Consider following sums of fractions: A. \(\frac{16}{19}+\frac{1}{4}\) B.…
2023
Consider following sums of fractions:
A. \(\frac{16}{19}+\frac{1}{4}\)
B. \(\frac{11}{14}+\frac{1}{5}\)
C. \(\frac{19}{21}+\frac{1}{3}\)
Choose the correct ascending order of above sums of fractions from the following options:
Answer: B. B < A < C — CONCEPTTo compare sums of fractions, first express each sum exactly as a single fraction. Compare two positive fractions by cross-multiplication: for a/b and…
- A.
A < B < C
- B.
B < A < C
- C.
A < C < B
- D.
C < A < B
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Correct answer: B
CONCEPT
To compare sums of fractions, first express each sum exactly as a single fraction. Compare two positive fractions by cross-multiplication: for a/b and c/d with positive denominators, a/b < c/d exactly when ad < bc.
APPLICATION
A = 16/19 + 1/4 = (64 + 19)/76 = 83/76.
B = 11/14 + 1/5 = (55 + 14)/70 = 69/70.
C = 19/21 + 1/3 = (19 + 7)/21 = 26/21.
Compare B and A: 69 × 76 = 5244, while 83 × 70 = 5810; therefore B < A.
Compare A and C: 83 × 21 = 1743, while 26 × 76 = 1976; therefore A < C.
CROSS-CHECK
The decimal values are B ≈ 0.9857, A ≈ 1.0921, and C ≈ 1.2381. They confirm the ascending order B < A < C.