Let's Find 1 2 − 1 8 \frac{1}{2}-\frac{1}{8} 2 1 ​ − 8 1 ​ .First, Write The Subtraction So The Fractions Have A Common Denominator Of 8. Then Subtract. 1 2 − 1 8 = □ 8 − 1 8 = □ □ \frac{1}{2}-\frac{1}{8}=\frac{\square}{8}-\frac{1}{8}=\frac{\square}{\square} 2 1 ​ − 8 1 ​ = 8 □ ​ − 8 1 ​ = □ □ ​

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Introduction

Subtracting fractions can be a challenging task, especially when the fractions have different denominators. However, with a few simple steps, we can make the process easier and more manageable. In this article, we will explore how to subtract fractions with different denominators, using the example of 12−18\frac{1}{2}-\frac{1}{8}. We will learn how to find a common denominator, rewrite the fractions, and then subtract them.

Finding a Common Denominator

To subtract fractions, we need to find a common denominator. The common denominator is the smallest number that both fractions can divide into evenly. In the case of 12\frac{1}{2} and 18\frac{1}{8}, the least common multiple (LCM) of 2 and 8 is 8. Therefore, we can rewrite 12\frac{1}{2} as 48\frac{4}{8}, since 4 is half of 8.

Rewriting the Fractions

Now that we have found the common denominator, we can rewrite the fractions. We will rewrite 12\frac{1}{2} as 48\frac{4}{8} and leave 18\frac{1}{8} as is.

12−18=48−18\frac{1}{2}-\frac{1}{8}=\frac{4}{8}-\frac{1}{8}

Subtracting the Fractions

Now that we have rewritten the fractions, we can subtract them. To subtract fractions, we subtract the numerators (the numbers on top) and keep the denominator the same.

48−18=4−18=38\frac{4}{8}-\frac{1}{8}=\frac{4-1}{8}=\frac{3}{8}

Conclusion

Subtracting fractions with different denominators can be a challenging task, but with a few simple steps, we can make the process easier and more manageable. By finding a common denominator, rewriting the fractions, and then subtracting them, we can find the result of 12−18\frac{1}{2}-\frac{1}{8}. In this case, the result is 38\frac{3}{8}.

Tips and Tricks

  • When subtracting fractions, make sure to find a common denominator.
  • Rewrite the fractions with the common denominator.
  • Subtract the numerators and keep the denominator the same.
  • Simplify the fraction, if possible.

Common Denominator Examples

  • 14−18=28−18=18\frac{1}{4}-\frac{1}{8}=\frac{2}{8}-\frac{1}{8}=\frac{1}{8}
  • 34−18=68−18=58\frac{3}{4}-\frac{1}{8}=\frac{6}{8}-\frac{1}{8}=\frac{5}{8}
  • 23−16=46−16=36=12\frac{2}{3}-\frac{1}{6}=\frac{4}{6}-\frac{1}{6}=\frac{3}{6}=\frac{1}{2}

Real-World Applications

Subtracting fractions has many real-world applications. For example, in cooking, you may need to subtract fractions of ingredients to make a recipe. In science, you may need to subtract fractions of measurements to calculate the results of an experiment. In finance, you may need to subtract fractions of investments to calculate the returns on investment.

Conclusion

Subtracting fractions with different denominators can be a challenging task, but with a few simple steps, we can make the process easier and more manageable. By finding a common denominator, rewriting the fractions, and then subtracting them, we can find the result of 12−18\frac{1}{2}-\frac{1}{8}. In this case, the result is 38\frac{3}{8}. With practice and patience, you can become proficient in subtracting fractions and apply this skill to real-world situations.

Final Thoughts

Subtracting fractions is an essential skill in mathematics, and with practice, you can become proficient in this skill. Remember to find a common denominator, rewrite the fractions, and then subtract them. With this skill, you can apply it to real-world situations and make calculations easier and more manageable.

