Question

To make grape juice by using frozen juice concen-trate, you must mix the frozen juice concentrate with water in a ratio of 1 to 3. How much frozen juice concentrate and how much water should you use to make 11 this problem in two different ways by reasoning about multiplication and division with quanti-ties, explaining your reasoning in each case.

Answer 1

To make 11 grape juice, you will need:

11 (1 * 11) frozen juice concentrate and

33 (3 * 11) water.

Explanation:

Since you are making 11 grape juice containers and each container requires 1 frozen juice concentrate and 3 quantities of water, to get the maximum quantities of ingredients required, you will multiply each ingredient by 11.

With the sum of ratio as 4 (1:3), we can also say that 44 (4 * 11) units of both frozen juice concentrate and water are required to produce 11 units of the grape juice. Dividing 44 by 4 also gives 11 units. Similarly, dividing the total ingredients of the frozen juice of 11 units by 11 juice concentrate gives 1 unit each and dividing 33 units by 11 quantity of water gives 3 units each in every unit of the juice produced.