The expression
6
5−[
4
3
+{2
2
1
−(
2
1
+
6
1
−
7
1
)}]
equals:
- A\frac{13}{56}
- B\frac{97}{168}
- C\frac{191}{504}
- D\frac{19}{54}
Solution & Step-by-step Explanation
Let's simplify the expression using the BODMAS rule step-by-step.
The given expression is:
6
5−[
4
3
+{2
2
1
−(
2
1
+
6
1
−
7
1
)}]
Step 1: Simplify the innermost parentheses (
2
1
+
6
1
−
7
1
)
The LCM of 2,6, and 7 is 42.
2
1
+
6
1
−
7
1
=
42
21+7−6
=
42
22
=
21
11
Step 2: Simplify the curly braces {2
2
1
−
21
11
}
Convert the mixed fraction 2
2
1
=
2
5
.
{
2
5
−
21
11
}
The LCM of 2 and 21 is 42.
42
5×21−11×2
=
42
105−22
=
42
83
Step 3: Simplify the square brackets [
4
3
+
42
83
]
The LCM of 4 and 42 is 84.
84
3×21+83×2
=
84
63+166
=
84
229
Step 4: Solve the numerator 5−
84
229
5−
84
229
=
84
5×84−229
=
84
420−229
=
84
191
Step 5: Divide by the denominator 6
Final Value=
6
84
191
=
84×6
191
=
504
191
The given expression is:
6
5−[
4
3
+{2
2
1
−(
2
1
+
6
1
−
7
1
)}]
Step 1: Simplify the innermost parentheses (
2
1
+
6
1
−
7
1
)
The LCM of 2,6, and 7 is 42.
2
1
+
6
1
−
7
1
=
42
21+7−6
=
42
22
=
21
11
Step 2: Simplify the curly braces {2
2
1
−
21
11
}
Convert the mixed fraction 2
2
1
=
2
5
.
{
2
5
−
21
11
}
The LCM of 2 and 21 is 42.
42
5×21−11×2
=
42
105−22
=
42
83
Step 3: Simplify the square brackets [
4
3
+
42
83
]
The LCM of 4 and 42 is 84.
84
3×21+83×2
=
84
63+166
=
84
229
Step 4: Solve the numerator 5−
84
229
5−
84
229
=
84
5×84−229
=
84
420−229
=
84
191
Step 5: Divide by the denominator 6
Final Value=
6
84
191
=
84×6
191
=
504
191