Answer:
(a) 5 : 8 < 7 : 10
(b) 9/6 = 36/24
Step-by-step explanation:
(a)
Perhaps simplest to explain is the use of a common denominator: 40.
[tex]5 : 8 = (5\cdot5):(8\cdot5)=25:40\\\\7:10=(7\cdot4):(10\codt4)=28:40\\\\25:40 < 28:40\quad\leftrightarrow\quad\boxed{5:8 < 7:10}[/tex]
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Other ways you can do this comparison are ...
Multiply by 8·10 = 80, the product of the denominators:
5·10 = 50 < 7·8 = 56
Convert the fractions to decimal:
5/8 = 0.625 < 7/10 = 0.700
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(b)
Remove a factor of 4 from the second fraction:
[tex]\dfrac{9}{6}\text{ and }\dfrac{36}{24}\quad\leftrightarrow\quad\boxed{\dfrac{9}{6}=\dfrac{9\cdot4}{6\cdot4}}[/tex]
