a)
Given:
[tex]5\colon8\text{ and 7:10}[/tex]
Rewrite the ratio into fraction form as follows.
[tex]\frac{5}{8}\text{ and }\frac{7}{10}[/tex]
The least common multiple of 8 and 10 is 40.
Make the denominator 40 to compare the fractions.
[tex]\frac{5\times5}{8\times5}\text{ and }\frac{7\times4}{10\times4}[/tex]
[tex]\frac{25}{40}\text{ and }\frac{28}{40}[/tex]
We know that
[tex]25<28[/tex]
[tex]\frac{25}{40}<\frac{28}{40}[/tex]
[tex]\frac{5}{8}<\frac{7}{10}[/tex][tex]5\colon8<7\colon10[/tex]
Hence the answer is
[tex]5\colon8<7\colon10[/tex]
b)
Given:
[tex]\frac{9}{6}\text{ and }\frac{36}{24}[/tex]
Given fractions can be written as follows.
[tex]\frac{3\times3}{3\times2}\text{ and }\frac{12\times3}{12\times2}[/tex]
Cancel out the common fractions.
[tex]\frac{3}{2}\text{ and }\frac{3}{2}[/tex]
We know that
[tex]\frac{3}{2}\text{=}\frac{3}{2}[/tex]
[tex]\frac{9}{6}\text{= }\frac{36}{24}[/tex]
Hence the answer is
[tex]\frac{9}{6}\text{= }\frac{36}{24}[/tex]
