Problem Description:
The task involves simplifying basic arithmetic expressions and performing division operations. The goal is to solve each problem step by step, showing all work.
Solution:
####
Part 1: Computation
1.
Problem 1: \( \frac{7}{6} \)
- This is already in its simplest form as a fraction.
-
Answer: \( \frac{7}{6} \)
2.
Problem 2: \( \frac{18}{4} \)
- Simplify the fraction by dividing both the numerator and denominator by their greatest common divisor (GCD), which is 2.
- \( \frac{18 \div 2}{4 \div 2} = \frac{9}{2} \)
-
Answer: \( \frac{9}{2} \)
3.
Problem 3: \( \frac{195}{234} \)
- Find the GCD of 195 and 234. The GCD is 39.
- Simplify the fraction: \( \frac{195 \div 39}{234 \div 39} = \frac{5}{6} \)
-
Answer: \( \frac{5}{6} \)
4.
Problem 4: \( \frac{9}{4} \)
- This is already in its simplest form as a fraction.
-
Answer: \( \frac{9}{4} \)
5.
Problem 5: \( \frac{24}{1} \)
- Any number divided by 1 remains the same.
-
Answer: \( 24 \)
6.
Problem 6: \( \frac{198}{33} \)
- Find the GCD of 198 and 33. The GCD is 33.
- Simplify the fraction: \( \frac{198 \div 33}{33 \div 33} = \frac{6}{1} = 6 \)
-
Answer: \( 6 \)
7.
Problem 7: \( \frac{8}{6} \)
- Simplify the fraction by dividing both the numerator and denominator by their GCD, which is 2.
- \( \frac{8 \div 2}{6 \div 2} = \frac{4}{3} \)
-
Answer: \( \frac{4}{3} \)
8.
Problem 8: \( \frac{15}{4} \)
- This is already in its simplest form as a fraction.
-
Answer: \( \frac{15}{4} \)
9.
Problem 9: \( \frac{138}{72} \)
- Find the GCD of 138 and 72. The GCD is 6.
- Simplify the fraction: \( \frac{138 \div 6}{72 \div 6} = \frac{23}{12} \)
-
Answer: \( \frac{23}{12} \)
10.
Problem 10: \( 72 \div 9 \)
- Perform the division: \( 72 \div 9 = 8 \)
-
Answer: \( 8 \)
11.
Problem 11: \( 126 \div 3 \)
- Perform the division: \( 126 \div 3 = 42 \)
-
Answer: \( 42 \)
12.
Problem 12: \( 4137 \div 17 \)
- Perform the division:
- \( 4137 \div 17 = 243 \) (since \( 17 \times 243 = 4131 \) and the remainder is 6)
-
Answer: \( 243 \) (with a remainder of 6, but typically only the quotient is asked for in such problems unless specified otherwise)
Final Answers:
1. \( \boxed{\frac{7}{6}} \)
2. \( \boxed{\frac{9}{2}} \)
3. \( \boxed{\frac{5}{6}} \)
4. \( \boxed{\frac{9}{4}} \)
5. \( \boxed{24} \)
6. \( \boxed{6} \)
7. \( \boxed{\frac{4}{3}} \)
8. \( \boxed{\frac{15}{4}} \)
9. \( \boxed{\frac{23}{12}} \)
10. \( \boxed{8} \)
11. \( \boxed{42} \)
12. \( \boxed{243} \)
Boxed Final Answer:
\[
\boxed{
\begin{array}{ccc}
1. & \frac{7}{6} & 2. & \frac{9}{2} & 3. & \frac{5}{6} \\
4. & \frac{9}{4} & 5. & 24 & 6. & 6 \\
7. & \frac{4}{3} & 8. & \frac{15}{4} & 9. & \frac{23}{12} \\
10. & 8 & 11. & 42 & 12. & 243 \\
\end{array}
}
\]
Parent Tip: Review the logic above to help your child master the concept of basic skill math worksheet.
