Which Expression Uses A Common Denominator To Rewrite 1 4 − 1 7 \frac{1}{4} - \frac{1}{7} 4 1 ​ − 7 1 ​ ?A. 7 28 − 4 28 \frac{7}{28} - \frac{4}{28} 28 7 ​ − 28 4 ​ B. 4 1 − 7 1 \frac{4}{1} - \frac{7}{1} 1 4 ​ − 1 7 ​ C. 4 28 − 1 28 \frac{4}{28} - \frac{1}{28} 28 4 ​ − 28 1 ​ D. $\frac{7}{12} -

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Introduction

When working with fractions, it's often necessary to rewrite them in a way that makes it easier to perform operations such as addition and subtraction. One common technique for doing this is to use a common denominator, which is a number that both fractions can be divided by. In this article, we'll explore how to use a common denominator to rewrite the expression 14−17\frac{1}{4} - \frac{1}{7}.

What is a Common Denominator?

A common denominator is a number that both fractions can be divided by. For example, if we have the fractions 14\frac{1}{4} and 17\frac{1}{7}, we can find a common denominator by listing the multiples of each fraction's denominator and finding the smallest number that appears in both lists.

Finding the Least Common Multiple (LCM)

To find the common denominator, we need to find the least common multiple (LCM) of the two fractions' denominators. The LCM is the smallest number that both fractions can be divided by.

For the fractions 14\frac{1}{4} and 17\frac{1}{7}, the denominators are 4 and 7, respectively. To find the LCM, we can list the multiples of each denominator:

  • Multiples of 4: 4, 8, 12, 16, 20, 24, 28, ...
  • Multiples of 7: 7, 14, 21, 28, 35, 42, ...

As we can see, the smallest number that appears in both lists is 28. Therefore, the common denominator is 28.

Rewriting the Fractions

Now that we have found the common denominator, we can rewrite each fraction using this denominator. To do this, we need to multiply the numerator and denominator of each fraction by the same number, which is the common denominator divided by the original denominator.

For the fraction 14\frac{1}{4}, we can multiply the numerator and denominator by 7, which is the common denominator divided by the original denominator:

14⋅77=728\frac{1}{4} \cdot \frac{7}{7} = \frac{7}{28}

Similarly, for the fraction 17\frac{1}{7}, we can multiply the numerator and denominator by 4, which is the common denominator divided by the original denominator:

17⋅44=428\frac{1}{7} \cdot \frac{4}{4} = \frac{4}{28}

Subtracting the Fractions

Now that we have rewritten the fractions using the common denominator, we can subtract them:

728−428=7−428=328\frac{7}{28} - \frac{4}{28} = \frac{7-4}{28} = \frac{3}{28}

Conclusion

In this article, we have seen how to use a common denominator to rewrite the expression 14−17\frac{1}{4} - \frac{1}{7}. By finding the least common multiple (LCM) of the two fractions' denominators and rewriting each fraction using this denominator, we can perform operations such as subtraction with ease.

Answer

The correct answer is C. 428−128\frac{4}{28} - \frac{1}{28}.

Common Denominator Examples

Here are a few more examples of using a common denominator to rewrite fractions:

  • 12−13\frac{1}{2} - \frac{1}{3}: The common denominator is 6. The rewritten fractions are 36−26\frac{3}{6} - \frac{2}{6}.
  • 15+110\frac{1}{5} + \frac{1}{10}: The common denominator is 10. The rewritten fractions are 210+110\frac{2}{10} + \frac{1}{10}.
  • 16−19\frac{1}{6} - \frac{1}{9}: The common denominator is 18. The rewritten fractions are 318−218\frac{3}{18} - \frac{2}{18}.

Tips and Tricks

Here are a few tips and tricks for using a common denominator:

  • Always find the least common multiple (LCM) of the two fractions' denominators.
  • Rewrite each fraction using the common denominator.
  • Perform operations such as addition and subtraction with ease.

Conclusion

Frequently Asked Questions

Q: What is a common denominator?

A: A common denominator is a number that both fractions can be divided by. It's used to rewrite fractions in a way that makes it easier to perform operations such as addition and subtraction.

Q: How do I find the common denominator?

A: To find the common denominator, you need to find the least common multiple (LCM) of the two fractions' denominators. You can do this by listing the multiples of each denominator and finding the smallest number that appears in both lists.

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

A: The least common multiple (LCM) is the smallest number that both fractions can be divided by. It's used to find the common denominator.

Q: How do I rewrite fractions using a common denominator?

A: To rewrite fractions using a common denominator, you need to multiply the numerator and denominator of each fraction by the same number, which is the common denominator divided by the original denominator.

Q: Can I use a common denominator to add fractions?

A: Yes, you can use a common denominator to add fractions. By rewriting each fraction using the common denominator, you can add them together.

Q: Can I use a common denominator to subtract fractions?

A: Yes, you can use a common denominator to subtract fractions. By rewriting each fraction using the common denominator, you can subtract them.

Q: What are some examples of using a common denominator?

A: Here are a few examples of using a common denominator:

  • 12−13\frac{1}{2} - \frac{1}{3}: The common denominator is 6. The rewritten fractions are 36−26\frac{3}{6} - \frac{2}{6}.
  • 15+110\frac{1}{5} + \frac{1}{10}: The common denominator is 10. The rewritten fractions are 210+110\frac{2}{10} + \frac{1}{10}.
  • 16−19\frac{1}{6} - \frac{1}{9}: The common denominator is 18. The rewritten fractions are 318−218\frac{3}{18} - \frac{2}{18}.

Q: What are some tips and tricks for using a common denominator?

A: Here are a few tips and tricks for using a common denominator:

  • Always find the least common multiple (LCM) of the two fractions' denominators.
  • Rewrite each fraction using the common denominator.
  • Perform operations such as addition and subtraction with ease.

Q: Why is it important to use a common denominator?

A: Using a common denominator is important because it makes it easier to perform operations such as addition and subtraction. By rewriting fractions using a common denominator, you can avoid having to deal with different denominators and make calculations easier.

Q: Can I use a common denominator with mixed numbers?

A: Yes, you can use a common denominator with mixed numbers. To do this, you need to convert the mixed number to an improper fraction and then find the common denominator.

Q: Can I use a common denominator with decimals?

A: Yes, you can use a common denominator with decimals. To do this, you need to convert the decimal to a fraction and then find the common denominator.

Conclusion

In conclusion, using a common denominator is a powerful technique for rewriting fractions and performing operations such as addition and subtraction. By following the steps outlined in this article, you can master this technique and become a pro at working with fractions.