What Is 1 5 − 1 8 \frac{1}{5}-\frac{1}{8} 5 1 ​ − 8 1 ​ ?A. 3 40 \frac{3}{40} 40 3 ​ B. 1 13 \frac{1}{13} 13 1 ​ C. 13 40 \frac{13}{40} 40 13 ​ D. 2 13 \frac{2}{13} 13 2 ​

Introduction

In mathematics, fractions are a way to represent a part of a whole. When we subtract one fraction from another, we need to find a common denominator to ensure that we are comparing the same units. In this article, we will explore the concept of subtracting fractions and apply it to the problem of finding the value of $\frac{1}{5}-\frac{1}{8}$.

Understanding Fractions

A fraction is a way to represent a part of a whole. It consists of two parts: the numerator and the denominator. The numerator represents the number of equal parts we have, and the denominator represents the total number of parts the whole is divided into. For example, the fraction $\frac{1}{5}$ represents one part out of five equal parts.

Subtracting Fractions

When we subtract one fraction from another, we need to find a common denominator. The common denominator is the least common multiple (LCM) of the two denominators. Once we have the common denominator, we can subtract the numerators and keep the common denominator.

Finding the Common Denominator

To find the common denominator of $\frac{1}{5}$ and $\frac{1}{8}$, we need to find the least common multiple (LCM) of 5 and 8. The LCM of 5 and 8 is 40.

Subtracting the Fractions

Now that we have the common denominator, we can subtract the numerators. The numerator of $\frac{1}{5}$ is 1, and the numerator of $\frac{1}{8}$ is 1. We can subtract 1 from 1, but we need to keep the common denominator of 40.

$\frac{1}{5}-\frac{1}{8} = \frac{1 \times 8}{5 \times 8} - \frac{1 \times 5}{8 \times 5}$

$\frac{1}{5}-\frac{1}{8} = \frac{8}{40} - \frac{5}{40}$

$\frac{1}{5}-\frac{1}{8} = \frac{8-5}{40}$

$\frac{1}{5}-\frac{1}{8} = \frac{3}{40}$

Conclusion

In conclusion, the value of $\frac{1}{5}-\frac{1}{8}$ is $\frac{3}{40}$. This is because we found the common denominator of 40 and subtracted the numerators, keeping the common denominator.

Answer

The correct answer is A. $\frac{3}{40}$.

Additional Examples

Here are a few more examples of subtracting fractions:

• $\frac{1}{4}-\frac{1}{6} = \frac{3}{12} - \frac{2}{12} = \frac{1}{12}$
• $\frac{1}{3}-\frac{1}{9} = \frac{3}{9} - \frac{1}{9} = \frac{2}{9}$
• $\frac{1}{2}-\frac{1}{4} = \frac{2}{4} - \frac{1}{4} = \frac{1}{4}$

Tips and Tricks

Here are a few tips and tricks to help you subtract fractions:

• Always find the common denominator before subtracting the numerators.
• Use the least common multiple (LCM) to find the common denominator.
• Keep the common denominator when subtracting the numerators.
• Simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor (GCD).

Conclusion

Q: What is the common denominator?

A: The common denominator is the least common multiple (LCM) of the two denominators. It is the smallest number that both denominators can divide into evenly.

Q: How do I find the common denominator?

A: To find the common denominator, you can list the multiples of each denominator and find the smallest number that appears in both lists. Alternatively, you can use the formula: LCM(a, b) = (a × b) / GCD(a, b), where GCD is the greatest common divisor.

Q: What is the greatest common divisor (GCD)?

A: The greatest common divisor (GCD) is the largest number that divides both numbers evenly. For example, the GCD of 12 and 18 is 6, because 6 is the largest number that divides both 12 and 18 evenly.

Q: How do I subtract fractions with different denominators?

A: To subtract fractions with different denominators, you need to find the common denominator and then subtract the numerators while keeping the common denominator.

Q: What is the rule for subtracting fractions?

A: The rule for subtracting fractions is:

1. Find the common denominator.
2. Subtract the numerators while keeping the common denominator.
3. Simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor (GCD).

Q: Can I subtract fractions with unlike denominators?

A: Yes, you can subtract fractions with unlike denominators. To do this, you need to find the common denominator and then subtract the numerators while keeping the common denominator.

Q: How do I simplify a fraction?

A: To simplify a fraction, you need to divide both the numerator and the denominator by their greatest common divisor (GCD). For example, the fraction 6/8 can be simplified by dividing both the numerator and the denominator by 2, resulting in 3/4.

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

A: The main difference between adding and subtracting fractions is that when adding fractions, you need to find the least common multiple (LCM) of the two denominators, while when subtracting fractions, you need to find the least common multiple (LCM) of the two denominators and then subtract the numerators while keeping the common denominator.

Q: Can I add and subtract fractions with unlike denominators?

A: Yes, you can add and subtract fractions with unlike denominators. To do this, you need to find the common denominator and then add or subtract the numerators while keeping the common denominator.

Q: How do I convert a mixed number to an improper fraction?

A: To convert a mixed number to an improper fraction, you need to multiply the whole number by the denominator and then add the numerator. For example, the mixed number 3 1/2 can be converted to an improper fraction by multiplying the whole number by the denominator and then adding the numerator: 3 × 2 + 1 = 7, resulting in the improper fraction 7/2.

Q: How do I convert an improper fraction to a mixed number?

A: To convert an improper fraction to a mixed number, you need to divide the numerator by the denominator and then write the remainder as the new numerator. For example, the improper fraction 7/2 can be converted to a mixed number by dividing the numerator by the denominator: 7 ÷ 2 = 3 with a remainder of 1, resulting in the mixed number 3 1/2.