The highest possible value of fraction [tex]\frac{a}{b}[/tex] is [tex]\frac{36}{20}[/tex]
A factor is one of two or more numbers that divides a given number without a remainder. A multiple of a number is a number that can be divided evenly by another number without a remainder.
Factors of [tex]72=1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72[/tex]
Factors of [tex]108=1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108[/tex]
Common factors of [tex]72,108[/tex] are [tex]1,2,3,...,36[/tex]
Multiples of [tex]4[/tex] are [tex]4, 8, 12, 16, 20,...[/tex]
Multiples of [tex]10[/tex] are [tex]10, 20, 30, 40, 50, 60,...[/tex]
Common multiples of [tex]4,10[/tex] are [tex]20,40,...[/tex]
Fraction has the highest possible values when denominator is least and numerator is greatest.
So, the highest possible value of fraction [tex]\frac{a}{b}[/tex] is [tex]\frac{36}{20}[/tex]
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