\[8\frac{2}{7}-(3\frac{4}{9}+4\frac{2}{7})\]
1
Convert 8278\frac{2}{7} to improper fraction. Use this rule: abc=ac+bca \frac{b}{c}=\frac{ac+b}{c}.
8×7+27−(349+427)\frac{8\times 7+2}{7}-(3\frac{4}{9}+4\frac{2}{7})

2
Simplify  8×78\times 7  to  5656.
56+27−(349+427)\frac{56+2}{7}-(3\frac{4}{9}+4\frac{2}{7})

3
Simplify  56+256+2  to  5858.
587−(349+427)\frac{58}{7}-(3\frac{4}{9}+4\frac{2}{7})

4
Add the whole numbers first.
7+49+277+\frac{4}{9}+\frac{2}{7}

5
Find the Least Common Denominator (LCD) of 49,27\frac{4}{9},\frac{2}{7}. In other words, find the Least Common Multiple (LCM) of 9,79,7.
LCD = 6363

6
Make the denominators the same as the LCD.
7+4×79×7+2×97×97+\frac{4\times 7}{9\times 7}+\frac{2\times 9}{7\times 9}

7
Simplify. Denominators are now the same.
7+2863+18637+\frac{28}{63}+\frac{18}{63}

8
Join the denominators.
7+28+18637+\frac{28+18}{63}

9
Simplify  3+49+4+273+\frac{4}{9}+4+\frac{2}{7}  to  746637\frac{46}{63}.
587−74663\frac{58}{7}-7\frac{46}{63}

10
Convert 746637\frac{46}{63} to improper fraction. Use this rule: abc=ac+bca \frac{b}{c}=\frac{ac+b}{c}.
587−7×63+4663\frac{58}{7}-\frac{7\times 63+46}{63}

11
Simplify  7×637\times 63  to  441441.
587−441+4663\frac{58}{7}-\frac{441+46}{63}

12
Simplify  441+46441+46  to  487487.
587−48763\frac{58}{7}-\frac{487}{63}

13
Find the Least Common Denominator (LCD) of 587,48763\frac{58}{7},\frac{487}{63}. In other words, find the Least Common Multiple (LCM) of 7,637,63.
LCD = 6363

14
Make the denominators the same as the LCD.
58×97×9−48763\frac{58\times 9}{7\times 9}-\frac{487}{63}

15
Simplify. Denominators are now the same.
52263−48763\frac{522}{63}-\frac{487}{63}

16
Join the denominators.
522−48763\frac{522-487}{63}

17
Simplify.
3563\frac{35}{63}

18
Simplify.
59\frac{5}{9}

Done

Decimal Form: 0.555556
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