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:
B < A < C
To compare the three sums, convert each pair of fractions to a single fraction or decimal so they can be directly compared.
Sum A: 16/19 + 1/4 = (16 × 4 + 1 × 19)/(19 × 4) = (64 + 19)/76 = 83/76 ≈ 1.092.
Sum B: 11/14 + 1/5 = (11 × 5 + 1 × 14)/(14 × 5) = (55 + 14)/70 = 69/70 ≈ 0.986.
Sum C: 19/21 + 1/3 = (19 × 3 + 1 × 21)/(21 × 3) = (57 + 21)/63 = 78/63 = 26/21 ≈ 1.238.
Comparing the decimal values: B ≈ 0.986 is the smallest, A ≈ 1.092 is the middle value, and C ≈ 1.238 is the largest.
Therefore, the correct ascending order of the sums is B < A < C.
Similar Questions
If numerator of a fraction is increased by 25% and the denominator is decreased by 15%, the fraction becomes 15/17. Find the value of the original fraction?
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