A school chorus has 45 sixth-grade students and 70 seventh-grade students. The music director wants to make groups of performers, with the same combination of sixth- and seventh-grade students in each group. She wants to form as many groups as possible. What is the largest number of groups that could be formed?

How much dextrose 70% must be mixed with dextrose 5% to prepare 1,000 ml of dextrose 20%?

1- is the product of two rational numbers irrational or rational? first, make a hypothesis by multiplying two rational numbers. then, use variables such as x=a/b and y=c/d and the closure property of integers to prove your hypothesis. 2- 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. 3- 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 part b?

What happens to the area as the sliders are adjusted? what do you think the formula for the area of a triangle is divided by 2?