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.

a. draw a tape - diagram to represent this ratio.
b. how many cups of water should be mixed with 4 cups of rice?

1. 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:

1a. Drawing tape - diagram for 2:1 ratio

Draw two rectangles (representing cups of water) and one rectangle (representing cups of rice). Each rectangle represents one - unit in the ratio.

1b. Finding cups of water for 4 cups of rice

The ratio of water to rice is 2:1. Let the number of cups of water be $x$ and cups of rice be $y$. The ratio is $\frac{x}{y}=\frac{2}{1}$. Given $y = 4$, we can cross - multiply:
$x=\frac{2\times4}{1}$
$x = 8$

2a. Drawing tape - diagram for 4:3 and 20:15

For the ratio 4:3, draw 4 small rectangles for the first quantity and 3 small rectangles for the second quantity. For the ratio 20:15, since $20\div4 = 5$ and $15\div3=5$, we can group the small rectangles into groups of 5. So, draw 4 groups of 5 small rectangles for the first quantity and 3 groups of 5 small rectangles for the second quantity to show the equivalence.

2b. Identifying Yuna's mistake and correct method

Yuna's mistake: To find an equivalent ratio, we multiply both terms of the ratio by the same non - zero number, not add the same number to both terms.
The correct method: To find an equivalent ratio of 4:3, we can multiply both 4 and 3 by the same non - zero number. For example, if we multiply by 2, we get 8:6; if we multiply by 5, we get 20:15.

Answer:

1a. Draw two rectangles for water and one for rice.
1b. 8 cups
2a. Draw 4 groups of 5 rectangles for the first part and 3 groups of 5 rectangles for the second part to show equivalence to 4:3.
2b. Mistake: Adding the same number to both terms of the ratio instead of multiplying. Correct method: Multiply both terms of the ratio by the same non - zero number.