Question

1. in a rice recipe, a ratio that relates the number of cups of water to the number of cups of rice is 2:1. how many cups of water should be mixed with 4 cups of rice? 2. the tape - diagram shows that the ratio 4:3 is equivalent to the ratio 8:6. a. draw a tape diagram to show that the ratio 4:3 is equivalent to the ratio 20:15. b. yuna thinks that the ratio 4:3 is equivalent to the ratio 10:9 because 6 + 4 = 10 and 6+3 = 9. what is yunas mistake? what can she do to find an equivalent ratio?

Explanation:

Step1: Analyze the first - part of question 1

We are given a ratio of water to rice. Let's assume the ratio of water to rice is \(2:1\) (from the context of the problem).

Step2: Calculate water for 4 cups of rice

If the ratio of water to rice is \(2:1\), when there are 4 cups of rice, we multiply the number of cups of rice by the ratio of water to rice. So the number of cups of water \(= 4\times2=8\) cups.

Step3: Analyze question 2a

To show \(4:3\) is equivalent to \(20:15\) using a tape - diagram:
For the ratio \(4:3\), we draw one set of 4 equal - sized rectangles for the first part and 3 equal - sized rectangles for the second part. For the ratio \(20:15\), since \(20\div4 = 5\) and \(15\div3=5\), we can draw 5 sets of the 4 - rectangle and 3 - rectangle groups. Each small rectangle in the first ratio represents 1 unit, and in the second ratio, each group of 4 and 3 rectangles represents 5 units.

Step4: Analyze question 2b

Yuna's mistake is that to find an equivalent ratio, we must multiply both parts of the ratio by the same non - zero number, not add the same number to both parts. To find an equivalent ratio of \(4:3\), we can multiply both 4 and 3 by the same number. For example, if we multiply by 2, we get \(8:6\); if we multiply by 5, we get \(20:15\).

Answer:

1. 8 cups

2.
a. Draw 5 sets of a group of 4 rectangles for the first part and 3 rectangles for the second part to show the equivalence between \(4:3\) and \(20:15\).
b. Yuna's mistake is adding instead of multiplying to find an equivalent ratio. To find an equivalent ratio, multiply both parts of the ratio by the same non - zero number.