Subtract: 7 9 − 1 3 \frac{7}{9} - \frac{1}{3} 9 7 − 3 1 Remember To Get Common Denominators. Subtract, Then Simplify If Possible.

Mar 9, 2025 by ADMIN 134 views

$Subtract: $\frac{7}{9} - \frac{1}{3}$$

Understanding the Problem

When dealing with fractions, it's essential to have a common denominator to perform operations such as addition and subtraction. In this case, we need to subtract $\frac{1}{3}$ from $\frac{7}{9}$ . To do this, we must first find a common denominator for both fractions.

Finding a Common Denominator

To find a common denominator, we need to identify the least common multiple (LCM) of the denominators. The denominators are 9 and 3. The multiples of 9 are 9, 18, 27, 36, and so on. The multiples of 3 are 3, 6, 9, 12, and so on. As we can see, the least common multiple of 9 and 3 is 9.

Converting Fractions to Have a Common Denominator

Since the common denominator is 9, we need to convert both fractions to have a denominator of 9. To convert $\frac{1}{3}$ to have a denominator of 9, we multiply both the numerator and the denominator by 3. This gives us $\frac{3}{9}$ . Now, both fractions have a common denominator of 9.

Subtracting the Fractions

Now that we have a common denominator, we can subtract the fractions. We subtract the numerators while keeping the common denominator the same. So, $\frac{7}{9} - \frac{3}{9} = \frac{7-3}{9} = \frac{4}{9}$ .

Simplifying the Result

The result of the subtraction is $\frac{4}{9}$ . Since the numerator and the denominator have no common factors, the fraction cannot be simplified further.

Conclusion

In conclusion, to subtract $\frac{7}{9} - \frac{1}{3}$ , we need to find a common denominator, which is 9. We then convert both fractions to have a denominator of 9 and subtract the numerators while keeping the common denominator the same. The result is $\frac{4}{9}$ , which cannot be simplified further.

Real-World Applications

Understanding how to subtract fractions is essential in various real-world applications, such as:

Cooking: When a recipe calls for a certain amount of an ingredient, and you need to adjust the amount, you may need to subtract fractions to get the correct amount.
Building: When building a structure, you may need to subtract fractions to calculate the amount of materials needed.
Science: In scientific calculations, you may need to subtract fractions to get accurate results.

Tips and Tricks

When subtracting fractions, make sure to find a common denominator.
Use the least common multiple (LCM) of the denominators to find the common denominator.
Convert both fractions to have the common denominator before subtracting.
Simplify the result, if possible.

Common Mistakes to Avoid

Not finding a common denominator before subtracting fractions.
Not converting both fractions to have the common denominator.
Not simplifying the result, if possible.

Practice Problems

Subtract $\frac{5}{6} - \frac{2}{3}$ .
Subtract $\frac{3}{4} - \frac{1}{2}$ .
Subtract $\frac{2}{3} - \frac{1}{4}$ .

Solutions to Practice Problems

$\frac{5}{6} - \frac{2}{3} = \frac{5}{6} - \frac{4}{6} = \frac{1}{6}$ .
$\frac{3}{4} - \frac{1}{2} = \frac{3}{4} - \frac{2}{4} = \frac{1}{4}$ .
$\frac{2}{3} - \frac{1}{4} = \frac{8}{12} - \frac{3}{12} = \frac{5}{12}$ .

Conclusion

In conclusion, subtracting fractions requires finding a common denominator, converting both fractions to have the common denominator, and then subtracting the numerators while keeping the common denominator the same. The result may need to be simplified, if possible. Understanding how to subtract fractions is essential in various real-world applications, and it's crucial to avoid common mistakes to get accurate results.

Frequently Asked Questions

Q: What is the first step in subtracting fractions?

A: The first step in subtracting fractions is to find a common denominator. This is the least common multiple (LCM) of the denominators of the two fractions.

Q: How do I find a common denominator?

A: To find a common denominator, you need to identify the least common multiple (LCM) of the denominators. You can do this by listing the multiples of each denominator and finding 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, you can find the least common multiple (LCM) by multiplying the denominators together and then dividing by their greatest common divisor (GCD).

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

A: To convert a fraction to have a common denominator, you need to multiply both the numerator and the denominator by the same number. This number is the common denominator divided by the original denominator.

Q: Can I simplify the result of subtracting fractions?

A: Yes, you can simplify the result of subtracting fractions by dividing both the numerator and the denominator by their greatest common divisor (GCD).

Q: What if the result of subtracting fractions is a fraction with a denominator of 1?

A: If the result of subtracting fractions is a fraction with a denominator of 1, it means that the numerator is equal to the denominator. In this case, the fraction can be simplified to a whole number.

Q: Can I subtract fractions with different signs?

A: Yes, you can subtract fractions with different signs. When subtracting fractions with different signs, you need to change the sign of the second fraction and then follow the usual procedure for subtracting fractions.

Q: What if I get a negative result when subtracting fractions?

A: If you get a negative result when subtracting fractions, it means that the second fraction is larger than the first fraction. In this case, you can change the sign of the result to make it positive.

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

A: Yes, you can add and subtract fractions with different denominators. However, you need to find a common denominator before performing the operation.

Q: What is the difference between adding and subtracting fractions?

A: The difference between adding and subtracting fractions is that when adding fractions, you add the numerators while keeping the common denominator the same. When subtracting fractions, you subtract the numerators while keeping the common denominator the same.

Q: Can I use a calculator to subtract fractions?

A: Yes, you can use a calculator to subtract fractions. However, it's always a good idea to check your work by performing the operation manually.

Q: What if I make a mistake when subtracting fractions?

A: If you make a mistake when subtracting fractions, you can try to identify the error and correct it. If you're still having trouble, you can ask for help from a teacher or tutor.