A recipe for stir fry calls for 8 cups of rice for every 6 cups of veggies. Suppose a restaurant is making a large batch of stir fry using 15 cups of veggies. How much rice would they need?

Question

Start by labeling the double number line with the cups of veggies and cups of rice that the recipe calls for.
Veggies (cups)
0
6
Rice (cups)
0
8
Great job!
To find how many cups of rice they’d need for 15 cups of veggies, it can be helpful to first find the unit rate, or the amount of rice needed for 1 cup of veggies. Partition the number line to find the number of cups of rice needed for every 1 cup of veggies.
Veggies (cups)
0
6
Rice (cups)
0
8
You got it!
Label the bottom number line to find the number of cups of rice the restaurant would need for 1 cup of veggies.

Answer 1

To find the unit rate, or the amount of rice needed for 1 cup of veggies, we start with the ratio from the recipe:

8 cups of rice for every 6 cups of veggies.

This can be expressed as the ratio:

\[ \frac{8 \text{ cups of rice}}{6 \text{ cups of veggies}} \]

To find the amount of rice needed for 1 cup of veggies, we can divide both the numerator and the denominator by 6:

\[ \frac{8 \div 6 \text{ cups of rice}}{6 \div 6 \text{ cups of veggies}} = \frac{4/3 \text{ cups of rice}}{1 \text{ cup of veggies}} \approx 1.33 \text{ cups of rice} \]

This means for every 1 cup of veggies, approximately 1.33 cups (or \( \frac{4}{3} \) cups) of rice is needed.

Now, using this unit rate, we can determine how much rice is needed for 15 cups of veggies:

\[ 15 \text{ cups of veggies} \times \frac{4/3 \text{ cups of rice}}{1 \text{ cup of veggies}} = 15 \times \frac{4}{3} = 20 \text{ cups of rice} \]

So, the restaurant would need 20 cups of rice for 15 cups of veggies.

Here’s how the double number line looks with the calculations:

Veggies (cups)

0      6     12    15
|------|------|------|

Rice (cups)

0      8     16    20
|------|------|------|

• For every 6 cups of veggies (8 cups of rice), when reaching 12 cups of veggies, we have 16 cups of rice. Approaching 15 cups means we calculate that we need a little less than 16 cups of rice, thus ending up with 20 cups based on the unit rate calculated.