How do you compare each pair of fractions with <, > or = given #5/4, 7/6#?
1 Answer
Explanation:
The easiest way to compare two fractions is to rewrite one (or both) of them so that their denominators match.
You can think about the denominator of a fraction like a unit, similar to inches, centimeters, feet, etc. If you were asked to compare 5 inches to 7 centimeters, you'd first need to convert one value (or both) so that their units matched.
In fractions, the "unit" is the denominator. The first value is 5 "fourths", and the second value is 7 "sixths". These aren't in the same unit, so we can't just compare 5 to 7. But, we can convert the numbers to the same unit.
The best way to do this is to find the lowest multiple that 4 and 6 have in common. Without too much effort, this is found to be 12
So we need to convert
For every fourth, there are 3 twelfths. We have 5 fourths, so we have:
This was just for explanation. There's a much more concise way to write this change of "unit":
What we're doing in this shorter method is multiplying
Similarly, if we have 7 sixths, and there are 2 twelfths in a sixth, then we have 14 twelfths:
Now the values represented by
Bonus:
There's a trick to comparing fractions where the numerator is 1 more than the denominator:
This works because the numerators are getting proportionally closer to their denominators.
Think of a really big number. Now consider the fraction
This is a little taste of calculus for you. It's not so bad. ;)