Answer:
(a)
[tex]\frac{12}{18}=\frac{2}{3}[/tex]
(b)
[tex]\frac{48}{54}=\frac{8}{9}[/tex]
(c)
[tex]\frac{27}{90}=\frac{3}{10}[/tex]
(d)
[tex]\frac{63}{77}=\frac{9}{11}[/tex]
(e)
[tex]\frac{24}{32}=\frac{3}{4}[/tex]
(f)
[tex]\frac{73}{365}=\frac{1}{5}[/tex]
Step-by-step explanation:
(a)
[tex]\frac{12}{18}[/tex]
we can factor numerator and denominator
and then we can simplify it
Numerator:
[tex]12=2\times 2\times 3[/tex]
Denominator:
[tex]18=2\times 3\times 3[/tex]
now, we can replace by factors
[tex]\frac{12}{18}=\frac{2\times 2\times 3}{2\times 3\times 3}[/tex]
now, we can cancel and simplify it
[tex]\frac{12}{18}=\frac{2}{3}[/tex]
(b)
[tex]\frac{48}{54}[/tex]
we can factor numerator and denominator
and then we can simplify it
Numerator:
[tex]48=2\times 2\times 2\times 2\times 3[/tex]
Denominator:
[tex]54=2\times 3\times 3\times 3[/tex]
now, we can replace by factors
[tex]\frac{48}{54}=\frac{2\times 2\times 2\times 2\times 3}{2\times 3\times 3\times 3}[/tex]
now, we can cancel and simplify it
[tex]\frac{48}{54}=\frac{8}{9}[/tex]
(c)
[tex]\frac{27}{90}[/tex]
we can factor numerator and denominator
and then we can simplify it
Numerator:
[tex]27=3\times 3\times 3[/tex]
Denominator:
[tex]90=2\times 3\times 3\times 5[/tex]
now, we can replace by factors
[tex]\frac{27}{90}=\frac{3\times 3\times 3}{2\times 3\times 3\times 5}[/tex]
now, we can cancel and simplify it
[tex]\frac{27}{90}=\frac{3}{10}[/tex]
(d)
[tex]\frac{63}{77}[/tex]
we can factor numerator and denominator
and then we can simplify it
Numerator:
[tex]63=3\times 3\times 7[/tex]
Denominator:
[tex]77=7\times 11[/tex]
now, we can replace by factors
[tex]\frac{63}{77}=\frac{3\times 3\times 7}{7\times 11}[/tex]
now, we can cancel and simplify it
we get
[tex]\frac{63}{77}=\frac{9}{11}[/tex]
(e)
[tex]\frac{24}{32}[/tex]
we can factor numerator and denominator
and then we can simplify it
Numerator:
[tex]24=2\times 2\times 2\times 3[/tex]
Denominator:
[tex]32=2\times 2\times 2\times 2\times 2[/tex]
now, we can replace by factors
[tex]\frac{24}{32}=\frac{2\times 2\times 2\times 3}{2\times 2\times 2\times 2\times 2}[/tex]
now, we can cancel and simplify it
[tex]\frac{24}{32}=\frac{3}{4}[/tex]
(f)
[tex]\frac{73}{365}[/tex]
we can factor numerator and denominator
and then we can simplify it
since, 73 can not be factored
[tex]365=5\times 73[/tex]
now, we can plug it
[tex]\frac{73}{365}=\frac{73}{5\times 73}[/tex]
now, we can cancel and simplify it
[tex]\frac{73}{365}=\frac{1}{5}[/tex]
