Problem 41 - Prealgebra

Question

What is the value of sixty divided by the sum of two and ten?

Step-by-Step Solution

Answer

The value is 5.

Step 1: Understand the Problem

We need to find the value of 60 divided by the sum of 2 and 10. In mathematical terms, this means we calculate the sum of 2 and 10 first, and then divide 60 by that result.

Step 2: Sum Calculation

Add the two given numbers, 2 and 10. \[ 2 + 10 = 12 \]

Step 3: Division

Now divide 60 by the result from the previous step, which is 12. \[ 60 \div 12 = 5 \]

Key Concepts

Division

Division is one of the four fundamental operations in arithmetic that deals with splitting a large number into equal smaller parts. Imagine you've got a pie and you want to share it equally with your friends. Division helps us do that. In our exercise, we're interested in finding out how many times one group can fit into another. Here, we divide the number 60 by the sum of 2 and 10, which is 12. This means we are looking to see how many sets of 12 can fit into 60.

A simple way to write this operation is \(60 \div 12\). When you perform this calculation, you find that 60 divided by 12 results in 5. This means that you can have 5 equal groups of 12 from 60.

• The number you are dividing is called the dividend (in this case, 60).
• The number you divide by is the divisor (here, the sum 12).
• The result is the quotient (5 in our problem).

Understanding division is key in problem-solving, as it helps you work out how resources can be evenly distributed.

Addition

Addition is the process of combining two or more numbers to get a total sum. It is the most basic form of arithmetic used in almost every calculation.
In our exercise, the first step is addition where you add 2 and 10. When you add \(2 + 10\), you get 12. This operation tells you the total when two amounts are combined. Addition is handy in everyday situations, like when you calculate your expenses or combine quantities.

• It is commutative, meaning \(a + b = b + a\).
• It is associative, which means \(a + (b + c) = (a + b) + c\).
• The number 0 is the identity element because any number plus zero equals the original number.

Addition is essential for breaking down and simplifying more complex mathematical processes, laying the groundwork for operations like our division task.

Problem Solving

Problem-solving means breaking down a question into manageable parts to find a solution. It requires critical thinking and often involves implementing basic mathematical operations like addition and division. Here, the process of solving our problem involves understanding both operations sequentially.
Effective problem-solving involves several steps:

• Understand the problem: Translate the words into mathematical operations. Here, it was breaking down "sixty divided by the sum of two and ten" into its mathematical form.
• Plan: Identify the operations needed (addition, then division in our case).
• Solve: Apply the operations. Add 2 and 10 to get 12, then divide 60 by 12.
• Review: Check if your result makes sense. In this instance, it checks out as 60 divided equally by 12 resulting in 5.

Mastering problem-solving in math will help you apply these concepts in real-life scenarios, making it a valuable skill beyond just learning arithmetic.