Introduction

Subtracting fractions can be a challenging task, especially when the fractions have different denominators. However, with a few simple steps, we can make the process easier and more manageable. In this article, we will answer some frequently asked questions about subtracting fractions, using the example of 12−18\frac{1}{2}-\frac{1}{8}.

Q: What is the first step in subtracting fractions?

A: The first step in subtracting fractions is to find a common denominator. The common denominator is the smallest number that both fractions can divide into evenly.

Q: How do I find a common denominator?

A: To find a common denominator, you can list the multiples of each denominator and find the smallest number that appears in both lists. For example, to find the common denominator of 2 and 8, you can list the multiples of 2 and 8:

Multiples of 2: 2, 4, 6, 8, 10, ... Multiples of 8: 8, 16, 24, 32, ...

The smallest number that appears in both lists is 8, so the common denominator is 8.

Q: How do I rewrite the fractions with the common denominator?

A: To rewrite the fractions with the common denominator, you can multiply the numerator and denominator of each fraction by the necessary factor to get the common denominator. For example, to rewrite 12\frac{1}{2} with a denominator of 8, you can multiply the numerator and denominator by 4:

12=1⋅42⋅4=48\frac{1}{2}=\frac{1\cdot4}{2\cdot4}=\frac{4}{8}

Q: How do I subtract the fractions?

A: To subtract the fractions, you can subtract the numerators (the numbers on top) and keep the denominator the same. For example, to subtract 48\frac{4}{8} and 18\frac{1}{8}, you can subtract the numerators:

48−18=4−18=38\frac{4}{8}-\frac{1}{8}=\frac{4-1}{8}=\frac{3}{8}

Q: What if the fractions have different signs?

A: If the fractions have different signs, you can subtract the fractions as usual. For example, to subtract 38\frac{3}{8} and −18-\frac{1}{8}, you can subtract the numerators:

38−(−18)=38+18=48=12\frac{3}{8}-\left(-\frac{1}{8}\right)=\frac{3}{8}+\frac{1}{8}=\frac{4}{8}=\frac{1}{2}

Q: Can I simplify the fraction after subtracting?

A: Yes, you can simplify the fraction after subtracting. For example, to simplify 38\frac{3}{8}, you can divide both the numerator and denominator by their greatest common divisor (GCD), which is 1:

38=3÷18÷1=38\frac{3}{8}=\frac{3\div1}{8\div1}=\frac{3}{8}

Q: What if I get a negative result?

A: If you get a negative result, it means that the second fraction is larger than the first fraction. For example, to subtract 18\frac{1}{8} and 38\frac{3}{8}, you can subtract the numerators:

18−38=1−38=−28=−14\frac{1}{8}-\frac{3}{8}=\frac{1-3}{8}=\frac{-2}{8}=-\frac{1}{4}

Q: Can I use a calculator to subtract fractions?

A: Yes, you can use a calculator to subtract fractions. However, make sure to enter the fractions in the correct format and follow the instructions on the calculator.

Q: What if I have a fraction with a variable in the numerator or denominator?

A: If you have a fraction with a variable in the numerator or denominator, you can follow the same steps as before. For example, to subtract x2\frac{x}{2} and 18\frac{1}{8}, you can find a common denominator, rewrite the fractions, and then subtract them:

x2−18=4x8−18=4x−18\frac{x}{2}-\frac{1}{8}=\frac{4x}{8}-\frac{1}{8}=\frac{4x-1}{8}

Conclusion

Subtracting fractions can be a challenging task, but with a few simple steps, we can make the process easier and more manageable. By finding a common denominator, rewriting the fractions, and then subtracting them, we can find the result of 12−18\frac{1}{2}-\frac{1}{8}. In this article, we have answered some frequently asked questions about subtracting fractions, using the example of 12−18\frac{1}{2}-\frac{1}{8}. With practice and patience, you can become proficient in subtracting fractions and apply this skill to real-world situations.