Problem 26 - Fundamentals of Mathematics

Question

Find the value of each of the following. Use a calculator to check each result. $$ \frac{42}{6} $$

Step-by-Step Solution

Answer

The value of \( \frac{42}{6} \) is 7.

Step 1: Understand the Problem

We need to find the value of the division \( \frac{42}{6} \). This means we need to determine how many times the number 6 is contained in the number 42.

Step 2: Perform the Division

Divide 42 by 6. To do this, ask how many times 6 fits into 42. Since 6 times 7 equals 42, the division \( \frac{42}{6} \) is equal to 7.

Step 3: Verify with Calculator

Use a calculator to check that dividing 42 by 6 gives you the result 7. Enter '42', press the division sign, enter '6', and then press equals. You should see the number 7 displayed.

Key Concepts

Arithmetic

In the world of numbers, arithmetic serves as the basic playground. It is where we perform operations such as addition, subtraction, multiplication, and division. Each of these operations helps us understand more complex mathematical concepts. Here, we focus on division, a key part of arithmetic, where we determine how many times one number fits into another. This is represented as \( \frac{a}{b} \), meaning how many times \( b \) can divide \( a \). In simpler terms, division asks the question, "How many groups of \( b \) can we form from \( a \)?" In our example \( \frac{42}{6} \), we ask how many sets of 6 fit into 42, which is 7 sets.

Division Process

The division process is a straightforward yet critical part of arithmetic. It consists of a few basic steps:

• Identify the dividend: This is the number you want to divide. In our example, it is 42.
• Identify the divisor: This is the number you want to divide by. In our example, it is 6.
• Calculate how many times the divisor fits into the dividend: Using multiplication as a guide, we see 6 fits into 42 exactly 7 times, without leftovers.

Thus, the result of our division \( \frac{42}{6} \) is 7. This step-by-step breakdown ensures that we understand the division, not just get the answer. It's vital to remember, division is about grouping or partitioning a number into equal parts.

Calculator Verification

Once we've performed the division manually, it's time to use technology to ensure accuracy. A calculator is a handy tool when verifying results. Here's how you can verify your division with a calculator:

• Enter the dividend (42 in our example).
• Press the division symbol, often shown as / or ÷.
• Enter the divisor (6 in our example).
• Press the equals sign to compute the result.
• Check the displayed result, which should be 7.

This method not only confirms your manual calculations but also reinforces trust in using calculators as reliable tools for arithmetic tasks. It's always good practice to double-check, especially when accuracy is essential.