Problem 88 - Prealgebra

Question

Compute the quotient \(21 / 38\), and round your answer to the nearest tenth.

Step-by-Step Solution

Answer

The quotient is approximately 0.6.

Step 1: Understand the Problem

We need to divide 21 by 38 and then round the result to the nearest tenth.

Step 2: Perform the Division

Divide 21 by 38 to find the quotient. Use a calculator or long division for this step.\[\frac{21}{38} \approx 0.5526\]

Step 3: Round the Quotient

Look at the hundredths place (the second digit after the decimal point) in our quotient, 0.5526, which is '5'. Since '5' is 5 or greater, we round the tenths place up by one. Thus, round 0.5526 to 0.6.

Key Concepts

Understanding the Quotient

The term 'quotient' is a fundamental concept in division. It is the result you get after dividing one number by another. Dividing involves taking a larger number (the dividend) and splitting it into smaller slots defined by another number (the divisor). In this case, 21 is the dividend and 38 is the divisor.
When you perform the division of 21 by 38, you'll find that the quotient falls between 0 and 1, because 21 is smaller than 38. More precisely, by using a calculator or long division, we find the quotient to be approximately 0.5526. This tells us how many times the divisor, 38, goes into the dividend, 21, in whole and in part.

• Dividend: The number being divided, here it is 21.
• Divisor: The number you are dividing by, here it is 38.
• Quotient: The result of the division, which is approximately 0.5526.

Rounding for Simplicity

Rounding is the process of adjusting the digits of a number according to certain rules. It's used to simplify numbers to make them easier to work with. In the original exercise, we must round the quotient of 0.5526 to the nearest tenth.
Rounding involves checking the digit right after the decimal place we want to round to—the tenths place in this instance. The hundredths place is the deciding factor. The rule is simple:

• If the digit in the hundredths place is 5 or more, increase the tenths place by 1.
• If the digit is less than 5, leave the tenths place as it is.

Using our quotient 0.5526, the hundredths place is 5. Since it's 5 or higher, we round up our tenths place from 5 to 6. So, 0.5526 becomes 0.6 when rounded to the nearest tenth.

Grasping Long Division

Long division is a traditional method for dividing two numbers and finding the quotient manually. It's helpful for understanding the division process thoroughly, especially when you don't have a calculator on hand.
To perform long division, you follow a sequence of steps:

• Divide: Determine how many times the divisor can go into the dividend's first digit or first few digits.
• Multiply: Multiply the divisor by that digit and write it beneath the dividend.
• Subtract: Subtract this product from the dividend or the current number you're working with.
• Bring down: Bring down the next digit of the dividend to form a new number.
• Repeat: Repeat these steps until no digits remain to bring down.

In our example of dividing 21 by 38, you would find that 38 goes into 21 zero times initially, leading you to expand your division into numbers with decimals, ultimately reaching the quotient of 0.5526. Although a calculator can quickly give you this result, long division provides deep insights into how division really works.