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What is the least common denominator of 1/3 and 4/7?

Sagot :

MrIvanidn

[tex] \red{•••••••••••••••••••••••••••••••••••••••••••••••••}[/tex]

QUESTION:

What is the least common denominator of 1/3 and 4/7?

[tex]\red{•••••••••••••••••••••••••••••••••••••••••••••••••}[/tex]

FORMULA:

∵Find the Least Common Denominator

  • [tex] \boxed{LCD=21} \\ [/tex]

∵Hint Put The Fractions In [tex] \frac{1}{3} + \frac{4}{7} \\ [/tex]

  • [tex] \frac{1}{3} + \frac{4}{7} = \frac{7}{21} + \frac{3 \times 4}{21} = \green{ \frac{7}{21} + \frac{3 \times 4}{21} } \\ [/tex]

∵Decimal approximation

0.904761904761904761904761904761904761

9047619047619047619047619047619047619

04761904761904761904761904761904761904

76190476190476190476190476190476190476

19047619047619047619047619047619047619

04761904761904761904761904761904761904

∵Reapeating Decimal

  • [tex] \purple{ 0.904761(period \: 6)}[/tex]

∵Egyptian Fraction Expansion

  • [tex] \frac{1}{2} + \frac{1}{3} + \frac{1}{14} \\ [/tex]

∵Occurrence in convergents

  • [tex] \frac{e}{3} ≈0,1. \frac{9}{10} . \frac{10}{11} .( \frac{19}{21} ). \frac{29}{32} . \frac{164}{181} \\ [/tex]

The Result:

  • [tex] \boxed{ \purple{\frac{19}{21}} }[/tex]

[tex] \red{•••••••••••••••••••••••••••••••••••••••••••••••}[/tex]

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