Complete two and five-sixths compared to two and 12 17ths using less than, equal to, or greater than.
We’re trying to compare these two mixed numbers. The whole number portion of each mixed number is the same. That means we need to look at the fraction piece. We need to compare five-sixths to 12 17ths. To compare them accurately, they need a common denominator.
To do that, we’ll multiply six by 17 and we’ll multiply 17 by six. Six times 17 equals 102. 17 times six equals 102. Remember if we multiply by something in the denominator, we must multiply by that same value in the numerator. That means for five-sixths, we’ll need to multiply five times 17, which equals 85. And for 12 17ths, we’ll multiply 12 by six, which equals 72. Next, we bring down our twos.
Now that the fractional pieces of our mixed number have the same denominator, we can compare: two and 85 over 102 compared to two and 72 over 102. 85 over 102 is larger than 72 over 102. And that makes two and 85 over 102 greater than two and 72 over 102.
Going back to our original problem, two and five-sixths is greater than two and 12 17ths.