

Therefore, the sum of −13-\frac{1}{3} and 49\frac{4}{9} is 19\frac{1}{9}.

Problem 17: Adding a Negative Decimal and a Negative Decimal

Problem Statement

Find the sum of −0.21-0.21 and −6.3-6.3.

Solution

To add these two decimals, we can simply add the numbers as we would with whole numbers.

-0.21 + (-6.3) = -6.51

Therefore, the sum of −0.21-0.21 and −6.3-6.3 is −6.51-6.51.

Problem 18: Adding a Mixed Number and a Mixed Number

Problem Statement

Find the sum of −412-4 \frac{1}{2} and 1121 \frac{1}{2}.

Solution

To add these two mixed numbers, we need to convert them to improper fractions first.

-4 \frac{1}{2} = -\frac{9}{2}
1 \frac{1}{2} = \frac{3}{2}

Now, we can add the two fractions:

-\frac{9}{2} + \frac{3}{2} = -\frac{6}{2} = -3

Therefore, the sum of −412-4 \frac{1}{2} and 1121 \frac{1}{2} is −3-3.

Conclusion

In this article, we have explored four different problems that involve adding fractions and decimals. We have provided step-by-step solutions to each problem, and we have used various techniques to simplify the complex fractions and decimals. By following these techniques, we can solve problems efficiently and accurately, and we can develop a deeper understanding of the underlying mathematical concepts.

Key Takeaways

  • To add fractions, we need to find a common denominator.
  • To add decimals, we can simply add the numbers as we would with whole numbers.
  • To add mixed numbers, we need to convert them to improper fractions first.
  • Simplifying complex fractions and decimals is an essential skill that helps us solve problems efficiently and accurately.

Further Reading

If you want to learn more about adding fractions and decimals, I recommend checking out the following resources:

  • Khan Academy: Adding Fractions and Decimals
  • Mathway: Adding Fractions and Decimals
  • IXL: Adding Fractions and Decimals

Q: What is the difference between adding fractions and adding decimals?

A: Adding fractions and adding decimals are two different operations. When adding fractions, we need to find a common denominator, while when adding decimals, we can simply add the numbers as we would with whole numbers.

Q: How do I add fractions with different denominators?

A: To add fractions with different denominators, we need to find a common denominator. The least common multiple (LCM) of the two denominators is the common denominator. We can then convert each fraction to have the common denominator and add them.

Q: Can I add a fraction and a decimal?

A: Yes, you can add a fraction and a decimal. To do this, we need to convert the fraction to a decimal first. We can do this by dividing the numerator by the denominator. Then, we can add the decimal and the fraction.

Q: How do I add mixed numbers?

A: To add mixed numbers, we need to convert them to improper fractions first. We can do this by multiplying the whole number by the denominator and adding the numerator. Then, we can add the two fractions.

Q: What is the rule for adding negative numbers?

A: When adding negative numbers, we need to follow the rule that two negative numbers make a positive number. So, when adding two negative numbers, we need to change the sign of the result to positive.

Q: Can I add a fraction and a percentage?

A: Yes, you can add a fraction and a percentage. To do this, we need to convert the percentage to a decimal first. We can do this by dividing the percentage by 100. Then, we can add the decimal and the fraction.

Q: How do I add decimals with different places?

A: To add decimals with different places, we need to line up the decimal points and add the numbers as we would with whole numbers. We can also use a calculator to add decimals with different places.

Q: Can I add a fraction and a decimal with different places?

A: Yes, you can add a fraction and a decimal with different places. To do this, we need to convert the fraction to a decimal first. We can do this by dividing the numerator by the denominator. Then, we can add the decimal and the fraction.

Q: How do I add decimals with repeating decimals?

A: To add decimals with repeating decimals, we need to convert the repeating decimals to fractions first. We can do this by using a formula to convert the repeating decimal to a fraction. Then, we can add the fractions.

Q: Can I add a fraction and a decimal with repeating decimals?

A: Yes, you can add a fraction and a decimal with repeating decimals. To do this, we need to convert the repeating decimals to fractions first. We can do this by using a formula to convert the repeating decimal to a fraction. Then, we can add the fractions.

Conclusion

In this article, we have answered some frequently asked questions about adding fractions and decimals. We have covered topics such as adding fractions with different denominators, adding mixed numbers, and adding decimals with different places. By following these tips and techniques, you can add fractions and decimals with confidence.

Key Takeaways

  • To add fractions with different denominators, we need to find a common denominator.
  • To add mixed numbers, we need to convert them to improper fractions first.
  • To add decimals with different places, we need to line up the decimal points and add the numbers as we would with whole numbers.
  • To add decimals with repeating decimals, we need to convert the repeating decimals to fractions first.

Further Reading

If you want to learn more about adding fractions and decimals, I recommend checking out the following resources:

  • Khan Academy: Adding Fractions and Decimals
  • Mathway: Adding Fractions and Decimals
  • IXL: Adding Fractions and Decimals

I hope this article has been helpful in answering your questions about adding fractions and decimals. If you have any more questions or need further clarification, please don't hesitate to ask.