Answer:
25/138
Explanation:
1 Convert 4\frac{3}{5}4
5
3
to improper fraction. Use this rule: a \frac{b}{c}=\frac{ac+b}{c}a
c
b
=
c
ac+b
.
\frac{1}{-(\frac{4\times 5+3}{5})}(-\frac{2}{6}-\frac{2}{4})
−(
5
4×5+3
)
1
(−
6
2
−
4
2
)
2 Simplify 4\times 54×5 to 2020.
\frac{1}{-(\frac{20+3}{5})}(-\frac{2}{6}-\frac{2}{4})
−(
5
20+3
)
1
(−
6
2
−
4
2
)
3 Simplify 20+320+3 to 2323.
\frac{1}{-(\frac{23}{5})}(-\frac{2}{6}-\frac{2}{4})
−(
5
23
)
1
(−
6
2
−
4
2
)
4 Simplify \frac{2}{6}
6
2
to \frac{1}{3}
3
1
.
\frac{1}{-(\frac{23}{5})}(-\frac{1}{3}-\frac{2}{4})
−(
5
23
)
1
(−
3
1
−
4
2
)
5 Simplify \frac{2}{4}
4
2
to \frac{1}{2}
2
1
.
\frac{1}{-(\frac{23}{5})}(-\frac{1}{3}-\frac{1}{2})
−(
5
23
)
1
(−
3
1
−
2
1
)
6 Find the Least Common Denominator (LCD) of \frac{1}{3},\frac{1}{2}
3
1
,
2
1
. In other words, find the Least Common Multiple (LCM) of 3,23,2.
LCD = 66
7 Make the denominators the same as the LCD.
-\frac{1\times 2}{3\times 2}-\frac{1\times 3}{2\times 3}−
3×2
1×2
−
2×3
1×3
8 Simplify. Denominators are now the same.
-\frac{2}{6}-\frac{3}{6}−
6
2
−
6
3
9 Join the denominators.
\frac{-2-3}{6}
6
−2−3
10 Simplify -\frac{1}{3}-\frac{1}{2}−
3
1
−
2
1
to -\frac{5}{6}−
6
5
.
\frac{1}{-(\frac{23}{5})}\times \frac{-5}{6}
−(
5
23
)
1
×
6
−5
11 Move the negative sign to the left.
-\frac{1}{\frac{23}{5}}\times \frac{-5}{6}−
5
23
1
×
6
−5
12 Invert and multiply.
-\frac{5}{23}\times \frac{-5}{6}−
23
5
×
6
−5
13 Use this rule: \frac{a}{b} \times \frac{c}{d}=\frac{ac}{bd}
b
a
×
d
c
=
bd
ac
.
-\frac{5\times -5}{23\times 6}−
23×6
5×−5
14 Simplify 5\times -55×−5 to -25−25.
-\frac{-25}{23\times 6}−
23×6
−25
15 Simplify 23\times 623×6 to 138138.
-\frac{-25}{138}−
138
−25
16 Move the negative sign to the left.
-(-\frac{25}{138})−(−
138
25
)
17 Remove parentheses.
\frac{25}{138}
138
25