Answer :
Sure! Let's solve each of the problems step-by-step:
### 3. Find the difference:
[tex]\[
\frac{4}{7} - \frac{12}{21}
\][/tex]
Solution:
Both fractions need a common denominator to be subtracted. Notice that [tex]\( \frac{12}{21} \)[/tex] simplifies to [tex]\( \frac{4}{7} \)[/tex], as 12 divided by 3 is 4, and 21 divided by 3 is 7.
Now we subtract:
[tex]\[
\frac{4}{7} - \frac{4}{7} = 0
\][/tex]
So, the difference is [tex]\(0\)[/tex].
### 4. Find the difference:
[tex]\[
\frac{5}{8} - \frac{1}{3} - \frac{7}{27} - \frac{1}{4}
\][/tex]
Solution:
We'll convert all fractions to a common denominator. Let's choose the least common multiple of the denominators 8, 3, 27, and 4, which is 216. Then, we calculate:
1. Convert [tex]\(\frac{5}{8}\)[/tex] to a denominator of 216:
[tex]\[
\frac{5}{8} = \frac{135}{216}
\][/tex]
2. Convert [tex]\(\frac{1}{3}\)[/tex] to a denominator of 216:
[tex]\[
\frac{1}{3} = \frac{72}{216}
\][/tex]
3. Convert [tex]\(\frac{7}{27}\)[/tex] to a denominator of 216:
[tex]\[
\frac{7}{27} = \frac{56}{216}
\][/tex]
4. Convert [tex]\(\frac{1}{4}\)[/tex] to a denominator of 216:
[tex]\[
\frac{1}{4} = \frac{54}{216}
\][/tex]
Now, perform the subtraction:
[tex]\[
\frac{135}{216} - \frac{72}{216} - \frac{56}{216} - \frac{54}{216} = \frac{-47}{216}
\][/tex]
So, the difference is [tex]\(-\frac{47}{216}\)[/tex].
### 5. Find the difference:
[tex]\[
\frac{7}{8}
\][/tex]
Solution:
There's only one fraction given, so there's nothing to subtract.
The answer is [tex]\( \frac{7}{8} \)[/tex].
### 6. Find the difference:
[tex]\[
\frac{4}{5} - \frac{24}{30} - \frac{1}{6} - \frac{5}{3}
\][/tex]
Solution:
Convert all fractions to a common denominator. The least common multiple of 5, 30, 6, and 3 is 30. Then, calculate:
1. Convert [tex]\(\frac{4}{5}\)[/tex] to a denominator of 30:
[tex]\[
\frac{4}{5} = \frac{24}{30}
\][/tex]
2. Note that [tex]\( \frac{24}{30} \)[/tex] is already with the same denominator.
3. Convert [tex]\(\frac{1}{6}\)[/tex] to a denominator of 30:
[tex]\[
\frac{1}{6} = \frac{5}{30}
\][/tex]
4. Convert [tex]\(\frac{5}{3}\)[/tex] to a denominator of 30:
[tex]\[
\frac{5}{3} = \frac{50}{30}
\][/tex]
Now, perform the subtraction:
[tex]\[
\frac{24}{30} - \frac{24}{30} - \frac{5}{30} - \frac{50}{30} = -\frac{11}{6}
\][/tex]
So, the difference is [tex]\(-\frac{11}{6}\)[/tex].
I hope this helps! Let me know if you have any other questions.
### 3. Find the difference:
[tex]\[
\frac{4}{7} - \frac{12}{21}
\][/tex]
Solution:
Both fractions need a common denominator to be subtracted. Notice that [tex]\( \frac{12}{21} \)[/tex] simplifies to [tex]\( \frac{4}{7} \)[/tex], as 12 divided by 3 is 4, and 21 divided by 3 is 7.
Now we subtract:
[tex]\[
\frac{4}{7} - \frac{4}{7} = 0
\][/tex]
So, the difference is [tex]\(0\)[/tex].
### 4. Find the difference:
[tex]\[
\frac{5}{8} - \frac{1}{3} - \frac{7}{27} - \frac{1}{4}
\][/tex]
Solution:
We'll convert all fractions to a common denominator. Let's choose the least common multiple of the denominators 8, 3, 27, and 4, which is 216. Then, we calculate:
1. Convert [tex]\(\frac{5}{8}\)[/tex] to a denominator of 216:
[tex]\[
\frac{5}{8} = \frac{135}{216}
\][/tex]
2. Convert [tex]\(\frac{1}{3}\)[/tex] to a denominator of 216:
[tex]\[
\frac{1}{3} = \frac{72}{216}
\][/tex]
3. Convert [tex]\(\frac{7}{27}\)[/tex] to a denominator of 216:
[tex]\[
\frac{7}{27} = \frac{56}{216}
\][/tex]
4. Convert [tex]\(\frac{1}{4}\)[/tex] to a denominator of 216:
[tex]\[
\frac{1}{4} = \frac{54}{216}
\][/tex]
Now, perform the subtraction:
[tex]\[
\frac{135}{216} - \frac{72}{216} - \frac{56}{216} - \frac{54}{216} = \frac{-47}{216}
\][/tex]
So, the difference is [tex]\(-\frac{47}{216}\)[/tex].
### 5. Find the difference:
[tex]\[
\frac{7}{8}
\][/tex]
Solution:
There's only one fraction given, so there's nothing to subtract.
The answer is [tex]\( \frac{7}{8} \)[/tex].
### 6. Find the difference:
[tex]\[
\frac{4}{5} - \frac{24}{30} - \frac{1}{6} - \frac{5}{3}
\][/tex]
Solution:
Convert all fractions to a common denominator. The least common multiple of 5, 30, 6, and 3 is 30. Then, calculate:
1. Convert [tex]\(\frac{4}{5}\)[/tex] to a denominator of 30:
[tex]\[
\frac{4}{5} = \frac{24}{30}
\][/tex]
2. Note that [tex]\( \frac{24}{30} \)[/tex] is already with the same denominator.
3. Convert [tex]\(\frac{1}{6}\)[/tex] to a denominator of 30:
[tex]\[
\frac{1}{6} = \frac{5}{30}
\][/tex]
4. Convert [tex]\(\frac{5}{3}\)[/tex] to a denominator of 30:
[tex]\[
\frac{5}{3} = \frac{50}{30}
\][/tex]
Now, perform the subtraction:
[tex]\[
\frac{24}{30} - \frac{24}{30} - \frac{5}{30} - \frac{50}{30} = -\frac{11}{6}
\][/tex]
So, the difference is [tex]\(-\frac{11}{6}\)[/tex].
I hope this helps! Let me know if you have any other questions.
