Find The Difference. 1 2 − 1 5 = □ ? \frac{1}{2} - \frac{1}{5} = \frac{\square}{?} 2 1 ​ − 5 1 ​ = ? □ ​

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Find the Difference: A Step-by-Step Guide to Solving Fractions

When it comes to solving fractions, one of the most common operations is subtraction. However, subtracting fractions can be a bit tricky, especially when the denominators are different. In this article, we will explore the concept of subtracting fractions with different denominators and provide a step-by-step guide on how to solve them.

What are Fractions?

A fraction is a way of expressing a part of a whole. It consists of two numbers: a numerator and a denominator. The numerator represents the number of equal parts we have, while the denominator represents the total number of parts the whole is divided into. For example, the fraction 1/2 represents one half of a whole.

Subtracting Fractions with Different Denominators

When subtracting fractions with different denominators, 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.

Example: 12−15=□?\frac{1}{2} - \frac{1}{5} = \frac{\square}{?}

Let's use the example given in the problem: 12−15=□?\frac{1}{2} - \frac{1}{5} = \frac{\square}{?}. To solve this problem, we need to find the common denominator of 2 and 5.

Step 1: Find the Common Denominator

The least common multiple (LCM) of 2 and 5 is 10. Therefore, the common denominator is 10.

Step 2: Convert the Fractions

To convert the fractions to have a common denominator, we need to multiply the numerator and denominator of each fraction by the necessary factor.

  • 12=1×52×5=510\frac{1}{2} = \frac{1 \times 5}{2 \times 5} = \frac{5}{10}
  • 15=1×25×2=210\frac{1}{5} = \frac{1 \times 2}{5 \times 2} = \frac{2}{10}

Step 3: Subtract the Numerators

Now that we have the fractions with a common denominator, we can subtract the numerators.

510−210=5−210=310\frac{5}{10} - \frac{2}{10} = \frac{5 - 2}{10} = \frac{3}{10}

In conclusion, subtracting fractions with different denominators requires finding a common denominator and then subtracting the numerators. By following the steps outlined in this article, you can solve fractions with different denominators and find the difference.

  • Always find the least common multiple (LCM) of the two denominators to ensure that you have a common denominator.
  • Multiply the numerator and denominator of each fraction by the necessary factor to convert them to have a common denominator.
  • Subtract the numerators and keep the common denominator.

Here are some common denominators for different pairs of numbers:

  • 2 and 3: 6
  • 2 and 4: 4
  • 2 and 5: 10
  • 3 and 4: 12
  • 3 and 5: 15

Here are some practice problems to help you practice subtracting fractions with different denominators:

  • 13−14=□?\frac{1}{3} - \frac{1}{4} = \frac{\square}{?}
  • 25−12=□?\frac{2}{5} - \frac{1}{2} = \frac{\square}{?}
  • 34−13=□?\frac{3}{4} - \frac{1}{3} = \frac{\square}{?}

Here are the answers to the practice problems:

  • 13−14=4−312=112\frac{1}{3} - \frac{1}{4} = \frac{4 - 3}{12} = \frac{1}{12}
  • 25−12=4−510=−110\frac{2}{5} - \frac{1}{2} = \frac{4 - 5}{10} = \frac{-1}{10}
  • 34−13=9−412=512\frac{3}{4} - \frac{1}{3} = \frac{9 - 4}{12} = \frac{5}{12}
    Find the Difference: A Q&A Guide to Solving Fractions

In our previous article, we explored the concept of subtracting fractions with different denominators and provided a step-by-step guide on how to solve them. However, we know that practice makes perfect, and the best way to learn is by asking questions and getting answers. In this article, we will provide a Q&A guide to help you understand and practice subtracting fractions with different denominators.

Q: What is the first step in subtracting fractions with different denominators?

A: The first step in subtracting fractions with different denominators is to find the least common multiple (LCM) of the two denominators. This will give you the common denominator that you need to subtract the fractions.

Q: How do I find the least common multiple (LCM) of two numbers?

A: To find the LCM of two numbers, you can list the multiples of each number and find the smallest multiple that they have in common. Alternatively, you can use the following formula:

LCM(a, b) = (a × b) / GCD(a, b)

where GCD(a, b) is the greatest common divisor of a and b.

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

A: The GCD of two numbers is the largest number that divides both numbers without leaving a remainder. For example, the GCD of 12 and 15 is 3, because 3 is the largest number that divides both 12 and 15 without leaving a remainder.

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 necessary factor. This will give you fractions with the same denominator, which you can then subtract.

Q: What is the formula for subtracting fractions with different denominators?

A: The formula for subtracting fractions with different denominators is:

ab−cd=ad−bcbd\frac{a}{b} - \frac{c}{d} = \frac{ad - bc}{bd}

where a, b, c, and d are the numerators and denominators of the fractions.

Q: Can I subtract fractions with different denominators if the denominators are not multiples of each other?

A: Yes, you can subtract fractions with different denominators even if the denominators are not multiples of each other. In this case, you need to find the least common multiple (LCM) of the two denominators and convert the fractions to have the LCM as the denominator.

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

A: The main difference between subtracting fractions and subtracting whole numbers is that fractions have a denominator, which represents the total number of parts the whole is divided into. When subtracting fractions, you need to find the common denominator and subtract the numerators, whereas when subtracting whole numbers, you can simply subtract the numbers.

Q: Can I use a calculator to subtract fractions with different denominators?

A: Yes, you can use a calculator to subtract fractions with different denominators. However, it's always a good idea to understand the concept and be able to do it manually, as this will help you to develop your problem-solving skills and understand the underlying math.

Q: What are some common mistakes to avoid when subtracting fractions with different denominators?

A: Some common mistakes to avoid when subtracting fractions with different denominators include:

  • Not finding the least common multiple (LCM) of the two denominators
  • Not converting the fractions to have the LCM as the denominator
  • Subtracting the denominators instead of the numerators
  • Not simplifying the fraction after subtracting

In conclusion, subtracting fractions with different denominators requires finding the least common multiple (LCM) of the two denominators and then subtracting the numerators. By following the steps outlined in this article and practicing with different problems, you can become proficient in subtracting fractions with different denominators.

Here are some practice problems to help you practice subtracting fractions with different denominators:

  • 13−14=□?\frac{1}{3} - \frac{1}{4} = \frac{\square}{?}
  • 25−12=□?\frac{2}{5} - \frac{1}{2} = \frac{\square}{?}
  • 34−13=□?\frac{3}{4} - \frac{1}{3} = \frac{\square}{?}

Here are the answers to the practice problems:

  • 13−14=4−312=112\frac{1}{3} - \frac{1}{4} = \frac{4 - 3}{12} = \frac{1}{12}
  • 25−12=4−510=−110\frac{2}{5} - \frac{1}{2} = \frac{4 - 5}{10} = \frac{-1}{10}
  • 34−13=9−412=512\frac{3}{4} - \frac{1}{3} = \frac{9 - 4}{12} = \frac{5}{12}