Add. Enter A Number Only As Your Answer In The Space Provided. − 4 5 + 4 5 = -\frac{4}{5} + \frac{4}{5} = − 5 4 ​ + 5 4 ​ = □ \square □

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Understanding the Basics of Fractions

When it comes to adding fractions, it's essential to understand the basics of fractions and how they work. A fraction is a way of expressing a part of a whole as a ratio of two numbers. It consists of a numerator (the number on top) and a denominator (the number on the bottom). For example, the fraction 3/4 represents 3 parts out of a total of 4 parts.

The Concept of Adding Fractions

Adding fractions involves combining two or more fractions with the same denominator. When the denominators are the same, we can simply add the numerators and keep the denominator the same. However, when the denominators are different, we need to find a common denominator before we can add the fractions.

Simplifying the Given Expression

In the given expression, −45+45-\frac{4}{5} + \frac{4}{5}, we have two fractions with the same denominator, which is 5. Since the denominators are the same, we can simply add the numerators and keep the denominator the same.

Step-by-Step Solution

To simplify the given expression, we can follow these steps:

  1. Identify the numerators and denominators: The numerators are -4 and 4, and the denominator is 5.
  2. Add the numerators: Since the denominators are the same, we can simply add the numerators: -4 + 4 = 0.
  3. Keep the denominator the same: The denominator remains the same, which is 5.
  4. Write the simplified fraction: The simplified fraction is 05\frac{0}{5}.

The Final Answer

The final answer is 0\boxed{0}.

Why is the Answer 0?

The answer is 0 because when we add the numerators, we get 0. This means that the two fractions are equal in value, and when we add them together, the result is 0.

Real-World Applications

Understanding how to add fractions is essential in many real-world applications, such as cooking, science, and finance. For example, when a recipe calls for 3/4 cup of flour, and you need to add 1/4 cup more, you can simply add the fractions together to get the total amount of flour needed.

Conclusion

In conclusion, adding fractions is a simple process that involves combining two or more fractions with the same denominator. By following the steps outlined above, we can simplify the given expression and arrive at the final answer of 0. Understanding how to add fractions is essential in many real-world applications, and it's a fundamental concept in mathematics that can be applied in various contexts.

Common Mistakes to Avoid

When adding fractions, there are several common mistakes to avoid. These include:

  • Not finding a common denominator: When the denominators are different, it's essential to find a common denominator before adding the fractions.
  • Not adding the numerators: When the denominators are the same, it's essential to add the numerators and keep the denominator the same.
  • Not simplifying the fraction: After adding the fractions, it's essential to simplify the fraction by dividing the numerator and denominator by their greatest common divisor.

Tips and Tricks

Here are some tips and tricks to help you add fractions like a pro:

  • Use a common denominator: When the denominators are different, use a common denominator to make it easier to add the fractions.
  • Add the numerators: When the denominators are the same, add the numerators and keep the denominator the same.
  • Simplify the fraction: After adding the fractions, simplify the fraction by dividing the numerator and denominator by their greatest common divisor.

Practice Problems

Here are some practice problems to help you practice adding fractions:

  • 12+12=□\frac{1}{2} + \frac{1}{2} = \square
  • 34+14=□\frac{3}{4} + \frac{1}{4} = \square
  • 23+23=□\frac{2}{3} + \frac{2}{3} = \square

Answer Key

Here is the answer key for the practice problems:

  • 12+12=1\frac{1}{2} + \frac{1}{2} = \boxed{1}
  • 34+14=1\frac{3}{4} + \frac{1}{4} = \boxed{1}
  • 23+23=4/3\frac{2}{3} + \frac{2}{3} = \boxed{4/3}

Q: What is the difference between adding fractions and adding whole numbers?

A: When adding fractions, we need to find a common denominator and add the numerators, whereas when adding whole numbers, we simply add the numbers together.

Q: How do I find a common denominator when adding fractions?

A: To find a common denominator, we need to list the multiples of each denominator and find the smallest multiple that is common to both. For example, if we have fractions with denominators 4 and 6, we can list the multiples of each denominator as follows:

  • Multiples of 4: 4, 8, 12, 16, 20, ...
  • Multiples of 6: 6, 12, 18, 24, 30, ...

The smallest multiple that is common to both is 12, so we can use 12 as the common denominator.

Q: What is the greatest common divisor (GCD) and how do I use it to simplify fractions?

A: The GCD is the largest number that divides both the numerator and denominator of a fraction. To simplify a fraction, we can divide both the numerator and denominator by their GCD. For example, if we have a fraction with a numerator of 12 and a denominator of 18, we can find the GCD by listing the factors of each number:

  • Factors of 12: 1, 2, 3, 4, 6, 12
  • Factors of 18: 1, 2, 3, 6, 9, 18

The largest number that is common to both is 6, so we can divide both the numerator and denominator by 6 to simplify the fraction.

Q: Can I add fractions with different signs?

A: Yes, you can add fractions with different signs. When adding fractions with different signs, we need to follow the rules of addition, which state that when we add two numbers with different signs, we need to subtract the smaller number from the larger number. For example, if we have fractions with signs of + and -, we can add them as follows:

  • 23+(−13)=23−13=13\frac{2}{3} + (-\frac{1}{3}) = \frac{2}{3} - \frac{1}{3} = \frac{1}{3}

Q: Can I add fractions with zero as the numerator?

A: Yes, you can add fractions with zero as the numerator. When adding fractions with zero as the numerator, we can simply ignore the zero and add the fractions as usual. For example, if we have fractions with numerators of 0 and 2, we can add them as follows:

  • 03+23=23\frac{0}{3} + \frac{2}{3} = \frac{2}{3}

Q: Can I add fractions with negative numbers as the numerator?

A: Yes, you can add fractions with negative numbers as the numerator. When adding fractions with negative numbers as the numerator, we need to follow the rules of addition, which state that when we add two numbers with different signs, we need to subtract the smaller number from the larger number. For example, if we have fractions with numerators of -2 and 3, we can add them as follows:

  • −23+33=−23+1=13-\frac{2}{3} + \frac{3}{3} = -\frac{2}{3} + 1 = \frac{1}{3}

Q: Can I add fractions with different denominators?

A: Yes, you can add fractions with different denominators. When adding fractions with different denominators, we need to find a common denominator and add the fractions as usual. For example, if we have fractions with denominators of 4 and 6, we can find a common denominator and add them as follows:

  • 14+16=312+212=512\frac{1}{4} + \frac{1}{6} = \frac{3}{12} + \frac{2}{12} = \frac{5}{12}

Q: Can I add fractions with decimals as the numerator?

A: Yes, you can add fractions with decimals as the numerator. When adding fractions with decimals as the numerator, we need to convert the decimals to fractions and add them as usual. For example, if we have fractions with numerators of 0.5 and 0.25, we can convert the decimals to fractions and add them as follows:

  • 0.51+0.251=12+14=34\frac{0.5}{1} + \frac{0.25}{1} = \frac{1}{2} + \frac{1}{4} = \frac{3}{4}