Calculate The Following: 1 2 − 1 3 = ? ? \frac{1}{2} - \frac{1}{3} = \frac{?}{?} 2 1 − 3 1 = ? ? Pound

Mar 12, 2025 by ADMIN 109 views

**Solving a Simple Fraction Problem: A Step-by-Step Guide**

Introduction

In mathematics, fractions are a fundamental concept that helps us represent part of a whole. When dealing with fractions, we often need to perform operations such as addition, subtraction, multiplication, and division. In this article, we will focus on solving a simple fraction problem: $\frac{1}{2} - \frac{1}{3} = \frac{?}{?}$ pound.

Understanding the Problem

To solve this problem, we need to understand the concept of fractions and how to subtract them. A fraction is a way of representing a part of a whole as a ratio of two numbers. In this case, we have two fractions: $\frac{1}{2}$ and $\frac{1}{3}$ . We need to find the difference between these two fractions.

Step 1: Find a Common Denominator

To subtract fractions, we need to have a common denominator. The common denominator is the least common multiple (LCM) of the denominators of the two fractions. In this case, the denominators are 2 and 3. The LCM of 2 and 3 is 6.

Step 2: Convert Fractions to Have a Common Denominator

Now that we have a common denominator, we can convert both fractions to have a denominator of 6.

$\frac{1}{2} = \frac{1 \times 3}{2 \times 3} = \frac{3}{6}$

$\frac{1}{3} = \frac{1 \times 2}{3 \times 2} = \frac{2}{6}$

Step 3: Subtract the Fractions

Now that both fractions have a common denominator, we can subtract them.

$\frac{3}{6} - \frac{2}{6} = \frac{3 - 2}{6} = \frac{1}{6}$

Conclusion

In this article, we solved a simple fraction problem: $\frac{1}{2} - \frac{1}{3} = \frac{?}{?}$ pound. We found the common denominator, converted both fractions to have a common denominator, and then subtracted the fractions. The final answer is $\frac{1}{6}$ pound.

Real-World Applications

Fractions are used in many real-world applications, such as:

Cooking: When a recipe calls for a certain amount of an ingredient, we can use fractions to measure it accurately.
Building: When building a structure, we need to use fractions to calculate the amount of materials needed.
Finance: When dealing with money, we use fractions to calculate interest rates and investment returns.

Tips and Tricks

Here are some tips and tricks to help you solve fraction problems:

Use a common denominator: When subtracting fractions, make sure to have a common denominator.
Convert fractions to have a common denominator: If the fractions don't have a common denominator, convert them to have a common denominator.
Subtract the numerators: Once you have a common denominator, subtract the numerators to find the final answer.

Common Mistakes

Here are some common mistakes to avoid when solving fraction problems:

Not finding a common denominator: Failing to find a common denominator can lead to incorrect answers.
Not converting fractions to have a common denominator: Failing to convert fractions to have a common denominator can lead to incorrect answers.
Not subtracting the numerators: Failing to subtract the numerators can lead to incorrect answers.

Conclusion

Q: What is a fraction?

A: A fraction is a way of representing a part of a whole as a ratio of two numbers. It consists of a numerator (the top number) and a denominator (the bottom number).

Q: What is the difference between a numerator and a denominator?

A: The numerator is the top number in a fraction, and it represents the part of the whole. The denominator is the bottom number in a fraction, and it represents the total number of parts.

Q: How do I find the common denominator of two fractions?

A: To find the common denominator of two fractions, you need to find the least common multiple (LCM) of the denominators. The LCM is the smallest number that both denominators can divide into evenly.

Q: What is the least common multiple (LCM)?

A: The LCM is the smallest number that two or more numbers can divide into evenly. For example, the LCM of 2 and 3 is 6, because 6 is the smallest number that both 2 and 3 can divide into evenly.

Q: How do I convert fractions to have a common denominator?

A: To convert fractions to have a common denominator, you need to multiply the numerator and denominator of each fraction by the same number, so that the denominators are equal.

Q: What is the rule for subtracting fractions?

A: The rule for subtracting fractions is to subtract the numerators and keep the same denominator.

Q: Can I add fractions with different denominators?

A: Yes, you can add fractions with different denominators, but you need to find the common denominator first.

Q: How do I add fractions with different denominators?

A: To add fractions with different denominators, you need to find the common denominator, convert both fractions to have the common denominator, and then add the numerators.

Q: Can I multiply fractions?

A: Yes, you can multiply fractions. To multiply fractions, you need to multiply the numerators and denominators separately.

Q: How do I multiply fractions?

A: To multiply fractions, you need to multiply the numerators and denominators separately, and then simplify the result.

Q: Can I divide fractions?

A: Yes, you can divide fractions. To divide fractions, you need to invert the second fraction (i.e. flip the numerator and denominator) and then multiply.

Q: How do I divide fractions?

A: To divide fractions, you need to invert the second fraction (i.e. flip the numerator and denominator) and then multiply.

Q: What is the difference between a proper fraction and an improper fraction?

A: A proper fraction is a fraction where the numerator is less than the denominator, and an improper fraction is a fraction where the numerator is greater than or equal to the denominator.

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

A: To convert a proper fraction to an improper fraction, you need to multiply the numerator and denominator by the same number, so that the numerator is greater than or equal to the denominator.

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

A: To convert an improper fraction to a proper fraction, you need to divide the numerator by the denominator and then simplify the result.

Conclusion

In conclusion, solving fraction problems requires a clear understanding of the concept of fractions and how to add, subtract, multiply, and divide them. By following the steps outlined in this article, you can solve fraction problems with ease. Remember to use a common denominator, convert fractions to have a common denominator, and subtract or add the numerators to find the final answer.