Math Problem Statement

There are 50 students in a middle school band. Two out of every five are in the 7th grade. Build a diagram that shows, for all students in the band, the number who are in 7th grade and the number who are not.

Solution

To solve this problem, we need to determine how many students are in the 7th grade and how many are not, based on the given ratios.

Given Information:

  • There are 50 students in total.
  • Two out of every five students are in the 7th grade.

Step-by-Step Solution:

  1. Calculate the Fraction in 7th Grade:

    • Since two out of every five students are in the 7th grade, we can express this as a fraction: 25 of the total students are in 7th grade.\frac{2}{5} \text{ of the total students are in 7th grade.}
  2. Determine the Number of 7th Grade Students:

    • Multiply the total number of students by 25\frac{2}{5}: Number of 7th graders=25×50=20.\text{Number of 7th graders} = \frac{2}{5} \times 50 = 20.
  3. Calculate the Number of Students Not in 7th Grade:

    • Subtract the number of 7th graders from the total: Number not in 7th grade=5020=30.\text{Number not in 7th grade} = 50 - 20 = 30.

Diagram Structure

The diagram should have two sections to represent:

  1. 7th Grade Students: 20 students.
  2. Other Students: 30 students.

You can label each section in the diagram accordingly and input "20" and "30" as the numbers of students in each section.

Would you like further assistance with this or additional details?


Related Questions:

  1. If there were 60 students instead of 50, how many would be in the 7th grade?
  2. What fraction of students are not in the 7th grade?
  3. If three out of every five students were in the 7th grade, how many would be in the 7th grade out of 50?
  4. How would the diagram change if only one out of every five students were in the 7th grade?
  5. How can you express the number of students not in the 7th grade as a percentage?

Tip:

Always check the total adds up to the initial number given in ratio problems.

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Math Problem Analysis

Mathematical Concepts

Ratios
Fractions
Basic Multiplication and Subtraction

Formulas

Fraction calculation: part = (ratio) * (total)
Subtraction: total - part

Theorems

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Suitable Grade Level

Grade 6-7