Find The Sum Of The Fractions: $\frac{4}{6} + \frac{1}{18}$1. Find The Least Common Multiple (LCM) Of The Denominators.2. Rewrite The Fractions With The Common Denominator.3. Add The Fractions.The Least Common Multiple Is

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Introduction

Fractions are a fundamental concept in mathematics, and learning to add them is an essential skill for students of all ages. In this article, we will explore the process of finding the sum of two fractions, 46+118\frac{4}{6} + \frac{1}{18}, using the least common multiple (LCM) method.

Step 1: Find the Least Common Multiple (LCM) of the Denominators

The first step in finding the sum of fractions is to find the least common multiple (LCM) of the denominators. The LCM is the smallest number that both denominators can divide into evenly. In this case, the denominators are 6 and 18.

To find the LCM, we can list the multiples of each denominator:

  • Multiples of 6: 6, 12, 18, 24, 30, ...
  • Multiples of 18: 18, 36, 54, 72, 90, ...

The smallest number that appears in both lists is 18, so the LCM of 6 and 18 is 18.

Step 2: Rewrite the Fractions with the Common Denominator

Now that we have found the LCM, we can rewrite each fraction with the common denominator. To do this, we need to multiply the numerator and denominator of each fraction by the necessary factor to get the LCM as the denominator.

For the first fraction, 46\frac{4}{6}, we need to multiply the numerator and denominator by 3 to get:

4×36×3=1218\frac{4 \times 3}{6 \times 3} = \frac{12}{18}

For the second fraction, 118\frac{1}{18}, we don't need to do anything because the denominator is already 18.

Step 3: Add the Fractions

Now that we have rewritten the fractions with the common denominator, we can add them together. To do this, we simply add the numerators and keep the denominator the same:

1218+118=12+118=1318\frac{12}{18} + \frac{1}{18} = \frac{12 + 1}{18} = \frac{13}{18}

Conclusion

In this article, we have learned how to find the sum of two fractions using the least common multiple (LCM) method. We found the LCM of the denominators, rewrote the fractions with the common denominator, and added the fractions together. The final answer is 1318\frac{13}{18}.

Real-World Applications

Finding the sum of fractions is an essential skill in many real-world applications, such as:

  • Cooking: When a recipe calls for a certain amount of ingredients, you may need to add fractions of ingredients together to get the correct amount.
  • Finance: When calculating interest rates or investment returns, you may need to add fractions of percentages together.
  • Science: When measuring the concentration of a solution, you may need to add fractions of concentrations together.

Tips and Tricks

Here are some tips and tricks to help you find the sum of fractions:

  • Always find the LCM of the denominators before adding the fractions.
  • Rewrite the fractions with the common denominator before adding them.
  • Add the numerators and keep the denominator the same.
  • Simplify the fraction, if possible, by dividing both the numerator and denominator by their greatest common divisor (GCD).

Common Mistakes

Here are some common mistakes to avoid when finding the sum of fractions:

  • Not finding the LCM of the denominators before adding the fractions.
  • Not rewriting the fractions with the common denominator before adding them.
  • Adding the denominators instead of the numerators.
  • Not simplifying the fraction, if possible, by dividing both the numerator and denominator by their GCD.

Conclusion

Q: What is the least common multiple (LCM) and why is it important?

A: The least common multiple (LCM) is the smallest number that both denominators can divide into evenly. It is important because it allows us to rewrite the fractions with a common denominator, making it easier to add them together.

Q: How do I find the LCM of two numbers?

A: To find the LCM of two numbers, you can list the multiples of each number 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) and how is it used?

A: The greatest common divisor (GCD) is the largest number that both numbers can divide into evenly. It is used to simplify fractions by dividing both the numerator and denominator by their GCD.

Q: Can I add fractions with different denominators without finding the LCM?

A: No, you cannot add fractions with different denominators without finding the LCM. If you try to add fractions with different denominators, you will get an incorrect answer.

Q: What if the LCM is not a whole number?

A: If the LCM is not a whole number, you can still use it to rewrite the fractions with a common denominator. However, you may need to simplify the fraction further by dividing both the numerator and denominator by their GCD.

Q: Can I use a calculator to find the LCM and GCD?

A: Yes, you can use a calculator to find the LCM and GCD. Most calculators have a built-in function to find the LCM and GCD.

Q: What if I get a fraction with a negative numerator or denominator?

A: If you get a fraction with a negative numerator or denominator, you can simplify it by dividing both the numerator and denominator by their GCD. Alternatively, you can multiply both the numerator and denominator by -1 to get a positive fraction.

Q: Can I add fractions with different signs?

A: Yes, you can add fractions with different signs. To do this, you need to find the LCM of the denominators and rewrite the fractions with a common denominator. Then, you can add the fractions together, taking into account the signs.

Q: What if I get a fraction that is not in simplest form?

A: If you get a fraction that is not in simplest form, you can simplify it by dividing both the numerator and denominator by their GCD.

Q: Can I use the LCM method to subtract fractions?

A: Yes, you can use the LCM method to subtract fractions. To do this, you need to find the LCM of the denominators and rewrite the fractions with a common denominator. Then, you can subtract the fractions together, taking into account the signs.

Conclusion

Finding the sum of fractions is a fundamental skill in mathematics that has many real-world applications. By following the steps outlined in this article and using the LCM method, you can add fractions with ease. Remember to always find the LCM of the denominators, rewrite the fractions with a common denominator, and add the fractions together. With practice and patience, you will become a pro at finding the sum of fractions in no time!