Question

Each year, 64 golfers participate in a golf tournament. The golfers play in groups of 4 . How many groups of 4 golfers are possible?

Short answer

There are 16 groups of 4 golfers.

Step-by-step solution

Identify the total number of golfers and the group size

In this exercise, the total number of golfers is 64 and each group should consist of 4 golfers.

Calculate the number of groups

To find out how many groups can be formed, divide the total number of golfers (64) by the number of golfers per group (4). Using a calculator or paper and pen, perform the division: \( \frac{64}{4} \).

Interpret the result

The result of the division operation is the number of groups of 4 golfers that can be formed from 64 golfers. This is the solution to the problem.

Key concepts

Grouping

Grouping is a fundamental concept in mathematics, particularly when dealing with division problems. It involves organizing a large set into smaller, manageable subsets.
In our exercise, the 64 golfers need to be divided into smaller groups of 4 golfers each. The purpose of grouping here is to determine how many separate teams or units can be formed from the whole.
Understanding grouping helps simplify tasks by breaking a complex problem into smaller, more straightforward components.

• It aids in systematic organization
• Facilitates easy counting and arrangements
• Refines problem-solving skills by delineating clear steps

The skill of grouping extends beyond math into everyday life, where organizing events or objects into groups can enhance efficiency and clarity.

Basic Arithmetic

Basic arithmetic forms the foundation for solving many math problems, including those involving division and grouping. This core concept encompasses the primary operations: addition, subtraction, multiplication, and division.
In our task of grouping golfers, division is utilized to determine the number of possible groups. However, understanding and mastering addition and multiplication are equally essential for verifying division calculations:

• Addition helps sum things together, like counting total golfers
• Subtraction allows figuring out remainders, which isn’t needed in our exact division, but useful otherwise
• Multiplication supports division by allowing reverse-checks: if 16 groups of 4 equals a total of 64

Fundamental arithmetic ensures that you can confidently maneuver through and solve straightforward and complex problems alike.

Problem Solving

Problem solving is a vital skill in mathematics, requiring a strategy to tackle questions systematically. In many cases, like the golf tournament problem, it involves identifying given information and deciding on mathematical operations to reach the solution.
The steps usually include:

• Comprehending what is being asked
• Breaking down the problem into smaller parts, like finding the total number and size of groups
• Applying the correct arithmetic operation, in this instance, division

Effective problem solving also means interpreting the results accurately, as the division tells us how many groups of 4 are possible.
Developing problem-solving skills can significantly aid in not just academics but also in everyday decision-making processes.

Division Operation

The division operation is a key part of arithmetic that allows us to determine how many times one number is contained within another. In simple terms, it’s about sharing or grouping quantities evenly.
For our question, division answers how many groups of 4 can be made from 64 golfers. The process involves:

• Setting up the problem: the total number divided by group size, i.e., \( \frac{64}{4} \)
• Calculating the result, which in this case is 16
• Understanding that the result signifies the number of equal groups formed

Mastery of the division operation allows efficient computation of resources, whether in dividing items or understanding proportions in broader scenarios.
Remember, division can often simplify large problems, making them more manageable and less daunting.