Add And Subtract Fractions With Like Denominators:${ \begin{array}{l} 16 - \frac{5}{8} \ 212 - \frac{87}{10} \end{array} }$

Introduction

Fractions are an essential part of mathematics, and understanding how to add and subtract them is crucial for success in various mathematical operations. In this article, we will delve into the world of fractions and explore the concept of adding and subtracting fractions with like denominators. We will also provide step-by-step examples and explanations to help you grasp this concept with ease.

What are Fractions with Like Denominators?

Fractions with like denominators are fractions that have the same denominator, but different numerators. For example, $\frac{1}{8}$ and $\frac{3}{8}$ are fractions with like denominators. When we add or subtract fractions with like denominators, we only need to add or subtract the numerators, while keeping the denominator the same.

Adding Fractions with Like Denominators

Adding fractions with like denominators is a straightforward process. We simply add the numerators and keep the denominator the same. Let's consider an example:

Example 1: Adding Fractions with Like Denominators

Suppose we want to add $\frac{1}{8}$ and $\frac{3}{8}$. To do this, we simply add the numerators (1 + 3 = 4) and keep the denominator the same (8).

$\frac{1}{8} + \frac{3}{8} = \frac{4}{8}$

We can simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor (GCD), which is 4.

$\frac{4}{8} = \frac{1}{2}$

Example 2: Adding Fractions with Like Denominators

Suppose we want to add $\frac{2}{10}$ and $\frac{5}{10}$. To do this, we simply add the numerators (2 + 5 = 7) and keep the denominator the same (10).

$\frac{2}{10} + \frac{5}{10} = \frac{7}{10}$

Subtracting Fractions with Like Denominators

Subtracting fractions with like denominators is also a straightforward process. We simply subtract the numerators and keep the denominator the same. Let's consider an example:

Example 1: Subtracting Fractions with Like Denominators

Suppose we want to subtract $\frac{3}{8}$ from $\frac{1}{8}$. To do this, we simply subtract the numerators (1 - 3 = -2) and keep the denominator the same (8).

$\frac{1}{8} - \frac{3}{8} = \frac{-2}{8}$

We can simplify the fraction by dividing both the numerator and the denominator by their GCD, which is 2.

$\frac{-2}{8} = \frac{-1}{4}$

Example 2: Subtracting Fractions with Like Denominators

Suppose we want to subtract $\frac{5}{10}$ from $\frac{2}{10}$. To do this, we simply subtract the numerators (2 - 5 = -3) and keep the denominator the same (10).

$\frac{2}{10} - \frac{5}{10} = \frac{-3}{10}$

Real-World Applications of Adding and Subtracting Fractions with Like Denominators

Adding and subtracting fractions with like denominators has numerous real-world applications. For example:

• Cooking: When cooking, we often need to measure ingredients in fractions. For instance, if a recipe calls for 1/4 cup of sugar and we want to add 1/4 cup more, we can simply add the fractions.
• Building: In building construction, fractions are often used to measure materials. For example, if a wall requires 1/2 inch of plywood and we want to add 1/4 inch more, we can simply add the fractions.
• Science: In science, fractions are often used to measure quantities. For example, if a scientist wants to measure the concentration of a solution, they may use fractions to express the concentration.

Conclusion

In conclusion, adding and subtracting fractions with like denominators is a fundamental concept in mathematics. By understanding how to add and subtract fractions with like denominators, we can solve a wide range of mathematical problems and apply our knowledge to real-world situations. We hope this article has provided you with a comprehensive guide to adding and subtracting fractions with like denominators and has helped you to master this essential mathematical concept.

Common Mistakes to Avoid

When adding and subtracting fractions with like denominators, there are several common mistakes to avoid:

• Not simplifying the fraction: After adding or subtracting the numerators, make sure to simplify the fraction by dividing both the numerator and the denominator by their GCD.
• Not keeping the denominator the same: When adding or subtracting fractions with like denominators, make sure to keep the denominator the same.
• Not using the correct operation: Make sure to use the correct operation (addition or subtraction) when working with fractions with like denominators.

Practice Problems

To reinforce your understanding of adding and subtracting fractions with like denominators, try the following practice problems:

• Add $\frac{1}{8}$ and $\frac{3}{8}$.
• Subtract $\frac{3}{8}$ from $\frac{1}{8}$.
• Add $\frac{2}{10}$ and $\frac{5}{10}$.
• Subtract $\frac{5}{10}$ from $\frac{2}{10}$.

Final Thoughts

Q: What are fractions with like denominators?

A: Fractions with like denominators are fractions that have the same denominator, but different numerators. For example, $\frac{1}{8}$ and $\frac{3}{8}$ are fractions with like denominators.

Q: How do I add fractions with like denominators?

A: To add fractions with like denominators, simply add the numerators and keep the denominator the same. For example, $\frac{1}{8} + \frac{3}{8} = \frac{4}{8}$.

Q: How do I subtract fractions with like denominators?

A: To subtract fractions with like denominators, simply subtract the numerators and keep the denominator the same. For example, $\frac{1}{8} - \frac{3}{8} = \frac{-2}{8}$.

Q: What is the greatest common divisor (GCD) and why is it important?

A: The greatest common divisor (GCD) is the largest number that divides two or more numbers without leaving a remainder. It is important because it helps us simplify fractions by dividing both the numerator and the denominator by their GCD.

Q: How do I simplify a fraction?

A: To simplify a fraction, divide both the numerator and the denominator by their GCD. For example, $\frac{4}{8} = \frac{1}{2}$.

Q: What are some real-world applications of adding and subtracting fractions with like denominators?

A: Adding and subtracting fractions with like denominators has numerous real-world applications, including cooking, building, and science.

Q: What are some common mistakes to avoid when adding and subtracting fractions with like denominators?

A: Some common mistakes to avoid when adding and subtracting fractions with like denominators include not simplifying the fraction, not keeping the denominator the same, and not using the correct operation.

Q: How can I practice adding and subtracting fractions with like denominators?

A: You can practice adding and subtracting fractions with like denominators by trying the following practice problems:

• Add $\frac{1}{8}$ and $\frac{3}{8}$.
• Subtract $\frac{3}{8}$ from $\frac{1}{8}$.
• Add $\frac{2}{10}$ and $\frac{5}{10}$.
• Subtract $\frac{5}{10}$ from $\frac{2}{10}$.

Q: What are some additional resources for learning about adding and subtracting fractions with like denominators?

A: Some additional resources for learning about adding and subtracting fractions with like denominators include online tutorials, math textbooks, and practice worksheets.

Q: How can I apply my knowledge of adding and subtracting fractions with like denominators to real-world situations?

A: You can apply your knowledge of adding and subtracting fractions with like denominators to real-world situations by using fractions to measure ingredients in cooking, to measure materials in building, and to measure quantities in science.

Conclusion

In conclusion, adding and subtracting fractions with like denominators is a fundamental concept in mathematics that has numerous real-world applications. By understanding how to add and subtract fractions with like denominators, we can solve a wide range of mathematical problems and apply our knowledge to real-world situations. We hope this article has provided you with a comprehensive guide to adding and subtracting fractions with like denominators and has helped you to master this essential mathematical concept.