Question

Ascending order of \( a=\frac{1}{4}, b=\frac{3}{5}, c=\frac{11}{12}, d=\frac{13}{16}, e=\frac{17}{18} \) is

• A. a, b, c, d, e
• B. a, c, d, b, e
• C. a, b, d, c, e
• D. e, c, d, b, a

Hint:

For fractions close to 1, comparing decimal values is often faster than finding a common denominator.

Answer 1

The Correct Option is C

Concept: Fractions can be compared conveniently by converting them into decimal form.

Step 1: Convert each fraction into decimal form.
\[ a=\frac14=0.25 \] \[ b=\frac35=0.60 \] \[ d=\frac{13}{16}=0.8125 \] \[ c=\frac{11}{12}=0.9166\ldots \] \[ e=\frac{17}{18}=0.9444\ldots \]

Step 2: Arrange them in increasing order.
Clearly, \[ 0.25<0.60<0.8125<0.9166\ldots<0.9444\ldots \] Therefore, \[ a<b<d<c<e \] Hence the ascending order is \[ \boxed{a,\;b,\;d,\;c,\;e} \]