The problem asks to order four drinks (Smoothie, Squash, Lemonade, and Soda) in ascending order based on the fraction of fruit they contain. The ratios of fruit, sugar, and water are given for each drink.

1. Problem Description

The problem asks to order four drinks (Smoothie, Squash, Lemonade, and Soda) in ascending order based on the fraction of fruit they contain. The ratios of fruit, sugar, and water are given for each drink.

2. Solution Steps

First, calculate the fraction of fruit in each drink by dividing the amount of fruit by the total amount of ingredients (fruit + sugar + water).

- Smoothie: Fruit : Sugar : Water = 1 : 0 :

0. Total = 1 + 0 + 0 =

1. Fraction of fruit = $\frac{1}{1} = 1$

- Squash: Fruit : Sugar : Water = 2 : 0 :

1. Total = 2 + 0 + 1 =

3. Fraction of fruit = $\frac{2}{3}$

- Lemonade: Fruit : Sugar : Water = 1 : 2 :

1. Total = 1 + 2 + 1 =

4. Fraction of fruit = $\frac{1}{4}$

- Soda: Fruit : Sugar : Water = 1 : 0 :

2. Total = 1 + 0 + 2 =

3. Fraction of fruit = $\frac{1}{3}$

Now, compare the fractions:

- Smoothie: 1

- Squash: $\frac{2}{3}$

- Lemonade: $\frac{1}{4}$

- Soda: $\frac{1}{3}$

Convert the fractions to have a common denominator to compare them easily. The least common multiple of 1, 3, and 4 is

1

2. Convert each fraction to have a denominator of 12:

- Smoothie: $1 = \frac{12}{12}$

- Squash: $\frac{2}{3} = \frac{8}{12}$

- Lemonade: $\frac{1}{4} = \frac{3}{12}$

- Soda: $\frac{1}{3} = \frac{4}{12}$

Now compare the numerators: 3 < 4 < 8 < 12

The order from smallest to largest fraction of fruit is: Lemonade, Soda, Squash, Smoothie.

3. Final Answer

Lemonade, Soda, Squash, Smoothie