4/6 discovered a strategy that it
wasn’t aware of. Decreasing the denominator by one
increases the value of the fraction. Surprise! 4/6
and Mayor 3/5 continued playing several more
rounds. So what did they need to know to
eventually pop the balloon?
1. You can make a fraction smaller if you leave the numerator alone and
increase the denominator. (For example, 5/9 is smaller than 5/8.)
2. You can make a fraction larger if you leave the numerator alone and
decrease the denominator. (For example, 5/7 is bigger than 5/8.)
At first glance, this doesn't seem to make sense. But it works because in 5/8, you are dividing your unit into more pieces than 5/7, so each piece of 5/8 will be smaller than the pieces in 5/7. See below.
1. You can make a fraction smaller if you leave the numerator alone and
increase the denominator. (For example, 5/9 is smaller than 5/8.)
2. You can make a fraction larger if you leave the numerator alone and
decrease the denominator. (For example, 5/7 is bigger than 5/8.)
At first glance, this doesn't seem to make sense. But it works because in 5/8, you are dividing your unit into more pieces than 5/7, so each piece of 5/8 will be smaller than the pieces in 5/7. See below.