Subtract: 8 21 − 7 9 \frac{8}{21} - \frac{7}{9} 21 8 ​ − 9 7 ​ Give Your Answer As A Reduced Proper Or Improper Fraction. □ \square □

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Introduction

When it comes to subtracting fractions, it's essential to have a solid understanding of the concept and the steps involved. In this article, we will delve into the world of fractions and explore how to subtract them. We will focus on the specific problem of subtracting 821\frac{8}{21} from 79\frac{7}{9} and provide a step-by-step guide on how to solve it.

Understanding Fractions

Before we dive into the problem, let's take a moment to understand what fractions are. A fraction is a way to represent a part of a whole. It consists of two parts: the numerator and the denominator. The numerator is the top number, and the denominator is the bottom number. For example, in the fraction 34\frac{3}{4}, the numerator is 3, and the denominator is 4.

Finding a Common Denominator

When subtracting fractions, we need to find a common denominator. The common denominator is the least common multiple (LCM) of the two denominators. In this case, we need to find the LCM of 21 and 9.

Calculating the LCM

To calculate the LCM of 21 and 9, we can list the multiples of each number and find the smallest multiple they have in common.

Multiples of 21: 21, 42, 63, 84, 105, 126, 147, 168, 189, 210, ... Multiples of 9: 9, 18, 27, 36, 45, 54, 63, 72, 81, 90, 99, 108, 117, 126, 135, 144, 153, 162, 171, 180, 189, 198, 207, 216, ...

As we can see, the smallest multiple they have in common is 63. Therefore, the LCM of 21 and 9 is 63.

Converting the Fractions

Now that we have found the common denominator, we can convert the fractions to have the same denominator.

821=8×321×3=2463\frac{8}{21} = \frac{8 \times 3}{21 \times 3} = \frac{24}{63}

79=7×79×7=4963\frac{7}{9} = \frac{7 \times 7}{9 \times 7} = \frac{49}{63}

Subtracting the Fractions

Now that the fractions have the same denominator, we can subtract them.

2463−4963=24−4963=−2563\frac{24}{63} - \frac{49}{63} = \frac{24 - 49}{63} = \frac{-25}{63}

Simplifying the Fraction

The fraction −2563\frac{-25}{63} can be simplified by dividing both the numerator and the denominator by their greatest common divisor (GCD).

The GCD of 25 and 63 is 1. Therefore, the fraction −2563\frac{-25}{63} cannot be simplified further.

Conclusion

In conclusion, subtracting fractions requires finding a common denominator and converting the fractions to have the same denominator. We can then subtract the fractions and simplify the result if possible. In this article, we have walked through the steps involved in subtracting 821\frac{8}{21} from 79\frac{7}{9} and provided a step-by-step guide on how to solve it.

Frequently Asked Questions

  • Q: What is the common denominator of 21 and 9? A: The common denominator of 21 and 9 is 63.
  • Q: How do I convert a fraction to have a common denominator? A: To convert a fraction to have a common denominator, multiply the numerator and the denominator by the same number.
  • Q: How do I subtract fractions? A: To subtract fractions, find a common denominator, convert the fractions to have the same denominator, and then subtract the fractions.

Final Answer

The final answer is −2563\boxed{\frac{-25}{63}}.

Introduction

In our previous article, we explored the concept of subtracting fractions and walked through the steps involved in subtracting 821\frac{8}{21} from 79\frac{7}{9}. In this article, we will provide a Q&A section to address some of the most frequently asked questions related to subtracting fractions.

Q&A

Q: What is the common denominator of 21 and 9?

A: The common denominator of 21 and 9 is 63. To find the common denominator, we can list the multiples of each number and find the smallest multiple they have in common.

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

A: To convert a fraction to have a common denominator, multiply the numerator and the denominator by the same number. For example, to convert 821\frac{8}{21} to have a denominator of 63, we can multiply the numerator and the denominator by 3.

821=8×321×3=2463\frac{8}{21} = \frac{8 \times 3}{21 \times 3} = \frac{24}{63}

Q: How do I subtract fractions?

A: To subtract fractions, find a common denominator, convert the fractions to have the same denominator, and then subtract the fractions. For example, to subtract 821\frac{8}{21} from 79\frac{7}{9}, we can follow these steps:

  1. Find the common denominator: 63
  2. Convert the fractions to have the same denominator: 821=8×321×3=2463\frac{8}{21} = \frac{8 \times 3}{21 \times 3} = \frac{24}{63} 79=7×79×7=4963\frac{7}{9} = \frac{7 \times 7}{9 \times 7} = \frac{49}{63}
  3. Subtract the fractions: 2463−4963=24−4963=−2563\frac{24}{63} - \frac{49}{63} = \frac{24 - 49}{63} = \frac{-25}{63}

Q: Can I simplify the fraction after subtracting?

A: Yes, you can simplify the fraction after subtracting. To simplify the fraction, divide both the numerator and the denominator by their greatest common divisor (GCD). For example, to simplify −2563\frac{-25}{63}, we can divide both the numerator and the denominator by 1.

−2563=−25÷163÷1=−2563\frac{-25}{63} = \frac{-25 \div 1}{63 \div 1} = \frac{-25}{63}

Q: What if the fractions have different signs?

A: If the fractions have different signs, you can subtract the fractions as usual. For example, to subtract 821\frac{8}{21} from −79-\frac{7}{9}, we can follow these steps:

  1. Find the common denominator: 63
  2. Convert the fractions to have the same denominator: 821=8×321×3=2463\frac{8}{21} = \frac{8 \times 3}{21 \times 3} = \frac{24}{63} −79=−7×79×7=−4963-\frac{7}{9} = -\frac{7 \times 7}{9 \times 7} = -\frac{49}{63}
  3. Subtract the fractions: 2463−(−4963)=2463+4963=24+4963=7363\frac{24}{63} - (-\frac{49}{63}) = \frac{24}{63} + \frac{49}{63} = \frac{24 + 49}{63} = \frac{73}{63}

Q: Can I add and subtract fractions with different denominators?

A: Yes, you can add and subtract fractions with different denominators. To do this, you need to find the least common multiple (LCM) of the two denominators and convert the fractions to have the same denominator.

Conclusion

In conclusion, subtracting fractions requires finding a common denominator and converting the fractions to have the same denominator. We can then subtract the fractions and simplify the result if possible. In this article, we have provided a Q&A section to address some of the most frequently asked questions related to subtracting fractions.

Final Answer

The final answer is −2563\boxed{\frac{-25}{63}}.