Simplify this expression: $[(6 - \frac{3}{5}) \times (\frac{1}{4} + \frac{2}{9} - \frac{5}{12}) + \frac{3}{2} \times (\frac{9}{2} - \frac{7}{4} - \frac{5}{2})] \times \frac{2}{27} + \frac{1}{4}$ $[(6-3/5)xx(1/4+2/9-5/12)+3/2xx(9/2-7/4-5/2)]xx2/27+1/4$ ?

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Simplify this expression: $[(6 - \frac{3}{5}) \times (\frac{1}{4} + \frac{2}{9} - \frac{5}{12}) + \frac{3}{2} \times (\frac{9}{2} - \frac{7}{4} - \frac{5}{2})] \times \frac{2}{27} + \frac{1}{4}$ $[(6-3/5)xx(1/4+2/9-5/12)+3/2xx(9/2-7/4-5/2)]xx2/27+1/4$ ?

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Answer 1 · 2018-03-09T18:24:57

$= \frac{3}{10}$ $= 3/10$

Explanation:

Step 1:

Resolve:
$a . (6 - \frac{3}{5}) = \frac{27}{5}$ $a. (6-3/5) = 27/5$

$b . (\frac{1}{4} + \frac{2}{9} - \frac{5}{12}) = \frac{1}{18}$ $b. (1/4+ 2/9 -5/12) = 1/18$

$c . (\frac{9}{2} - \frac{7}{4} - \frac{5}{2}) = \frac{1}{4}$ $c. (9/2 -7/4-5/2) = 1/4$

Step 2:

multiply

#a.(27/5) * (1/18) = 3/10#

$b . (\frac{3}{2}) \cdot (\frac{1}{4}) = \frac{3}{8}$ $b. (3/2) * (1/4) = 3/8$

Step 3:

We add the product

$a . (\frac{3}{10}) + (\frac{3}{8}) = \frac{27}{40}$ $a. (3/10)+(3/8) = 27/40$

Step 4:

multiply

$a . [\frac{27}{40}] \cdot (\frac{2}{27}) = \frac{1}{20}$ $a. [27/40] * (2/27) = 1/20$

Step 5:

We add the product (again :v)

$a . \frac{1}{20} + \frac{1}{4} = \frac{3}{10}$ $a. 1/20 + 1/4 = 3/10$

The summary is:

$= [(\frac{27}{5}) \cdot (\frac{1}{18}) + (\frac{3}{2}) \cdot (\frac{1}{4})] \cdot (\frac{2}{27}) + \frac{1}{4}$ $= [(27/5) * (1/18)+(3/2) * (1/4)] * (2/27) + 1/4$

$= [(\frac{3}{10}) + (\frac{3}{8})] \cdot (\frac{2}{27}) + \frac{1}{4}$ $= [(3/10)+(3/8)] * (2/27) + 1/4$

$= [\frac{27}{40}] \cdot (\frac{2}{27}) + \frac{1}{4}$ $= [27/40] * (2/27) + 1/4$

$= [cancel(27)/cancel(40)] * (cancel(2)/cancel(27)) + 1/4$

$= 1/20 + 1/4$

$= 3/10$

Answer 2 · 2018-03-09T18:55:41

$3/10$

Explanation:

Identify the individual terms and then simplify them separately

$color(blue)([(6-3/5)xx(1/4+2/9-5/12) +3/2xx(9/2-7/4-5/2)]xx2/27) color(red)(" "+" "1/4)$

Within the first term, shown in blue, simplify each bracket separately.

$=color(blue)([(5 2/5)xx((9+8-15)/36) +3/2xx((18-7 -10)/4)]xx2/27) color(red)(" "+" "1/4)$

$=color(blue)([color(green)((27/5)xx((2)/36)) color(limegreen)(+3/2xx((1)/4))]xx2/27) color(red)(" "+" "1/4)$

Now cancel where possible

$=color(blue)([color(green)(cancel27^3/5xx1/cancel18^2)color(limegreen)( " "+" "3/2xx1/4)]xx2/27) color(red)(" "+" "1/4)$

Multiply straight across to get:

$=color(blue)([ color(green)(3/10)color(limegreen)(+3/8)]xx2/27) color(red)(" "+" "1/4)$

$=color(blue)([(color(green)(12)color(limegreen)(+15))/40]xx2/27) color(red)(" "+" "1/4)$

$=color(blue)(27/40xx2/27) color(red)(" "+" "1/4)$

$=color(blue)(cancel27/cancel40^20xxcancel2/cancel27) color(red)(" "+" "1/4)$

$=color(blue)(1/20) color(red)(" "+" "1/4)$

Now add the two terms together,

$=(color(blue)(1)color(red)(+5))/20$

$=6/20$

$=3/10$

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Simplify this expression: $[(6 - \frac{3}{5}) \times (\frac{1}{4} + \frac{2}{9} - \frac{5}{12}) + \frac{3}{2} \times (\frac{9}{2} - \frac{7}{4} - \frac{5}{2})] \times \frac{2}{27} + \frac{1}{4}$ $[(6-3/5)xx(1/4+2/9-5/12)+3/2xx(9/2-7/4-5/2)]xx2/27+1/4$ ?

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Explanation:

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Simplify this expression: $[(6 - \frac{3}{5}) \times (\frac{1}{4} + \frac{2}{9} - \frac{5}{12}) + \frac{3}{2} \times (\frac{9}{2} - \frac{7}{4} - \frac{5}{2})] \times \frac{2}{27} + \frac{1}{4}$ $[(6-3/5)xx(1/4+2/9-5/12)+3/2xx(9/2-7/4-5/2)]xx2/27+1/4$ ?