Respuesta :

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Answer:

[tex]\sf{5\dfrac{41}{420}[/tex]

Step-by-step explanation:

  • [tex]\sf{\dfrac{5}{7}\:+\:\dfrac{6}{9}\:+\:\dfrac{2}{3}\:+\:\dfrac{5}{4}\:+\:\dfrac{9}{5}[/tex]

adjust the fractions:

  • [tex]\sf\dfrac{300}{420}+\dfrac{560}{420}+\dfrac{525}{420}+\dfrac{756}{420}[/tex]

least common multiple of 7, 9, 3, 4, 5 is 420

  • [tex]\sf\dfrac{300+560+525+756}{420}[/tex]

join fractions together:

  • [tex]\sf{\dfrac{2141}{420}[/tex]

final answer in mixed fraction:

  • [tex]\sf{5\dfrac{41}{420}[/tex]

Solution:

Note that:

  • Given expression: [tex]\frac{5}{7} + \frac{6}{9} + \frac{2}{3} + \frac{5}{4} + \frac{9}{5}[/tex]

Finding the LCM of 7, 9, 3, 4 and 5:

Refer to table uploaded

  • LCM = 1260

Multiplying the numerators and the denominators:

  • [tex]\frac{5(180)}{7(180)} + \frac{6(140)}{9(140)} + \frac{2(420)}{3(420)} + \frac{5(315)}{4(315)} + \frac{9(252)}{5(252)}[/tex]
  • ⇒ [tex]\frac{900}{1260} + \frac{840}{1260} + \frac{840}{1260} + \frac{1575}{1260} + \frac{2268}{1260}[/tex]
  • ⇒ [tex]\frac{900}{1260} + \frac{840}{1260} + \frac{840}{1260} + \frac{1575}{1260} + \frac{2268}{1260}[/tex]
  • ⇒ [tex]\frac{6423}{1260}[/tex]

Simplifying the fraction:

  • ⇒ [tex]\frac{6423}{1260}[/tex] =  [tex]\frac{2121}{420}[/tex]

The sum of the fractions is [tex]\frac{2121}{420}[/tex].

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