Shari Is Adding These Fractions: 1 3 + 1 4 \frac{1}{3} + \frac{1}{4} 3 1 + 4 1 What's Her Next Step?A. 1 3 + 1 4 = 2 12 \frac{1}{3} + \frac{1}{4} = \frac{2}{12} 3 1 + 4 1 = 12 2 B. 4 12 + 3 12 = 7 12 \frac{4}{12} + \frac{3}{12} = \frac{7}{12} 12 4 + 12 3 = 12 7 C. $\frac{4}{12} + \frac{3}{12} =

Mar 11, 2025 by ADMIN 312 views

**Adding Fractions: A Step-by-Step Guide**

Understanding the Basics of Adding Fractions

Adding fractions is a fundamental concept in mathematics that requires a clear understanding of the underlying principles. When adding fractions, it's essential to have a common denominator, which is the same number that the denominators of both fractions are multiplied by. In this article, we will explore the steps involved in adding fractions, using the example of Shari adding $\frac{1}{3} + \frac{1}{4}$ .

Step 1: Find the Least Common Multiple (LCM)

To add fractions, we need 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 3 and 4. The multiples of 3 are 3, 6, 9, 12, and so on. The multiples of 4 are 4, 8, 12, and so on. Therefore, the least common multiple of 3 and 4 is 12.

Step 2: Convert the Fractions to Have the Same Denominator

Once we have found the LCM, we need to convert both fractions to have the same denominator. To do this, we multiply the numerator and denominator of each fraction by the necessary factor to make the denominator equal to the LCM. In this case, we need to multiply the first fraction by 4 and the second fraction by 3 to make the denominators equal to 12.

$\frac{1}{3} \times \frac{4}{4} = \frac{4}{12}$

$\frac{1}{4} \times \frac{3}{3} = \frac{3}{12}$

Step 3: Add the Numerators

Now that both fractions have the same denominator, we can add the numerators. The numerator is the number on top of the fraction. In this case, the numerators are 4 and 3. We add these numbers together to get the new numerator.

$4 + 3 = 7$

Step 4: Write the Answer as a Fraction

The final step is to write the answer as a fraction. We have already found the numerator, which is 7. The denominator is the same as the LCM, which is 12. Therefore, the answer is $\frac{7}{12}$ .

Conclusion

In conclusion, adding fractions requires a clear understanding of the underlying principles. The steps involved in adding fractions are:

Find the least common multiple (LCM) of the denominators.
Convert both fractions to have the same denominator.
Add the numerators.
Write the answer as a fraction.

Using the example of Shari adding $\frac{1}{3} + \frac{1}{4}$ , we have demonstrated the steps involved in adding fractions. The correct answer is $\frac{7}{12}$ .

Common Mistakes to Avoid

When adding fractions, there are several common mistakes to avoid. These include:

Not finding the least common multiple (LCM) of the denominators.
Not converting both fractions to have the same denominator.
Not adding the numerators correctly.
Not writing the answer as a fraction.

By avoiding these common mistakes, you can ensure that you are adding fractions correctly.

Real-World Applications of Adding Fractions

Adding fractions has several real-world applications. For example, in cooking, you may need to add fractions of ingredients to a recipe. In science, you may need to add fractions of measurements to calculate the results of an experiment. In finance, you may need to add fractions of interest rates to calculate the total interest earned on an investment.

Practice Problems

To practice adding fractions, try the following problems:

$\frac{1}{2} + \frac{1}{3} = ?$
$\frac{2}{5} + \frac{3}{5} = ?$
$\frac{4}{9} + \frac{2}{9} = ?$

Answer Key

$\frac{1}{2} + \frac{1}{3} = \frac{5}{6}$
$\frac{2}{5} + \frac{3}{5} = \frac{5}{5} = 1$
$\frac{4}{9} + \frac{2}{9} = \frac{6}{9} = \frac{2}{3}$
Adding Fractions: A Q&A Guide =============================

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

A: The least common multiple (LCM) of two numbers is the smallest number that both numbers can divide into evenly. For example, the LCM of 3 and 4 is 12.

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 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 greatest common divisor (GCD) of two numbers is the largest number that both numbers can divide into evenly. For example, the GCD of 12 and 15 is 3.

Q: How do I add fractions with different denominators?

A: To add fractions with different denominators, you need to find the least common multiple (LCM) of the denominators and convert both fractions to have the same denominator. Then, you can add the numerators and write the answer as a fraction.

Q: What is the rule for adding fractions with the same denominator?

A: When adding fractions with the same denominator, you can simply add the numerators and write the answer as a fraction with the same denominator.

Q: Can I add fractions with unlike denominators by converting them to decimals?

A: Yes, you can add fractions with unlike denominators by converting them to decimals. However, this method is not always the most efficient or accurate way to add fractions.

Q: How do I subtract fractions?

A: To subtract fractions, you need to find the least common multiple (LCM) of the denominators and convert both fractions to have the same denominator. Then, you can subtract the numerators and write the answer as a fraction.

Q: Can I subtract fractions with unlike denominators by converting them to decimals?

A: Yes, you can subtract fractions with unlike denominators by converting them to decimals. However, this method is not always the most efficient or accurate way to subtract fractions.

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 are combining two or more quantities, while when subtracting fractions, you are finding the difference between two quantities.

Q: Can I add or subtract fractions with negative numbers?

A: Yes, you can add or subtract fractions with negative numbers. When adding or subtracting fractions with negative numbers, you need to follow the same rules as when adding or subtracting fractions with positive numbers.

Q: How do I multiply fractions?

A: To multiply fractions, you can simply multiply the numerators and multiply the denominators. Then, you can simplify the resulting fraction by dividing both the numerator and denominator by their greatest common divisor.

Q: Can I multiply fractions with unlike denominators by converting them to decimals?

A: Yes, you can multiply fractions with unlike denominators by converting them to decimals. However, this method is not always the most efficient or accurate way to multiply fractions.

Q: How do I divide fractions?

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

Q: Can I divide fractions with unlike denominators by converting them to decimals?

A: Yes, you can divide fractions with unlike denominators by converting them to decimals. However, this method is not always the most efficient or accurate way to divide fractions.

Q: What is the rule for multiplying and dividing fractions?

A: When multiplying or dividing fractions, you can follow the same rules as when adding or subtracting fractions, but with the added step of inverting the second fraction when dividing.