We are given a table with 3 different products. In this part of the exercise, we will focus on the first one. We want to determine why the product of 12 and 34 is less than 34. Let's consider the table.
Notice that 34 is one of the factors. The other one is 12, which is a proper fraction that is less than 1. When we multiply a number by such a fraction, the result is only a part — a fraction — of this number. Therefore, it has to be less than the original value. Our number here is 34, so the result has to be less than 34.
In this part of the exercise, we will focus on the second product from the table. We want to determine why the product of 1 and 34 is equal to 34. Consider the second row of the given table.
One of the factors is 34 again and the other one is 1. Remember that when we multiply any number by 1, the result is always the original number. In this case, we are multiplying 34 by 1, so the result must be 34.
Now we want to determine why the third product is greater than 34. Consider the third row of the given table.
One of the factors is 34, but the other one is 32. This is an improper fraction that is greater than 1. When we multiply a number by such a fraction, the result is greater than the original number. Our original number is 34, so the product has to be greater than 34.
