The product which is having its value less than 5/8 is the expression,[tex]A=\dfrac{7}{10}\times \dfrac{5}{8}[/tex],
Because, the value of the first term in the expression is less then 1 which makes the product less than 5/8.
Given information:
The expressions are given in the question to check which one is less than the fraction 5/8.
The expressions are,
[tex]A=\dfrac{7}{10}\times \dfrac{5}{8} \\[/tex],
[tex]B=\dfrac{9}{7} \times\dfrac{5}{8}[/tex],
[tex]C=\dfrac{3}{2}\times \dfrac{5}{8}[/tex],
As, we can see in the above expressions, all the given expressions are having common multiple of 5/8.
Hence, to find the expression less then 5/8, simply solve the first expression and see the value of first term.
If the first term is grater then 1, then the given product will be grater then 5/8.
On solving the first expression, we get,
[tex]A=\dfrac{7}{10}\times \dfrac{5}{8} \\\\A=0.7\times\dfrac{5}{8}[/tex]
In the above expression, the value of first term is less than 1, Hence the product will be less then 5/8.
Now, solving the second expression, we get
[tex]B=\dfrac{9}{7} \times\dfrac{5}{8}\\B=1.29\times \dfrac{5}{8} \\[/tex]
In the above expression, the value of first term is grater than 1, Hence the product will be grater then 5/8.
Now, solve the third expression as,
[tex]C=\dfrac{3}{2}\times \dfrac{5}{8}\\C=1.5\times \dfrac{5}{8}[/tex]
In the above expression, the value of first term is grater than 1, Hence the product will be grater then 5/8.
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