Question

Simplify $5\frac{1}{2} + 6\frac{1}{2} - 8\frac{1}{4} + 24 - [9 - \{6 - (10 - \overline{4 - 3})\}]$.

• A. $12\frac{1}{4}$
• B. $12\frac{3}{4}$
• C. $15\frac{1}{4}$
• D. $15\frac{3}{4}$

Answer 1

Answer:

$15\frac{3}{4}$

The simplified value of the expression is $15\frac{3}{4}$ (or $15.75$).

Follow the VBODMAS rule, which stands for Vinculum (Bar), Brackets (Innermost first), Of, Division, Multiplication, Addition, Subtraction.

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Step 1: Simplify the Brackets (from inside out)

1. Solve the Vinculum (Bar bracket):
   $\overline{4 - 3} = 1$

2. Solve the Parentheses ( ):
   $(10 - 1) = 9$

3. Solve the Curly Braces { }:
   $\{6 - 9\} = -3$

4. Solve the Square Brackets [ ]:
   $[9 - (-3)] = 9 + 3 = 12$

Now substitute this back into the main expression:
$5\frac{1}{2} + 6\frac{1}{2} - 8\frac{1}{4} + 24 - 12$

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Step 2: Simplify the Remaining Expression

1. Combine the simple whole numbers first:
   $24 - 12 = 12$

2. Add the first two mixed fractions:
   $5\frac{1}{2} + 6\frac{1}{2} = 12$

3. Put it all together:
   $12 - 8\frac{1}{4} + 12$
   $= 24 - 8\frac{1}{4}$
   $= 15\frac{3}{4}$