Question

1. try to reduce in one step.

(1) $\frac{14}{42}=$
(2) $\frac{21}{42}=$
(3) $\frac{33}{44}=$
(4) $\frac{18}{45}=$
(5) $\frac{35}{45}=$
(6) $\frac{30}{45}=$
(7) $\frac{12}{48}=$
(8) $\frac{32}{48}=$
(9) $\frac{30}{50}=$
(10) $\frac{30}{51}=$
(11) $\frac{48}{54}=$
(12) $\frac{14}{56}=$
(13) $\frac{15}{60}=$
(14) $\frac{36}{63}=$

Explanation:

Step1: Simplify \(\frac{14}{42}\)

Find the greatest common divisor (GCD) of 14 and 42, which is 14. Divide numerator and denominator by 14: \(\frac{14\div14}{42\div14}=\frac{1}{3}\)

Step2: Simplify \(\frac{21}{42}\)

GCD of 21 and 42 is 21. Divide: \(\frac{21\div21}{42\div21}=\frac{1}{2}\)

Step3: Simplify \(\frac{33}{44}\)

GCD of 33 and 44 is 11. Divide: \(\frac{33\div11}{44\div11}=\frac{3}{4}\)

Step4: Simplify \(\frac{18}{45}\)

GCD of 18 and 45 is 9. Divide: \(\frac{18\div9}{45\div9}=\frac{2}{5}\)

Step5: Simplify \(\frac{35}{45}\)

GCD of 35 and 45 is 5. Divide: \(\frac{35\div5}{45\div5}=\frac{7}{9}\)

Step6: Simplify \(\frac{30}{45}\)

GCD of 30 and 45 is 15. Divide: \(\frac{30\div15}{45\div15}=\frac{2}{3}\)

Step7: Simplify \(\frac{12}{48}\)

GCD of 12 and 48 is 12. Divide: \(\frac{12\div12}{48\div12}=\frac{1}{4}\)

Step8: Simplify \(\frac{32}{48}\)

GCD of 32 and 48 is 16. Divide: \(\frac{32\div16}{48\div16}=\frac{2}{3}\)

Step9: Simplify \(\frac{30}{50}\)

GCD of 30 and 50 is 10. Divide: \(\frac{30\div10}{50\div10}=\frac{3}{5}\)

Step10: Simplify \(\frac{30}{51}\)

GCD of 30 and 51 is 3. Divide: \(\frac{30\div3}{51\div3}=\frac{10}{17}\)

Step11: Simplify \(\frac{48}{54}\)

GCD of 48 and 54 is 6. Divide: \(\frac{48\div6}{54\div6}=\frac{8}{9}\)

Step12: Simplify \(\frac{14}{56}\)

GCD of 14 and 56 is 14. Divide: \(\frac{14\div14}{56\div14}=\frac{1}{4}\)

Step13: Simplify \(\frac{15}{60}\)

GCD of 15 and 60 is 15. Divide: \(\frac{15\div15}{60\div15}=\frac{1}{4}\)

Step14: Simplify \(\frac{36}{63}\)

GCD of 36 and 63 is 9. Divide: \(\frac{36\div9}{63\div9}=\frac{4}{7}\)

Answer:

(1) \(\frac{1}{3}\)
(2) \(\frac{1}{2}\)
(3) \(\frac{3}{4}\)
(4) \(\frac{2}{5}\)
(5) \(\frac{7}{9}\)
(6) \(\frac{2}{3}\)
(7) \(\frac{1}{4}\)
(8) \(\frac{2}{3}\)
(9) \(\frac{3}{5}\)
(10) \(\frac{10}{17}\)
(11) \(\frac{8}{9}\)
(12) \(\frac{1}{4}\)
(13) \(\frac{1}{4}\)
(14) \(\frac{4}{7}\)