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How to Calculate the Fraction of Tennis Club Members Aged 30-39 (Simplest Form)
Mathematics
Grade 6 (Primary School)
Question Content
What fraction of tennis club members are aged 30 to 39 years old? Give your answer in its simplest form. (A stacked bar graph shows the number of tennis club members by age group: 20 to 29: 4 members, 30 to 39: 13 members, 40 to 49: 2 members, 50+: 1 member)
Correct Answer
13/20
Detailed Solution Steps
1
Step 1: Calculate the total number of tennis club members by adding the number of members in each age group: 4 (20-29) + 13 (30-39) + 2 (40-49) + 1 (50+) = 20 total members.
2
Step 2: Identify the number of members aged 30 to 39, which is 13.
3
Step 3: Form the fraction by putting the number of 30-39 year olds over the total number of members: 13/20.
4
Step 4: Check if the fraction can be simplified. Since 13 is a prime number that does not divide 20, 13/20 is already in simplest form.
Knowledge Points Involved
1
Reading Stacked Bar Graphs
A stacked bar graph divides each bar into segments to represent different categories within a group. To find the value of a segment, read the height of the segment from the y-axis. This is used to extract numerical data from visual representations.
2
Fraction Representation of a Part-to-Whole Relationship
To represent a part of a whole as a fraction, the numerator is the quantity of the specific group, and the denominator is the total quantity of the entire set. This is used to express proportions of a group.
3
Simplifying Fractions
A fraction is in simplest form when the numerator and denominator have no common positive divisors other than 1. To simplify, divide both the numerator and denominator by their greatest common divisor. If the numerator is a prime number that does not divide the denominator, the fraction is already simplified.
4
Addition for Total Quantity Calculation
To find the total size of a set with multiple subgroups, add the sizes of all individual subgroups together. This is a basic arithmetic operation used to find whole quantities from parts.
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