Respuesta :
For now, assume 3/4 and 11/12 are equal. It is likely they are not equal, but we'll get to that later.
The equation we set up is 3/4 = 11/12
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3/4 = 11/12
3*12 = 4*11 ... cross multiply
36 = 44
The last equation is false, so the entire string of equations are false.
This tells us that 3/4 is not equal to 11/12.
Since the left hand side of the last equation is smaller, this means we must replace the equal sign with a less than sign. Do so with the other equal signs as well. We have this updated set of steps
3/4 < 11/12
3*12 < 4*11 ... cross multiply
36 < 44
We see that 3/4 is smaller than 11/12
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Another way to see that 3/4 is smaller is to use a calculator to find the decimal version of each fraction
3/4 = 0.75
11/12 = 0.9167 approximately
Since 0.75 is smaller than 0.9167, this means 3/4 is smaller than 11/12.
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If you want to stick with fractions and you don't want to cross multiply, then we can rewrite 3/4 as a fraction that has 12 in the denominator.
Multiply top and bottom of 3/4 by the value 3
This will make 3/4 turn into 9/12
3*3 = 9
4*3 = 12
So 3/4 = 9/12 is a true equation
Instead of comparing "3/4 and 11/12", we are equivalently comparing "9/12 and 11/12".
The numerator 9 is smaller than the numerator 11, so 9/12 is smaller than 11/12
This points to 3/4 being smaller than 11/12.
