Answer :
To decompose the fraction [tex]\(\frac{9}{10}\)[/tex], let's examine each option and see which expressions add up to [tex]\(\frac{9}{10}\)[/tex]:
1. Option: [tex]\(\frac{4}{10} + \frac{5}{10}\)[/tex]
- Calculate the sum:
[tex]\[
\frac{4}{10} + \frac{5}{10} = \frac{4+5}{10} = \frac{9}{10}
\][/tex]
- This option correctly decomposes [tex]\(\frac{9}{10}\)[/tex].
2. Option: [tex]\(\frac{3}{10} + \frac{1}{10} + \frac{1}{10} + \frac{1}{10} + \frac{1}{10} + \frac{1}{10}\)[/tex]
- Calculate the sum:
[tex]\[
\frac{3}{10} + \frac{1}{10} + \frac{1}{10} + \frac{1}{10} + \frac{1}{10} + \frac{1}{10} = \frac{3+1+1+1+1+1}{10} = \frac{8}{10}
\][/tex]
- This option does not add up to [tex]\(\frac{9}{10}\)[/tex].
3. Option: [tex]\(\frac{3}{10} + \frac{7}{10}\)[/tex]
- Calculate the sum:
[tex]\[
\frac{3}{10} + \frac{7}{10} = \frac{3+7}{10} = \frac{10}{10} = 1
\][/tex]
- This is greater than [tex]\(\frac{9}{10}\)[/tex] and does not decompose it correctly.
4. Option: [tex]\(\frac{1}{10} + \frac{1}{10} + \frac{3}{10} + \frac{4}{10}\)[/tex]
- Calculate the sum:
[tex]\[
\frac{1}{10} + \frac{1}{10} + \frac{3}{10} + \frac{4}{10} = \frac{1+1+3+4}{10} = \frac{9}{10}
\][/tex]
- This option correctly decomposes [tex]\(\frac{9}{10}\)[/tex].
Based on the analysis, the options that correctly decompose [tex]\(\frac{9}{10}\)[/tex] are:
- [tex]\(\frac{4}{10} + \frac{5}{10}\)[/tex]
- [tex]\(\frac{1}{10} + \frac{1}{10} + \frac{3}{10} + \frac{4}{10}\)[/tex]
1. Option: [tex]\(\frac{4}{10} + \frac{5}{10}\)[/tex]
- Calculate the sum:
[tex]\[
\frac{4}{10} + \frac{5}{10} = \frac{4+5}{10} = \frac{9}{10}
\][/tex]
- This option correctly decomposes [tex]\(\frac{9}{10}\)[/tex].
2. Option: [tex]\(\frac{3}{10} + \frac{1}{10} + \frac{1}{10} + \frac{1}{10} + \frac{1}{10} + \frac{1}{10}\)[/tex]
- Calculate the sum:
[tex]\[
\frac{3}{10} + \frac{1}{10} + \frac{1}{10} + \frac{1}{10} + \frac{1}{10} + \frac{1}{10} = \frac{3+1+1+1+1+1}{10} = \frac{8}{10}
\][/tex]
- This option does not add up to [tex]\(\frac{9}{10}\)[/tex].
3. Option: [tex]\(\frac{3}{10} + \frac{7}{10}\)[/tex]
- Calculate the sum:
[tex]\[
\frac{3}{10} + \frac{7}{10} = \frac{3+7}{10} = \frac{10}{10} = 1
\][/tex]
- This is greater than [tex]\(\frac{9}{10}\)[/tex] and does not decompose it correctly.
4. Option: [tex]\(\frac{1}{10} + \frac{1}{10} + \frac{3}{10} + \frac{4}{10}\)[/tex]
- Calculate the sum:
[tex]\[
\frac{1}{10} + \frac{1}{10} + \frac{3}{10} + \frac{4}{10} = \frac{1+1+3+4}{10} = \frac{9}{10}
\][/tex]
- This option correctly decomposes [tex]\(\frac{9}{10}\)[/tex].
Based on the analysis, the options that correctly decompose [tex]\(\frac{9}{10}\)[/tex] are:
- [tex]\(\frac{4}{10} + \frac{5}{10}\)[/tex]
- [tex]\(\frac{1}{10} + \frac{1}{10} + \frac{3}{10} + \frac{4}{10}\)[/tex]
