### Real-Life Situation:
Imagine you are preparing a special smoothie, and you have a recipe that requires a precise ratio of fruit to liquid base. According to the recipe:
- For every 9 parts (or units) of liquid base, you need 2 parts (or units) of fruit.
Let's say you decide to use 8 units of the liquid base for your smoothie. You need to figure out exactly how many units of fruit are required to maintain the same ratio.
### Solution:
1. Understand the Ratio:
The recipe calls for a ratio of 2 parts fruit to 9 parts liquid base. This means that for every 9 units of liquid base, 2 units of fruit are needed.
2. Set Up the Proportion:
We need to find out how many units of fruit correspond to 8 units of liquid base. We can set up a proportion based on the given ratio:
[tex]\[
\frac{2 \text{ units of fruit}}{9 \text{ units of liquid base}} = \frac{x \text{ units of fruit}}{8 \text{ units of liquid base}}
\][/tex]
Here, [tex]\( x \)[/tex] represents the number of units of fruit needed.
3. Solve the Proportion:
To solve for [tex]\( x \)[/tex], you can cross-multiply and divide:
[tex]\[
x = \left(\frac{2 \text{ units of fruit}}{9 \text{ units of liquid base}}\right) \times 8 \text{ units of liquid base}
\][/tex]
4. Calculate the Result:
Performing the multiplication gives us:
[tex]\[
x = \frac{2}{9} \times 8
\][/tex]
5. Evaluate the Expression:
By evaluating that expression, you find:
[tex]\[
x = \left(\frac{2}{9}\right) \times 8 = 0.2222222 \times 8 \approx 1.7777778
\][/tex]
Therefore, you will need approximately 1.778 units of fruit to maintain the correct ratio with the 8 units of liquid base.
