Question

1 2/3 - 1 3/7 ÷(1/2+4/7)

Answer 1

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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