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

by ADMIN 212 views

Understanding the Basics of Adding Fractions

When it comes to adding fractions, it's essential to understand the basics of fraction addition. A fraction is a way of representing a part of a whole, and it consists of two parts: the numerator and the denominator. The numerator is the top number, and it represents the number of equal parts we have. The denominator is the bottom number, and it represents the total number of parts the whole is divided into.

Finding a Common Denominator

To add fractions, we need to find a common denominator. The common denominator is the least common multiple (LCM) of the denominators of the fractions we are adding. In the case of Shari's problem, we need to find the LCM of 3 and 4.

Step 1: Find the LCM of 3 and 4

To find the LCM of 3 and 4, we need to list the multiples of each number and find the smallest number that appears in both lists.

  • Multiples of 3: 3, 6, 9, 12, 15, ...
  • Multiples of 4: 4, 8, 12, 16, 20, ...

As we can see, the smallest number that appears in both lists is 12. Therefore, the LCM of 3 and 4 is 12.

Step 2: Convert the Fractions to Have a Common Denominator

Now that we have found the LCM of 3 and 4, we can convert the fractions to have a common denominator of 12.

  • 13=1×43×4=412\frac{1}{3} = \frac{1 \times 4}{3 \times 4} = \frac{4}{12}
  • 14=1×34×3=312\frac{1}{4} = \frac{1 \times 3}{4 \times 3} = \frac{3}{12}

Step 3: Add the Fractions

Now that we have converted the fractions to have a common denominator, we can add them.

412+312=4+312=712\frac{4}{12} + \frac{3}{12} = \frac{4 + 3}{12} = \frac{7}{12}

Conclusion

In conclusion, to add fractions, we need to find a common denominator, convert the fractions to have a common denominator, and then add them. In Shari's problem, the correct next step is to convert the fractions to have a common denominator of 12 and then add them.

Answer

The correct answer is:

B. ${ \frac{4}{12} + \frac{3}{12} = \frac{7}{12} }$

Additional Examples

Here are a few additional examples of adding fractions:

  • 12+14=?\frac{1}{2} + \frac{1}{4} = ?
  • 23+16=?\frac{2}{3} + \frac{1}{6} = ?
  • 34+18=?\frac{3}{4} + \frac{1}{8} = ?

Solution to Additional Examples

  • 12+14=24+14=34\frac{1}{2} + \frac{1}{4} = \frac{2}{4} + \frac{1}{4} = \frac{3}{4}
  • 23+16=46+16=56\frac{2}{3} + \frac{1}{6} = \frac{4}{6} + \frac{1}{6} = \frac{5}{6}
  • 34+18=68+18=78\frac{3}{4} + \frac{1}{8} = \frac{6}{8} + \frac{1}{8} = \frac{7}{8}

Tips and Tricks

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

  • Make sure to find the LCM of the denominators before adding the fractions.
  • Convert the fractions to have a common denominator before adding them.
  • Use a common denominator to add the fractions.
  • Simplify the fraction after adding it.

Conclusion

Q: What is the first step in adding fractions?

A: The first step in adding fractions is to find a common denominator. The common denominator is the least common multiple (LCM) of the denominators of the fractions we are adding.

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

A: To find the LCM of two numbers, we need to list the multiples of each number and find the smallest number that appears in both lists.

Q: What if the denominators are not multiples of each other?

A: If the denominators are not multiples of each other, we need to find the LCM of the two numbers. For example, if we are adding 13\frac{1}{3} and 14\frac{1}{4}, we need to find the LCM of 3 and 4.

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

A: To convert a fraction to have a common denominator, we need to multiply the numerator and denominator by the same number. For example, if we want to convert 13\frac{1}{3} to have a denominator of 12, we need to multiply the numerator and denominator by 4.

Q: What is the next step after finding the common denominator?

A: After finding the common denominator, we need to convert the fractions to have a common denominator and then add them.

Q: Can I add fractions with different signs?

A: Yes, we can add fractions with different signs. For example, 12+(−14)=12−14=24−14=14\frac{1}{2} + (-\frac{1}{4}) = \frac{1}{2} - \frac{1}{4} = \frac{2}{4} - \frac{1}{4} = \frac{1}{4}.

Q: Can I add fractions with the same sign?

A: Yes, we can add fractions with the same sign. For example, 12+14=24+14=34\frac{1}{2} + \frac{1}{4} = \frac{2}{4} + \frac{1}{4} = \frac{3}{4}.

Q: What if the fractions have different numerators and denominators?

A: If the fractions have different numerators and denominators, we need to find the LCM of the denominators and then convert the fractions to have a common denominator.

Q: Can I simplify the fraction after adding it?

A: Yes, we can simplify the fraction after adding it. For example, 34+14=44=1\frac{3}{4} + \frac{1}{4} = \frac{4}{4} = 1.

Q: What are some common mistakes to avoid when adding fractions?

A: Some common mistakes to avoid when adding fractions include:

  • Not finding the LCM of the denominators
  • Not converting the fractions to have a common denominator
  • Not adding the fractions correctly
  • Not simplifying the fraction after adding it

Q: How can I practice adding fractions?

A: You can practice adding fractions by using online resources, such as fraction worksheets and online calculators. You can also practice adding fractions by using real-world examples, such as measuring ingredients for a recipe.

Conclusion

In conclusion, adding fractions is a simple process that requires finding a common denominator, converting the fractions to have a common denominator, and then adding them. By following these steps and using a few tips and tricks, you can add fractions with ease.