Respuesta :

Answer:

[tex]\boxed {\frac{1}{3}}[/tex]

Step-by-step explanation:

[tex]1\cfrac{2}{3}-1\cfrac{3}{7}\div \left(\cfrac{1}{2}+\cfrac{4}{7}\right)[/tex]

[tex]\boxed {\sf Convert \:mixed \:numbers\: to\: improper\: fractions:}[/tex]

  • [tex]1\cfrac{2}{3}=\cfrac{1\times 3+2}{3}=\cfrac{5}{3}[/tex]
  • [tex]1\cfrac{3}{7}=\cfrac{1\times 7+3}{7}=\cfrac{10}{7}[/tex]
  • [tex]\cfrac{5}{3}-\cfrac{10}{7}\div \left(\cfrac{1}{2}+\cfrac{4}{7}\right)[/tex]

Now, we'll follow the PEMDAS order of operations:

[tex]\boxed {\sf 1)\: Parentheses:}[/tex]

  • [tex]\left(\cfrac{1}{2}+\cfrac{4}{7}\right)[/tex]
  • [tex]\cfrac{1}{2}+\cfrac{4}{7}[/tex]
  • [tex]=\cfrac{15}{14}[/tex]
  • [tex]\cfrac{5}{3}-\cfrac{10}{7}\div \cfrac{15}{14}[/tex]

[tex]\boxed {\sf 2)\: Multiplication/Division}[/tex]

  • [tex]\cfrac{10}{7}\div \cfrac{15}{14}[/tex]

Apply Fraction rule:

  • [tex]\cfrac{10}{7}\times \cfrac{14}{15}[/tex]
  • [tex]\cfrac{10\times \:14}{7\times \:15}[/tex]
  • [tex]=\cfrac{140}{105}[/tex]

Common factor of 140 and 105: 35

  • [tex]=\cfrac{4}{3}[/tex]
  • [tex]\cfrac{5}{3}-\cfrac{4}{3}[/tex]

[tex]\boxed{\sf 3)\: Addition/Subtraction}[/tex]

  • [tex]\cfrac{1}{3}[/tex]

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