Answer:
[tex]\frac{1}{2},\frac{5}{8},\frac{7}{11},\frac{2}{3}[/tex]
Step-by-step explanation:
step 1
Decompose the number in the denominator into prime factors
2
8=2^3
11
3
Find the least common multiple (LCM)
The LCM is
[tex](2^3)(11)(3)=264[/tex]
Convert each fraction into an equivalent fraction that has LCM as its denominator.
so
[tex]\frac{1}{2}[/tex]
Multiply by 132 both numerator and denominator
[tex]\frac{1}{2}=\frac{132}{264}[/tex]
[tex]\frac{5}{8}[/tex]
Multiply by 33 both numerator and denominator
[tex]\frac{5}{8}=\frac{165}{264}[/tex]
[tex]\frac{7}{11}[/tex]
Multiply by 24 both numerator and denominator
[tex]\frac{7}{11}=\frac{168}{264}[/tex]
[tex]\frac{2}{3}[/tex]
Multiply by 88 both numerator and denominator
[tex]\frac{2}{3}=\frac{176}{264}[/tex]
Compare fractions with the same denominator
Remember that
When comparing fractions with like denominators, the larger fraction is the one with the greater numerator
so
[tex]\frac{176}{264}>\frac{168}{264}>\frac{165}{264}>\frac{132}{264}[/tex]
or
[tex]\frac{132}{264}<\frac{165}{264} <\frac{168}{264}<\frac{176}{264}[/tex]
therefore
The list in order to smallest to largest is
[tex]\frac{1}{2},\frac{5}{8},\frac{7}{11},\frac{2}{3}[/tex]
