25/138
Step-by-step explanation:
1 Convert 4\frac{3}{5}4
5
3
Β 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})
β(
5
4Γ5+3
)
1
(β
6
2
β
4
2
)
2 Simplify Β 4\times 54Γ5 Β to Β 2020.
\frac{1}{-(\frac{20+3}{5})}(-\frac{2}{6}-\frac{2}{4})
β(
5
20+3
)
1
(β
6
2
β
4
2
)
3 Simplify Β 20+320+3 Β to Β 2323.
\frac{1}{-(\frac{23}{5})}(-\frac{2}{6}-\frac{2}{4})
β(
5
23
)
1
(β
6
2
β
4
2
)
4 Simplify Β \frac{2}{6}
6
2
Β to Β \frac{1}{3}
3
1
.
\frac{1}{-(\frac{23}{5})}(-\frac{1}{3}-\frac{2}{4})
β(
5
23
)
1
(β
3
1
β
4
2
)
5 Simplify Β \frac{2}{4}
4
2
Β to Β \frac{1}{2}
2
1
.
\frac{1}{-(\frac{23}{5})}(-\frac{1}{3}-\frac{1}{2})
β(
5
23
)
1
(β
3
1
β
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}β
3Γ2
1Γ2
β
2Γ3
1Γ3
8 Simplify. Denominators are now the same.
-\frac{2}{6}-\frac{3}{6}β
6
2
β
6
3
9 Join the denominators.
\frac{-2-3}{6}
6
β2β3
10 Simplify Β -\frac{1}{3}-\frac{1}{2}β
3
1
β
2
1
Β to Β -\frac{5}{6}β
6
5
.
\frac{1}{-(\frac{23}{5})}\times \frac{-5}{6}
β(
5
23
)
1
Γ
6
β5
11 Move the negative sign to the left.
-\frac{1}{\frac{23}{5}}\times \frac{-5}{6}β
5
23
1
Γ
6
β5
12 Invert and multiply.
-\frac{5}{23}\times \frac{-5}{6}β
23
5
Γ
6
β5
13 Use this rule: \frac{a}{b} \times \frac{c}{d}=\frac{ac}{bd}
b
a
Γ
d
c
=
bd
ac
.
-\frac{5\times -5}{23\times 6}β
23Γ6
5Γβ5
14 Simplify Β 5\times -55Γβ5 Β to Β -25β25.
-\frac{-25}{23\times 6}β
23Γ6
β25
15 Simplify Β 23\times 623Γ6 Β to Β 138138.
-\frac{-25}{138}β
138
β25
16 Move the negative sign to the left.
-(-\frac{25}{138})β(β
138
25
)
17 Remove parentheses.
\frac{25}{138}
138
25