Subtract 9 16 − 1 4 \frac{9}{16} - \frac{1}{4} 16 9 ​ − 4 1 ​ .Remember To Find A Common Denominator First. Subtract, Then Simplify If Possible.

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Introduction

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When subtracting fractions, it's essential to find a common denominator to ensure that the fractions have a comparable value. In this article, we will explore how to subtract $\frac{9}{16} - \frac{1}{4}$ by finding a common denominator and simplifying the result.

Finding a Common Denominator

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To subtract fractions, we need to find a common denominator, which is the least common multiple (LCM) of the denominators. In this case, the denominators are 16 and 4. To find the LCM, we can list the multiples of each denominator:

• Multiples of 16: 16, 32, 48, 64, ...
• Multiples of 4: 4, 8, 12, 16, ...

As we can see, the least common multiple of 16 and 4 is 16. Therefore, we will convert the second fraction to have a denominator of 16.

Converting the Second Fraction

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To convert the second fraction, we need to multiply the numerator and denominator by the necessary factor to obtain a denominator of 16. In this case, we need to multiply the numerator and denominator by 4:

$$\frac{1}{4} = \frac{1 \times 4}{4 \times 4} = \frac{4}{16}$$

Subtracting the Fractions

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Now that we have a common denominator, we can subtract the fractions:

$$\frac{9}{16} - \frac{4}{16} = \frac{9 - 4}{16} = \frac{5}{16}$$

Simplifying the Result

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The result, $\frac{5}{16}$, is already in its simplest form. Therefore, we do not need to simplify it further.

Conclusion

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In conclusion, to subtract $\frac{9}{16} - \frac{1}{4}$, we need to find a common denominator, which is 16. We then convert the second fraction to have a denominator of 16 and subtract the fractions. The result is $\frac{5}{16}$, which is already in its simplest form.

Frequently Asked Questions

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Q: Why do we need to find a common denominator when subtracting fractions?

A: We need to find a common denominator to ensure that the fractions have a comparable value. This allows us to subtract the fractions accurately.

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

A: To find the LCM, we can list the multiples of each number and find the smallest multiple that appears in both lists.

Q: Can we simplify the result further?

A: In this case, the result, $\frac{5}{16}$, is already in its simplest form. Therefore, we do not need to simplify it further.

Additional Resources

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For more information on subtracting fractions, you can refer to the following resources:

• Khan Academy: Subtracting Fractions
• Mathway: Subtracting Fractions

Final Thoughts

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Subtracting fractions can be a challenging task, but with the right approach, it can be done accurately. By finding a common denominator and simplifying the result, we can ensure that our answer is correct. Remember to always find a common denominator when subtracting fractions, and don't hesitate to ask for help if you need it.

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Introduction

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Subtracting fractions can be a challenging task, but with the right approach, it can be done accurately. In this article, we will answer some of the most frequently asked questions about subtracting fractions.

Q: Why do we need to find a common denominator when subtracting fractions?

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A: We need to find a common denominator to ensure that the fractions have a comparable value. This allows us to subtract the fractions accurately.

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

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A: To find the LCM, we can list the multiples of each number and find the smallest multiple that appears in both lists. For example, to find the LCM of 16 and 4, we can list the multiples of each number:

• Multiples of 16: 16, 32, 48, 64, ...
• Multiples of 4: 4, 8, 12, 16, ...

As we can see, the least common multiple of 16 and 4 is 16.

Q: Can we simplify the result further?

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A: In some cases, the result may be able to be simplified further. However, in the case of $\frac{5}{16}$, the result is already in its simplest form. Therefore, we do not need to simplify it further.

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

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A: If the denominators are not multiples of each other, we can find the least common multiple (LCM) of the two denominators. For example, if we want to subtract $\frac{3}{5} - \frac{2}{7}$, we can find the LCM of 5 and 7, which is 35. We can then convert each fraction to have a denominator of 35:

$$\frac{3}{5} = \frac{3 \times 7}{5 \times 7} = \frac{21}{35}$$

$$\frac{2}{7} = \frac{2 \times 5}{7 \times 5} = \frac{10}{35}$$

We can then subtract the fractions:

$$\frac{21}{35} - \frac{10}{35} = \frac{21 - 10}{35} = \frac{11}{35}$$

Q: Can we subtract fractions with different signs?

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A: Yes, we can subtract fractions with different signs. For example, if we want to subtract $\frac{3}{4} - (-\frac{2}{3})$, we can convert the second fraction to have a positive sign:

$$-\frac{2}{3} = \frac{2}{3}$$

We can then subtract the fractions:

$$\frac{3}{4} - \frac{2}{3} = \frac{3}{4} - \frac{2 \times 4}{3 \times 4} = \frac{3}{4} - \frac{8}{12} = \frac{9}{12} - \frac{8}{12} = \frac{1}{12}$$

Q: Can we subtract fractions with unlike denominators?

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A: Yes, we can subtract fractions with unlike denominators. We can find the least common multiple (LCM) of the two denominators and convert each fraction to have a denominator of the LCM. We can then subtract the fractions.

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

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A: If the result is not a whole number, we can simplify the fraction by dividing the numerator and denominator by their greatest common divisor (GCD). For example, if we want to subtract $\frac{3}{4} - \frac{2}{3}$, we can find the LCM of 4 and 3, which is 12. We can then convert each fraction to have a denominator of 12:

$$\frac{3}{4} = \frac{3 \times 3}{4 \times 3} = \frac{9}{12}$$

$$\frac{2}{3} = \frac{2 \times 4}{3 \times 4} = \frac{8}{12}$$

We can then subtract the fractions:

$$\frac{9}{12} - \frac{8}{12} = \frac{9 - 8}{12} = \frac{1}{12}$$

Q: Can we subtract fractions with variables?

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A: Yes, we can subtract fractions with variables. We can find the least common multiple (LCM) of the two denominators and convert each fraction to have a denominator of the LCM. We can then subtract the fractions.

Q: What if the variables are not the same?

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A: If the variables are not the same, we can find the least common multiple (LCM) of the two variables and convert each fraction to have a denominator of the LCM. We can then subtract the fractions.

Conclusion

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Subtracting fractions can be a challenging task, but with the right approach, it can be done accurately. By finding a common denominator and simplifying the result, we can ensure that our answer is correct. Remember to always find a common denominator when subtracting fractions, and don't hesitate to ask for help if you need it.

Additional Resources

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For more information on subtracting fractions, you can refer to the following resources:

• Khan Academy: Subtracting Fractions
• Mathway: Subtracting Fractions

Final Thoughts

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Subtracting fractions is an essential skill in mathematics, and with practice, you can become proficient in subtracting fractions. Remember to always find a common denominator and simplify the result to ensure that your answer is correct.