To solve the problem, we need to evaluate each given expression and determine whether it is an integer or not. Let's go through each expression step by step.
---
1. \( \frac{7}{4} - \frac{3}{4} \)
\[
\frac{7}{4} - \frac{3}{4} = \frac{7 - 3}{4} = \frac{4}{4} = 1
\]
This is an integer.
---
2. \( \frac{5}{6} + \frac{7}{6} \)
\[
\frac{5}{6} + \frac{7}{6} = \frac{5 + 7}{6} = \frac{12}{6} = 2
\]
This is an integer.
---
3. \( \frac{8}{9} - \frac{5}{9} \)
\[
\frac{8}{9} - \frac{5}{9} = \frac{8 - 5}{9} = \frac{3}{9} = \frac{1}{3}
\]
This is
not an integer.
---
4. \( \frac{11}{12} - \frac{5}{12} \)
\[
\frac{11}{12} - \frac{5}{12} = \frac{11 - 5}{12} = \frac{6}{12} = \frac{1}{2}
\]
This is
not an integer.
---
5. \( \frac{10}{15} - \frac{4}{15} \)
\[
\frac{10}{15} - \frac{4}{15} = \frac{10 - 4}{15} = \frac{6}{15} = \frac{2}{5}
\]
This is
not an integer.
---
6. \( \frac{14}{20} + \frac{6}{20} \)
\[
\frac{14}{20} + \frac{6}{20} = \frac{14 + 6}{20} = \frac{20}{20} = 1
\]
This is an integer.
---
7. \( \frac{15}{25} - \frac{10}{25} \)
\[
\frac{15}{25} - \frac{10}{25} = \frac{15 - 10}{25} = \frac{5}{25} = \frac{1}{5}
\]
This is
not an integer.
---
8. \( \frac{18}{30} + \frac{12}{30} \)
\[
\frac{18}{30} + \frac{12}{30} = \frac{18 + 12}{30} = \frac{30}{30} = 1
\]
This is an integer.
---
9. \( \frac{21}{35} - \frac{14}{35} \)
\[
\frac{21}{35} - \frac{14}{35} = \frac{21 - 14}{35} = \frac{7}{35} = \frac{1}{5}
\]
This is
not an integer.
---
10. \( \frac{24}{40} + \frac{16}{40} \)
\[
\frac{24}{40} + \frac{16}{40} = \frac{24 + 16}{40} = \frac{40}{40} = 1
\]
This is an integer.
---
11. \( \frac{27}{54} - \frac{9}{54} \)
\[
\frac{27}{54} - \frac{9}{54} = \frac{27 - 9}{54} = \frac{18}{54} = \frac{1}{3}
\]
This is
not an integer.
---
12. \( \frac{30}{60} + \frac{30}{60} \)
\[
\frac{30}{60} + \frac{30}{60} = \frac{30 + 30}{60} = \frac{60}{60} = 1
\]
This is an integer.
---
Final Answer:
The expressions that are
not integers are:
- 3. \( \frac{8}{9} - \frac{5}{9} \)
- 4. \( \frac{11}{12} - \frac{5}{12} \)
- 5. \( \frac{10}{15} - \frac{4}{15} \)
- 7. \( \frac{15}{25} - \frac{10}{25} \)
- 9. \( \frac{21}{35} - \frac{14}{35} \)
- 11. \( \frac{27}{54} - \frac{9}{54} \)
Thus, the final answer is:
\[
\boxed{3, 4, 5, 7, 9, 11}
\]
Parent Tip: Review the logic above to help your child master the concept of solving rational equations worksheet answers.
