Step 1: Evaluate the Numerator
First, calculate the numerator using the order of operations (PEMDAS/BODMAS): Division and Multiplication from left to right, then Subtraction.
- Division: $32 \div 4 = 8$
- Multiplication: $5 \times 8 = 40$
- Division: $40 \div 3 = \frac{40}{3}$
- Numerator calculation: $8 - \frac{40}{3}$
- Find a common denominator: $\frac{8 \times 3}{3} - \frac{40}{3} = \frac{24}{3} - \frac{40}{3}$
- Subtract: $\frac{24 - 40}{3} = -\frac{16}{3}$
The value of the numerator is $-\frac{16}{3}$.
Step 2: Evaluate the Denominator
Next, calculate the denominator, again following the order of operations (PEMDAS/BODMAS): Parentheses/Brackets first, then Multiplication, then Subtraction.
- Parentheses/Brackets: $\{6 + 3\} = 9$
- Multiplication: $5 \times 3 = 15$
- Denominator calculation: $15 - 9 = 6$
The value of the denominator is $6$.
Step 3: Calculate the Final Fraction
Divide the value of the numerator by the value of the denominator.
- Fraction: $\frac{\text{Numerator}}{\text{Denominator}} = \frac{-\frac{16}{3}}{6}$
- Simplify the complex fraction: $-\frac{16}{3} \div 6 = -\frac{16}{3 \times 6}$
- Calculate: $-\frac{16}{18}$
Step 4: Simplify the Result
Simplify the fraction $-\frac{16}{18}$ by dividing both the numerator and the denominator by their greatest common divisor, which is 2.
- Simplified fraction: $-\frac{16 \div 2}{18 \div 2} = -\frac{8}{9}$
The final value of the expression is $-\frac{8}{9}$.
Similar Questions
What will the value of the following expression be?
$\left(\frac{6+3}{3}\right) - 5 \times (4+5)$
- What is the value of the following expression?
$\frac{\sqrt{225}}{14} \times \frac{\sqrt{196}}{22} \times \frac{\sqrt{484}}{15}$ - The value of $\frac{(5.4)^3 - 0.064}{(5.4)^2 + 2.16 + 0.16}$ is:
- The value of $\sqrt{10 + \sqrt{221 + \sqrt{12 + \sqrt{16}}}}$ is:
- Solve the following.
$(1 + \frac{1}{x})(1 + \frac{1}{x+1})(1 + \frac{1}{x+2})(1 + \frac{1}{x+3}) = ?$ - The value of $\sqrt{0.04} + \sqrt{1.44} + \sqrt{1.69} + \sqrt{0.0009}$ is:
- What is the value of $x$, if $-3 \times \sqrt{196} + \sqrt{x} = 8 \times 3 - 2$?
- What is the value of $\sqrt{\frac{1.21 \times 0.9}{1.1 \times 0.11}}$?
- The value of $\frac{\{(13)^3 - 4^3\}}{13 - 8 \div 2} \div 8 - \{2 + 6 \times 9\}$ is:
- What is the value of the following expression?
$\frac{81}{7} \times \frac{21}{3} - 4\frac{2}{3} \div \frac{7}{9} \times \frac{121}{6}$
Important Questions from Simplification
What will come in the place of the question mark ‘?’ in the following question?
(15 + 24) × 3 ÷ 13 + 18 – 5 = ?
What should come in place of the question mark '?' in the following question?
\n13 × 3 of 5 ÷ 26 = ? + 2.5What should come in place of the question mark '?' in the following question?
10% of 450 - (8 × 5) = ? × 5
What will come in the place of the question mark ‘?’ in the following question?
(66)2 - (34)2 + ?2 = (60)2
What will come in the place of the question mark ‘?’ in the following question?
3 × ? ÷ 9 = ∛729 × √121
