Let's work through the questions step by step.

1. The chorus at an elementary school is made up of fifth and sixth graders. The chorus has 12 fifth-grade girls, 9 fifth-grade boys, 14 sixth-grade girls, and 10 sixth-grade boys.

a. The ratio of girls to boys is:

We need to calculate the total number of girls and boys:

• Total girls = 12 (fifth-grade girls) + 14 (sixth-grade girls) = 26
• Total boys = 9 (fifth-grade boys) + 10 (sixth-grade boys) = 19

So, the ratio of girls to boys is 26 to 19, or 26:19.

b. The ratio of fifth graders to sixth graders is:

The fifth graders include both boys and girls:

• Total fifth graders = 12 (fifth-grade girls) + 9 (fifth-grade boys) = 21

The sixth graders also include both boys and girls:

• Total sixth graders = 14 (sixth-grade girls) + 10 (sixth-grade boys) = 24

So, the ratio of fifth graders to sixth graders is 21 to 24, or 21:24. This can be simplified by dividing both numbers by 3, resulting in 7:8.

c. The ratio of girls to the total number of students in the chorus is:

The total number of students in the chorus is:

• Total students = 12 (fifth-grade girls) + 9 (fifth-grade boys) + 14 (sixth-grade girls) + 10 (sixth-grade boys) = 45

The total number of girls is 26 (as calculated before).

So, the ratio of girls to total students is 26 to 45, or 26:45.

2. The school cafeteria orders 4 cartons of regular milk for every 3 cartons of chocolate milk.

a. Complete the bar diagram to show the ratio. The bar diagram is showing a ratio of 4 parts of regular milk to 3 parts of chocolate milk. You can visualize it as:

[Regular Milk: 4 parts] [Chocolate Milk: 3 parts]

In the diagram, the regular milk and chocolate milk will be represented in 4:3 proportions, where each "box" on the diagram represents a part in the ratio.

b. The school ordered 120 cartons of regular milk. Divide 120 cartons of regular milk by ______ because there are ______ boxes in the top row. There are 4 boxes representing regular milk in the ratio diagram. So, we divide the 120 cartons of regular milk by 4 (because there are 4 boxes in the top row for regular milk). This gives:

• 120 ÷ 4 = 30

Thus, the number of chocolate milk cartons would be:

• 30 × 3 = 90

So, the school ordered 90 cartons of chocolate milk.

Would you like to explore more details or have any questions on this?

Here are 5 related questions you might find helpful:

1. What are some real-world examples of ratios and their applications?
2. How do you simplify ratios further?
3. What is the relationship between a ratio and a proportion?
4. How do you calculate the percentage of girls in the chorus based on the ratio?
5. How can bar diagrams help in understanding ratios in different contexts?

Tip: To simplify a ratio, always check if the numbers have any common factors and divide both parts of the ratio by the greatest common divisor (GCD).