Simplify: \(\left\{\frac{14}{24} \div \frac{14}{9}\right\} \div \left(\frac{3}{7} \times \frac{14}{9} + \frac{5}{8}\right) + \frac{9}{10} \div \frac{31}{24} \text{ of } \frac{24}{10}\)
\(\frac{18}{31}\)
First evaluate the braces: \(\frac{14}{24} \div \frac{14}{9} = \frac{14}{24} \times \frac{9}{14} = \frac{9}{24} = \frac{3}{8}\).
Next the parentheses: \(\frac{3}{7} \times \frac{14}{9} = \frac{42}{63} = \frac{2}{3}\), so \(\frac{2}{3} + \frac{5}{8} = \frac{16}{24} + \frac{15}{24} = \frac{31}{24}\).
So the first part is \(\frac{3}{8} \div \frac{31}{24} = \frac{3}{8} \times \frac{24}{31} = \frac{9}{31}\).
For the last part, apply of first: \(\frac{31}{24} \text{ of } \frac{24}{10} = \frac{31}{24} \times \frac{24}{10} = \frac{31}{10}\).
Then \(\frac{9}{10} \div \frac{31}{10} = \frac{9}{10} \times \frac{10}{31} = \frac{9}{31}\).
Adding the two parts: \(\frac{9}{31} + \frac{9}{31} = \frac{18}{31}\).
Hence, the simplified value is \(\frac{18}{31}\).
Similar Questions
- Solve the following.
$3[35 + (45 + 10 \div 2 \times 3 - 50) + 5]$ What will the value of the following expression be?
$20 - [15 - \{4 - (8 - 6 + 3)\}]$
- What is the value of the following expression?
$103 - [144 \div (12 \times 12) + 5 + 12 \div (6 - 2) + 10]$ - What is the value of $(6 + 4) \times \frac{4}{2} + 5 - 3$?
- What is the value of $\frac{(6 \times 2)}{(8 - 1 + 5)}$?
Simplify the given expression using BODMAS.
$\frac{4}{11} \times \frac{121}{16} \times 24 (75^2 - 55^2) \times \frac{1}{100}$Simplify the given expression.
$\frac{5+5\times5}{5\times5+5} \times \frac{\frac{1}{5}\div(\frac{1}{5}\times\frac{1}{5})}{(\frac{1}{5}\times\frac{1}{5})\div\frac{1}{5}} - (5 - \frac{1}{5}) \times \frac{10}{2}$- Using BODMAS, simplify the following.
$\frac{7}{9} \times \frac{21}{5} \times 25 (65^2 - 55^2)$ - Find the value of $216 \div 6 + 6 \times 4 - 10$.
- Solve the following:
$240 \div 8 \times 512 \div 4$
Important Questions from Bodmas Rule
If 2945 ÷ 19 – 11 × 5 = 29 + a, find the value of a.
DIRECTIONS: What should come in place of the question mark (?) in the following question?
3800 - 22 × 1968 ÷ 48 = ? × 7
Solve: {7.88 × 2 + 2.4 × 5 - 242.4 ÷ 4 + [9.2 × 4 - 2.46 of 3 + (36.3 ÷ 3 - 1.42 × 2)]}
What will come in the place of question mark (?) in the given expression?
(420 ÷ 12 × 35 + 452- 152) = ?2
Evaluate: (13 × 8 - √81 × 6 + 1 ) ÷ (√49 + 72 - 18 × 2 + 19)
