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Kryger [21]
3 years ago
15

1 2/3 - 1 3/7 ÷(1/2+4/7)

Mathematics
1 answer:
Lina20 [59]3 years ago
7 0

Answer:

\boxed {\frac{1}{3}}

Step-by-step explanation:

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

\boxed {\sf Convert \:mixed \:numbers\: to\: improper\: fractions:}

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

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

\boxed {\sf 1)\: Parentheses:}

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

\boxed {\sf 2)\: Multiplication/Division}

  • \cfrac{10}{7}\div \cfrac{15}{14}

Apply Fraction rule:

  • \cfrac{10}{7}\times \cfrac{14}{15}
  • \cfrac{10\times \:14}{7\times \:15}
  • =\cfrac{140}{105}

Common factor of 140 and 105: 35

  • =\cfrac{4}{3}
  • \cfrac{5}{3}-\cfrac{4}{3}

\boxed{\sf 3)\: Addition/Subtraction}

  • \cfrac{1}{3}

___________________________

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