Question:
Simplify the following expression.
निम्नलिखित व्यंजक को सरल कीजिए।
Options:
- a) 2 1/6
- b) 4 1/6
- c) 1 1/6
- d) 3 1/6
- a) 2 1/6
- b) 4 1/6
- c) 1 1/6
- d) 3 1/6
correct answer : c)
Explanation:
Expression: 3 1/5 of 2 3/4 ÷ 11/3 + (2 1/5 ÷ 1 2/5 of 1 3/7 − 2 1/3)
Convert to improper fractions: 3 1/5 = 16/5, 2 3/4 = 11/4, 2 1/5 = 11/5, 1 2/5 = 7/5, 1 3/7 = 10/7, 2 1/3 = 7/3.
Part 1 (outside bracket): 3 1/5 of 2 3/4 ÷ 11/3
Apply “of” first (BODMAS): 16/5 × 11/4 = 44/5
Then ÷: 44/5 ÷ 11/3 = 44/5 × 3/11 = 12/5
Part 2 (inside bracket): 2 1/5 ÷ 1 2/5 of 1 3/7 − 2 1/3
Apply “of” first: 7/5 × 10/7 = 2
Then ÷: 11/5 ÷ 2 = 11/10
Then −: 11/10 − 7/3 = 33/30 − 70/30 = −37/30
Final: 12/5 + (−37/30) = 72/30 − 37/30 = 35/30 = 7/6 = 1 1/6
व्यंजक: 3 1/5 of 2 3/4 ÷ 11/3 + (2 1/5 ÷ 1 2/5 of 1 3/7 − 2 1/3)
अनुचित भिन्न: 3 1/5 = 16/5, 2 3/4 = 11/4, 2 1/5 = 11/5, 1 2/5 = 7/5, 1 3/7 = 10/7, 2 1/3 = 7/3.
भाग 1 (कोष्ठक के बाहर): 3 1/5 of 2 3/4 ÷ 11/3
BODMAS में “of” पहले: 16/5 × 11/4 = 44/5
फिर ÷: 44/5 ÷ 11/3 = 44/5 × 3/11 = 12/5
भाग 2 (कोष्ठक के अंदर): 2 1/5 ÷ 1 2/5 of 1 3/7 − 2 1/3
“of” पहले: 7/5 × 10/7 = 2
फिर ÷: 11/5 ÷ 2 = 11/10
फिर −: 11/10 − 7/3 = 33/30 − 70/30 = −37/30
अंतिम: 12/5 + (−37/30) = 72/30 − 37/30 = 35/30 = 7/6 = 1 1/6