Answer :
Sure! Let's solve each expression step-by-step, given that [tex]\( x = 1 \frac{1}{3} \)[/tex].
1. Expression 28: [tex]\( 4 \frac{1}{2} + x + 3 \frac{5}{6} \)[/tex]
- Convert [tex]\( x = 1 \frac{1}{3} \)[/tex] to an improper fraction: [tex]\( x = \frac{4}{3} \)[/tex].
- Convert [tex]\( 4 \frac{1}{2} \)[/tex] to an improper fraction: [tex]\( \frac{9}{2} \)[/tex].
- Convert [tex]\( 3 \frac{5}{6} \)[/tex] to an improper fraction: [tex]\( \frac{23}{6} \)[/tex].
Now, let's add these fractions:
[tex]\[
\frac{9}{2} + \frac{4}{3} + \frac{23}{6} = 9 \frac{1}{6}
\][/tex]
So, the answer is C. [tex]\( 9 \frac{1}{6} \)[/tex].
2. Expression 29: [tex]\( \frac{2}{5} + \left( x - \frac{1}{4} \right) \)[/tex]
- Subtract [tex]\( \frac{1}{4} \)[/tex] from [tex]\( x = \frac{4}{3} \)[/tex]:
[tex]\[
\frac{4}{3} - \frac{1}{4} = \frac{16}{12} - \frac{3}{12} = \frac{13}{12}
\][/tex]
- Now, add [tex]\( \frac{2}{5} \)[/tex]:
[tex]\[
\frac{2}{5} + \frac{13}{12} = \frac{49}{60}
\][/tex]
So, the answer is B. [tex]\( \frac{49}{60} \)[/tex].
3. Expression 30: [tex]\( \left( 5 \frac{5}{8} - x \right) + 1 \frac{5}{12} \)[/tex]
- Convert [tex]\( 5 \frac{5}{8} \)[/tex] to an improper fraction: [tex]\( \frac{45}{8} \)[/tex].
- Subtract [tex]\( x = \frac{4}{3} \)[/tex]:
[tex]\[
\frac{45}{8} - \frac{4}{3} = \frac{35}{24}
\][/tex]
- Add [tex]\( 1 \frac{5}{12} \)[/tex] (which is [tex]\( \frac{17}{12} \)[/tex]):
[tex]\[
\frac{35}{24} + \frac{17}{12} = \frac{171}{24} = 6 \frac{17}{24}
\][/tex]
So, the answer is D. [tex]\( 6 \frac{17}{24} \)[/tex].
4. Expression 31: [tex]\( 4 \frac{5}{6} - x + 3 \frac{1}{2} \)[/tex]
- Convert [tex]\( 4 \frac{5}{6} \)[/tex] to an improper fraction: [tex]\( \frac{29}{6} \)[/tex].
- Subtract [tex]\( x = \frac{4}{3} \)[/tex]:
[tex]\[
\frac{29}{6} - \frac{4}{3} = \frac{21}{6}
\][/tex]
- Add [tex]\( 3 \frac{1}{2} \)[/tex] (which is [tex]\( \frac{7}{2} \)[/tex]):
[tex]\[
\frac{21}{6} + \frac{21}{6} = 7
\][/tex]
So, the answer is A. 7.
These calculations should help clarify each step in evaluating the expressions with [tex]\( x = 1 \frac{1}{3} \)[/tex].
1. Expression 28: [tex]\( 4 \frac{1}{2} + x + 3 \frac{5}{6} \)[/tex]
- Convert [tex]\( x = 1 \frac{1}{3} \)[/tex] to an improper fraction: [tex]\( x = \frac{4}{3} \)[/tex].
- Convert [tex]\( 4 \frac{1}{2} \)[/tex] to an improper fraction: [tex]\( \frac{9}{2} \)[/tex].
- Convert [tex]\( 3 \frac{5}{6} \)[/tex] to an improper fraction: [tex]\( \frac{23}{6} \)[/tex].
Now, let's add these fractions:
[tex]\[
\frac{9}{2} + \frac{4}{3} + \frac{23}{6} = 9 \frac{1}{6}
\][/tex]
So, the answer is C. [tex]\( 9 \frac{1}{6} \)[/tex].
2. Expression 29: [tex]\( \frac{2}{5} + \left( x - \frac{1}{4} \right) \)[/tex]
- Subtract [tex]\( \frac{1}{4} \)[/tex] from [tex]\( x = \frac{4}{3} \)[/tex]:
[tex]\[
\frac{4}{3} - \frac{1}{4} = \frac{16}{12} - \frac{3}{12} = \frac{13}{12}
\][/tex]
- Now, add [tex]\( \frac{2}{5} \)[/tex]:
[tex]\[
\frac{2}{5} + \frac{13}{12} = \frac{49}{60}
\][/tex]
So, the answer is B. [tex]\( \frac{49}{60} \)[/tex].
3. Expression 30: [tex]\( \left( 5 \frac{5}{8} - x \right) + 1 \frac{5}{12} \)[/tex]
- Convert [tex]\( 5 \frac{5}{8} \)[/tex] to an improper fraction: [tex]\( \frac{45}{8} \)[/tex].
- Subtract [tex]\( x = \frac{4}{3} \)[/tex]:
[tex]\[
\frac{45}{8} - \frac{4}{3} = \frac{35}{24}
\][/tex]
- Add [tex]\( 1 \frac{5}{12} \)[/tex] (which is [tex]\( \frac{17}{12} \)[/tex]):
[tex]\[
\frac{35}{24} + \frac{17}{12} = \frac{171}{24} = 6 \frac{17}{24}
\][/tex]
So, the answer is D. [tex]\( 6 \frac{17}{24} \)[/tex].
4. Expression 31: [tex]\( 4 \frac{5}{6} - x + 3 \frac{1}{2} \)[/tex]
- Convert [tex]\( 4 \frac{5}{6} \)[/tex] to an improper fraction: [tex]\( \frac{29}{6} \)[/tex].
- Subtract [tex]\( x = \frac{4}{3} \)[/tex]:
[tex]\[
\frac{29}{6} - \frac{4}{3} = \frac{21}{6}
\][/tex]
- Add [tex]\( 3 \frac{1}{2} \)[/tex] (which is [tex]\( \frac{7}{2} \)[/tex]):
[tex]\[
\frac{21}{6} + \frac{21}{6} = 7
\][/tex]
So, the answer is A. 7.
These calculations should help clarify each step in evaluating the expressions with [tex]\( x = 1 \frac{1}{3} \)[/tex].
