Question

The descending order of \[ a=\frac12,\quad b=\frac29,\quad c=\frac7{12},\quad d=\frac8{15},\quad e=\frac{11}{16} \] is:

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

Hint:

When several fractions have different denominators, converting them into decimals often provides the fastest comparison.

Answer 1

The Correct Option is D

Step 1: Convert all fractions into decimals. \[ a=\frac12=0.5 \] \[ b=\frac29\approx0.222 \] \[ c=\frac7{12}\approx0.583 \] \[ d=\frac8{15}\approx0.533 \] \[ e=\frac{11}{16}=0.6875 \]

Step 2: Arrange from largest to smallest. \[ 0.6875>0.583>0.533>0.5>0.222 \] Therefore, \[ e>c>d>a>b \] Hence the descending order is \[ \boxed{e,c,d,a,b} \]