To simplify the given fractions to their lowest terms, we need to find the greatest common divisor (GCD) of the numerator and the denominator for each fraction and then divide both the numerator and the denominator by this GCD. Let's solve each fraction step by step.
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Example:
$$
\frac{10}{15} = \frac{10 \div 5}{15 \div 5} = \frac{2}{3}
$$
---
Problem 1:
$$
\frac{5}{10}
$$
- The GCD of 5 and 10 is 5.
- Divide both the numerator and the denominator by 5:
$$
\frac{5 \div 5}{10 \div 5} = \frac{1}{2}
$$
$$
\boxed{\frac{1}{2}}
$$
---
Problem 2:
$$
\frac{8}{10}
$$
- The GCD of 8 and 10 is 2.
- Divide both the numerator and the denominator by 2:
$$
\frac{8 \div 2}{10 \div 2} = \frac{4}{5}
$$
$$
\boxed{\frac{4}{5}}
$$
---
Problem 3:
$$
\frac{6}{9}
$$
- The GCD of 6 and 9 is 3.
- Divide both the numerator and the denominator by 3:
$$
\frac{6 \div 3}{9 \div 3} = \frac{2}{3}
$$
$$
\boxed{\frac{2}{3}}
$$
---
Problem 4:
$$
\frac{8}{12}
$$
- The GCD of 8 and 12 is 4.
- Divide both the numerator and the denominator by 4:
$$
\frac{8 \div 4}{12 \div 4} = \frac{2}{3}
$$
$$
\boxed{\frac{2}{3}}
$$
---
Problem 5:
$$
\frac{12}{15}
$$
- The GCD of 12 and 15 is 3.
- Divide both the numerator and the denominator by 3:
$$
\frac{12 \div 3}{15 \div 3} = \frac{4}{5}
$$
$$
\boxed{\frac{4}{5}}
$$
---
Problem 6:
$$
\frac{5}{15}
$$
- The GCD of 5 and 15 is 5.
- Divide both the numerator and the denominator by 5:
$$
\frac{5 \div 5}{15 \div 5} = \frac{1}{3}
$$
$$
\boxed{\frac{1}{3}}
$$
---
Problem 7:
$$
\frac{9}{18}
$$
- The GCD of 9 and 18 is 9.
- Divide both the numerator and the denominator by 9:
$$
\frac{9 \div 9}{18 \div 9} = \frac{1}{2}
$$
$$
\boxed{\frac{1}{2}}
$$
---
Problem 8:
$$
\frac{14}{21}
$$
- The GCD of 14 and 21 is 7.
- Divide both the numerator and the denominator by 7:
$$
\frac{14 \div 7}{21 \div 7} = \frac{2}{3}
$$
$$
\boxed{\frac{2}{3}}
$$
---
Problem 9:
$$
\frac{12}{18}
$$
- The GCD of 12 and 18 is 6.
- Divide both the numerator and the denominator by 6:
$$
\frac{12 \div 6}{18 \div 6} = \frac{2}{3}
$$
$$
\boxed{\frac{2}{3}}
$$
---
Final Answers:
1. $\boxed{\frac{1}{2}}$
2. $\boxed{\frac{4}{5}}$
3. $\boxed{\frac{2}{3}}$
4. $\boxed{\frac{2}{3}}$
5. $\boxed{\frac{4}{5}}$
6. $\boxed{\frac{1}{3}}$
7. $\boxed{\frac{1}{2}}$
8. $\boxed{\frac{2}{3}}$
9. $\boxed{\frac{2}{3}}$
---
Thus, the final boxed answers are:
$$
\boxed{\frac{1}{2}, \frac{4}{5}, \frac{2}{3}, \frac{2}{3}, \frac{4}{5}, \frac{1}{3}, \frac{1}{2}, \frac{2}{3}, \frac{2}{3}}
$$
Parent Tip: Review the logic above to help your child master the concept of reducing fractions worksheet and answer keys.
