Because of the commutative property of multiplication, it is true that 3 4 × 4 = 4 × 3 4 . However, these expressions can be calculated in different ways even though the solutions will be the same. Below, show two different ways of solving this problem. First, show how 3 4 × 4 can be solved using repeated addition.

Which equation represents a proportional relationship that has a constant of proportionality equal to 1/5

On a string instrument, the length of a string varies inversely as the frequency of its vibrations. an 11-inch string has a frequency of 400 cylces per second. find the frequency of a 10-icnch string.

1- what do you think the product of a nonzero rational number and an irrational number is? is it rational or irrational? make use of variables, the closure property of integers, and possibly a proof by contradiction to prove your hypothesis.2- why do we have to specify that the rational number must be nonzero when we determine what the product of a nonzero rational number and an irrational number is? if the rational number were 0, would it give us the same result we found in the first question?