Problem 10 - Fundamentals of Mathematics

Question

Find the following quotients. $$ \frac{51}{17} $$

Step-by-Step Solution

Answer

The quotient is 3.

Step 1: Understand the Problem

The problem requires us to find the result of dividing 51 by 17. Division asks how many times the divisor (17) goes into the dividend (51).

Step 2: Set Up the Division

Write the division expression as a fraction: \( \frac{51}{17} \). This indicates that 51 is to be divided by 17.

Step 3: Perform the Division

Divide 51 by 17 by determining how many times 17 can fit into 51. Start by estimating. 17 \(\times\) 3 is 51, meaning 17 fits exactly 3 times into 51 without a remainder.

Step 4: Verify the Answer

Multiply the result of the division (3) by the divisor (17) to ensure the product is the dividend. 3 \(\times\) 17 = 51. Since this product equals the dividend, the division was performed correctly.

Key Concepts

Dividend

In the world of division, the dividend is the number that you want to divide. It is the starting point of your division problem. When you have the expression \( \frac{51}{17} \), the number 51 is our dividend.

It represents the total quantity you aim to split into smaller, equal parts. The dividend is always on the top part of a fraction if you're using fraction notation for division.

Understanding the role of the dividend is crucial because it sets the context for the division problem:

• It is the total amount being divided.
• Determines how big of a division challenge you're tackling.

Whenever you're faced with a division problem, remember that everything starts by identifying your dividend.

Divisor

The divisor in a division problem is the number you divide the dividend by. It helps determine how many pieces we split our dividend into. In our expression \( \frac{51}{17} \), 17 is the divisor.

The divisor indicates the size of each piece once the number is divided. It's positioned on the bottom half of the division expression as a fraction. Understanding the divisor is key for these reasons:

• It shows how many equal parts we want.
• A deeper understanding reveals the significance of size in splitting.

So when you pick a divisor, you're deciding how extensively the dividend will be partitioned.

Quotient

The quotient is the answer you get after dividing the dividend by the divisor. It tells you the number of times the divisor fits into the dividend without exceeding it. With our problem, \( \frac{51}{17} \), the quotient is 3.

This result means 17 fits into 51 exactly 3 times, leaving no remainder. Remember these points about quotients:

• It provides the count of how many full times the divisor fits within the dividend.
• The quotient can be a whole number or sometimes a decimal if the division doesn't fit exactly.

Using the quotient helps summarize the division and quantify the relationship between the dividend and the divisor.

Remainder

In division, the remainder is what’s left after dividing. It represents the portion of the dividend that the divisor couldn’t evenly divide. However, in our case with \( \frac{51}{17} \), we have a special scenario where there's no remainder since 17 fits into 51 precisely 3 times.

Here’s why understanding the remainder is helpful:

• It shows if our division is exact or approximate.
• A remainder indicates that the division isn't perfectly even.

If there had been a remainder in this problem, it would signify the incomplete part of our division task.