\[6\frac{4}{5}-(1\frac{2}{3}+3\frac{4}{5})\]
1
Convert 6456\frac{4}{5} to improper fraction. Use this rule: abc=ac+bca \frac{b}{c}=\frac{ac+b}{c}.
6×5+45−(123+345)\frac{6\times 5+4}{5}-(1\frac{2}{3}+3\frac{4}{5})

2
Simplify  6×56\times 5  to  3030.
30+45−(123+345)\frac{30+4}{5}-(1\frac{2}{3}+3\frac{4}{5})

3
Simplify  30+430+4  to  3434.
345−(123+345)\frac{34}{5}-(1\frac{2}{3}+3\frac{4}{5})

4
Add the whole numbers first.
4+23+454+\frac{2}{3}+\frac{4}{5}

5
Find the Least Common Denominator (LCD) of 23,45\frac{2}{3},\frac{4}{5}. In other words, find the Least Common Multiple (LCM) of 3,53,5.
LCD = 1515

6
Make the denominators the same as the LCD.
4+2×53×5+4×35×34+\frac{2\times 5}{3\times 5}+\frac{4\times 3}{5\times 3}

7
Simplify. Denominators are now the same.
4+1015+12154+\frac{10}{15}+\frac{12}{15}

8
Join the denominators.
4+10+12154+\frac{10+12}{15}

9
Simplify.
4+22154+\frac{22}{15}

10
Convert 2215\frac{22}{15} to mixed fraction.
4+17154+1\frac{7}{15}

11
Simplify  1+23+3+451+\frac{2}{3}+3+\frac{4}{5}  to  57155\frac{7}{15}.
345−5715\frac{34}{5}-5\frac{7}{15}

12
Convert 57155\frac{7}{15} to improper fraction. Use this rule: abc=ac+bca \frac{b}{c}=\frac{ac+b}{c}.
345−5×15+715\frac{34}{5}-\frac{5\times 15+7}{15}

13
Simplify  5×155\times 15  to  7575.
345−75+715\frac{34}{5}-\frac{75+7}{15}

14
Simplify  75+775+7  to  8282.
345−8215\frac{34}{5}-\frac{82}{15}

15
Find the Least Common Denominator (LCD) of 345,8215\frac{34}{5},\frac{82}{15}. In other words, find the Least Common Multiple (LCM) of 5,155,15.
LCD = 1515

16
Make the denominators the same as the LCD.
34×35×3−8215\frac{34\times 3}{5\times 3}-\frac{82}{15}

17
Simplify. Denominators are now the same.
10215−8215\frac{102}{15}-\frac{82}{15}

18
Join the denominators.
102−8215\frac{102-82}{15}

19
Simplify.
2015\frac{20}{15}

20
Simplify.
43\frac{4}{3}

21
Convert to mixed fraction.
1131\frac{1}{3}

Done

Decimal Form: 1.333333
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