What is the value of \( {{99 \div 33 + 44 \div 11 of 4 } \over 24\div 12-4+3}\)?
4
The question asks for the value of a mathematical expression presented as a fraction:
\( {{99 \div 33 + 44 \div 11 of 4 } \over 24\div 12-4+3}\)
To solve this, we need to follow the order of operations, often remembered by acronyms like BODMAS or PEMDAS. BODMAS stands for:
- Brackets
- Of (or Orders/Exponents)
- Division and Multiplication (from left to right)
- Addition and Subtraction (from left to right)
The term 'of' typically means multiplication, but it's performed before division and multiplication in the standard order.
Solving the Numerator
The numerator is \(99 \div 33 + 44 \div 11 of 4\).
First, we handle the 'of' part:
- \(11 \text{ of } 4 = 11 \times 4 = 44\)
Now substitute this back into the numerator expression:
\(99 \div 33 + 44 \div 44\)
Next, perform the divisions from left to right:
- \(99 \div 33 = 3\)
- \(44 \div 44 = 1\)
Substitute these values back:
\(3 + 1\)
Finally, perform the addition:
- \(3 + 1 = 4\)
So, the value of the numerator is 4.
Solving the Denominator
The denominator is \(24\div 12-4+3\).
First, perform the division:
- \(24 \div 12 = 2\)
Substitute this back into the denominator expression:
\(2 - 4 + 3\)
Next, perform addition and subtraction from left to right:
- \(2 - 4 = -2\)
- \(-2 + 3 = 1\)
So, the value of the denominator is 1.
Calculating the Final Value
Now we have the value of the numerator (4) and the value of the denominator (1).
The expression is \( {{ \text{Numerator} } \over { \text{Denominator} }} \).
\( {{4} \over {1}} = 4 \)
The value of the given expression is 4.
| Part | Expression | Step-by-Step | Result |
|---|---|---|---|
| Numerator | \(99 \div 33 + 44 \div 11 \text{ of } 4\) |
|
4 |
| Denominator | \(24 \div 12 - 4 + 3\) |
|
1 |
| Final Fraction | \( {{4} \over {1}} \) | \(4 \div 1\) | 4 |
Conclusion
By applying the BODMAS rule carefully to both the numerator and the denominator, we found the value of the expression. The numerator simplifies to 4, and the denominator simplifies to 1. The final value is the numerator divided by the denominator, which is 4.
Revision Table: BODMAS Order
| Order | Operation | Description | Example |
|---|---|---|---|
| 1 | Brackets () | Operations inside brackets are done first. | \(2 \times (3+4) = 2 \times 7 = 14\) |
| 2 | Of / Orders (Exponents) | 'Of' means multiplication, done before regular multiplication/division. Exponents are also done here. | \(5 \text{ of } 3 = 15\), \(2^3 = 8\) |
| 3 | Division & Multiplication | Done from left to right. | \(10 \div 2 \times 3 = 5 \times 3 = 15\) |
| 4 | Addition & Subtraction | Done from left to right. | \(7 - 3 + 5 = 4 + 5 = 9\) |
Additional Information: Understanding 'Of' in Math Problems
The term 'of' in mathematical expressions, particularly in contexts like fractions or percentages, often implies multiplication. When 'of' appears in an expression alongside division and multiplication, it's conventionally performed after brackets but before standard division and multiplication.
For example:
- \( \frac{1}{2} \text{ of } 10 \) means \( \frac{1}{2} \times 10 = 5 \).
- \( 20\% \text{ of } 100 \) means \( \frac{20}{100} \times 100 = 20 \).
In the expression \(44 \div 11 \text{ of } 4\), we first calculate \(11 \text{ of } 4\) as \(11 \times 4 = 44\), and then perform the division \(44 \div 44 = 1\). If we had performed the division first (\(44 \div 11 = 4\)) and then multiplied by 4 (\(4 \times 4 = 16\)), the result would be different, highlighting the specific priority of 'of'.
Important Questions from Simplification
Simplify the following expression.
\(\left(\frac{7}{16} \div \frac{1}{2}\:of\: \frac{1}{5}\right)\times \frac{4}{5}-\frac{1}{3}\times\frac{5}{8}\div \frac{1}{2}+\frac{3}{4}\)
The value of \(\left( {2\frac{6}{7}of4\frac{1}{5} \div \frac{2}{3}} \right) \times 5\frac{1}{9} \div \left( {\frac{3}{4} \times 2\frac{2}{3}of\frac{1}{2} \div \frac{1}{4}} \right)\) is:
The value of \(\left[ {\frac{4}{7}\rm \;of\;2\frac{4}{5} \times 1\frac{2}{3} - \left( {3\frac{1}{2} - 2\frac{1}{6}} \right)} \right] \div \left( {3\frac{1}{5} \div 4\frac{1}{2}\;\rm of\;\;5\frac{1}{3}} \right)\) is:
The value of \(\frac{{0.0203 \times 2.92}}{{0.7 \times 0.0365 \times 2.9}} \div \frac{{{{\left( {12.12} \right)}^2} - {{\left( {8.12} \right)}^2}}}{{{{\left( {0.25} \right)}^2} + \left( {0.25} \right)\left( {19.99} \right)}}\) is:
The value of 4 ÷ 12 of [3 ÷ 4 of {(4 - 2) × 6 ÷ 2}] - 2 × 6 ÷ 8 + 3 is:
