Evaluate:
(1/2)-2
+(1/3)-2
+(1/4)-2
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Solution.)
The question is - ( 1 / 2 ) - 2 + ( 1 / 3 ) - 2 + ( 1 / 4 ) - 2
= we will solve the first part of the question -
( 1 / 2 ) - 2
= ( 1 / 2 ) - ( 2 / 1 )
= lcm = 2
1 / 2 - 2 * 2 / 2 * 1
1 / 2 - 4 / 2
= -3 / 2
Next , we will solve the second part -
= -3 / 2 + ( 1/3 - 2)
= - 3 / 2 + lcm = 6 ( 1 * 2 / 3 * 2 - 2 * 6 / 1 * 6 )
= - 3 / 2 + 2 / 6 - 12 / 6
= -3 / 2 + -10 / 6
= lcm = 6 , -3 * 3 / 2 * 3 + -10 / 6
= -9 / 6 + -10 / 6
= - 19 / 6
= - 19 / 6 + ( 1 / 4 + 2 )
= -19 / 6 + lcm = 4, 1 / 4 - 2 * 4 / 1 * 4
= -19 / 6 + - 7 / 4
= lcm = 24
= - 19 * 4 / 6 * 4 + -7 * 6 + 4 * 6
= - 76 / 24 + -42 / 24
= -76 + -42 / 24
= - 118 / 24
= bring it to lowest form =
= -59 / 12
= 11
4
12
The question is - ( 1 / 2 ) - 2 + ( 1 / 3 ) - 2 + ( 1 / 4 ) - 2
= we will solve the first part of the question -
( 1 / 2 ) - 2
= ( 1 / 2 ) - ( 2 / 1 )
= lcm = 2
1 / 2 - 2 * 2 / 2 * 1
1 / 2 - 4 / 2
= -3 / 2
Next , we will solve the second part -
= -3 / 2 + ( 1/3 - 2)
= - 3 / 2 + lcm = 6 ( 1 * 2 / 3 * 2 - 2 * 6 / 1 * 6 )
= - 3 / 2 + 2 / 6 - 12 / 6
= -3 / 2 + -10 / 6
= lcm = 6 , -3 * 3 / 2 * 3 + -10 / 6
= -9 / 6 + -10 / 6
= - 19 / 6
= - 19 / 6 + ( 1 / 4 + 2 )
= -19 / 6 + lcm = 4, 1 / 4 - 2 * 4 / 1 * 4
= -19 / 6 + - 7 / 4
= lcm = 24
= - 19 * 4 / 6 * 4 + -7 * 6 + 4 * 6
= - 76 / 24 + -42 / 24
= -76 + -42 / 24
= - 118 / 24
= bring it to lowest form =
= -59 / 12
= 11
4
12
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