Question

1. try to reduce in one step.

(1) $\frac{13}{26}=\frac{1}{2}$ (8) $\frac{13}{65}=$
(2) $\frac{17}{34}=\frac{1}{2}$ (9) $\frac{39}{65}=$
(3) $\frac{26}{39}=\frac{2}{3}$ (10) $\frac{34}{68}=$
(4) $\frac{17}{51}=\frac{1}{3}$ (11) $\frac{48}{72}=$
(5) $\frac{39}{52}=\frac{3}{4}$ (12) $\frac{38}{76}=$
(6) $\frac{42}{56}=$ (13) $\frac{17}{85}=$
(7) $\frac{19}{57}=$ (14) $\frac{51}{85}=$

Explanation:

Step1: Simplify \(\frac{13}{65}\)

Find the greatest common divisor (GCD) of 13 and 65. The GCD of 13 and 65 is 13. Divide both the numerator and the denominator by 13: \(\frac{13\div13}{65\div13}=\frac{1}{5}\)

Step2: Simplify \(\frac{39}{65}\)

The GCD of 39 and 65 is 13. Divide both by 13: \(\frac{39\div13}{65\div13}=\frac{3}{5}\)

Step3: Simplify \(\frac{34}{68}\)

The GCD of 34 and 68 is 34. Divide both by 34: \(\frac{34\div34}{68\div34}=\frac{1}{2}\)

Step4: Simplify \(\frac{48}{72}\)

The GCD of 48 and 72 is 24. Divide both by 24: \(\frac{48\div24}{72\div24}=\frac{2}{3}\)

Step5: Simplify \(\frac{38}{76}\)

The GCD of 38 and 76 is 38. Divide both by 38: \(\frac{38\div38}{76\div38}=\frac{1}{2}\)

Step6: Simplify \(\frac{17}{85}\)

The GCD of 17 and 85 is 17. Divide both by 17: \(\frac{17\div17}{85\div17}=\frac{1}{5}\)

Step7: Simplify \(\frac{51}{85}\)

The GCD of 51 and 85 is 17. Divide both by 17: \(\frac{51\div17}{85\div17}=\frac{3}{5}\)

Step8: Simplify \(\frac{42}{56}\)

The GCD of 42 and 56 is 14. Divide both by 14: \(\frac{42\div14}{56\div14}=\frac{3}{4}\)

Step9: Simplify \(\frac{19}{57}\)

The GCD of 19 and 57 is 19. Divide both by 19: \(\frac{19\div19}{57\div19}=\frac{1}{3}\)

Answer:

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