Simplify the given expression.
$\frac{5+5\times5}{5\times5+5} \times \frac{\frac{1}{5}\div(\frac{1}{5}\times\frac{1}{5})}{(\frac{1}{5}\times\frac{1}{5})\div\frac{1}{5}} - (5 - \frac{1}{5}) \times \frac{10}{2}$
Simplifying the Mathematical Expression
The question asks us to simplify the given mathematical expression:
$ \frac{5+5\times5}{5\times5+5} \times \frac{\frac{1}{5}\div(\frac{1}{5}\times\frac{1}{5})}{(\frac{1}{5}\times\frac{1}{5})\div\frac{1}{5}} - (5 - \frac{1}{5}) \times \frac{10}{2} $
We will simplify this expression step-by-step following the order of operations (PEMDAS/BODMAS): Parentheses/Brackets, Exponents/Orders, Multiplication and Division (from left to right), Addition and Subtraction (from left to right).
Step 1: Simplify the first fraction
Calculate the numerator and denominator separately:
- Numerator: $5 + 5 \times 5 = 5 + 25 = 30$
- Denominator: $5 \times 5 + 5 = 25 + 5 = 30$
The first fraction simplifies to: $\frac{30}{30} = 1$.
Step 2: Simplify the second fraction
This fraction involves divisions and multiplications of fractions. Let's simplify the numerator and denominator parts first.
- Numerator part: $\frac{1}{5}\div(\frac{1}{5}\times\frac{1}{5}) = \frac{1}{5}\div\frac{1}{25} = \frac{1}{5} \times \frac{25}{1} = 5$
- Denominator part: $(\frac{1}{5}\times\frac{1}{5})\div\frac{1}{5} = \frac{1}{25}\div\frac{1}{5} = \frac{1}{25} \times \frac{5}{1} = \frac{5}{25} = \frac{1}{5}$
Now, divide the simplified numerator part by the simplified denominator part:
$ \frac{5}{\frac{1}{5}} = 5 \times 5 = 25 $
The second fraction simplifies to $25$.
Step 3: Simplify the third part of the expression
This part involves subtraction inside parentheses and multiplication.
- Parentheses: $5 - \frac{1}{5} = \frac{25}{5} - \frac{1}{5} = \frac{24}{5}$
- Multiplication part: $\frac{10}{2} = 5$
Multiply the results: $\frac{24}{5} \times 5 = 24$.
The third part simplifies to $24$.
Step 4: Combine the simplified parts
Now substitute the simplified values back into the original expression:
$ (1) \times (25) - (24) $
Perform the multiplication first:
$ 25 - 24 $
Finally, perform the subtraction:
$ 1 $
The simplified value of the expression is $1$. This corresponds to Option D.
Similar Questions
- Solve
$49 + 1331 \div 121 - 72 - 5 = ?$ - Solve the following:
$11 + 11 \div 11 + 11 \times 11 - 11 = ?$ - Solve the following.
$4 \times 36 - 6[3 + 2(216 \div 6) - 51] = ?$ - Solve the following. $8000 + \frac{2000}{100} - 150 \times 60$
- Solve the following.
$3[35 + (45 + 10 \div 2 \times 3 - 50) + 5]$ - Using BODMAS, simplify the following.
$\frac{7}{9} \times \frac{21}{5} \times 25 (65^2 - 55^2)$ - Find the value of $216 \div 6 + 6 \times 4 - 10$.
- The value of $3 \div 1 - 2 + 3$ is:
- The value of $5 + 5 \times 2 \div 5$ is:
Simplify the given expression using BODMAS.
$\frac{4}{11} \times \frac{121}{16} \times 24 (75^2 - 55^2) \times \frac{1}{100}$
Important Questions from Bodmas Rule
The value of 90 ÷ 20 of 6 × [11 ÷ 4 of {3 × 2 - (3 - 8)}] ÷ (9 ÷ 3 × 2) is:
The value of 1800 ÷ 20 × {(12 - 6) + (24 - 12)} is:
The value of 20 ÷ 5 of 8 × [9 ÷ 6 × (6 - 3)] - (10 ÷ 2 of 20) is:
The value of \(\left( {18 \div 2\;of\frac{1}{4}} \right)\; \times \;\left( {\frac{2}{3} \div \frac{3}{4}\; \times \;\frac{5}{8}} \right) \div \left( {\frac{2}{3} \div \frac{3}{4}of\frac{3}{4}} \right)\) is:
The value of 18 ÷ [26 - {25 - (15 - 5) ÷ 2}] of 12 + 2 - 2 ÷ 4 × 16 is:
