Question

Using the information in the following chart, estimate to the nearest thousand the total number of tickets sold at the concert hall. (Note: You may not use a calculator.) \begin{tabular}{ll} \hline \hline pcert & Tickets Sold \\ \hline Ghastly Girls & 4,721 \\ \hline Directions & 5,301 \\ \hline lor Speedy & 8,783 \\ \hline oon 6 & 270 \\ \hline Subdominants 11,802 \\ \hline \hline \end{tabular} (A) 27,000 (B) 29,000 (C) 31,000 (D) 31,877

Short answer

The estimated total number of tickets sold at the concert hall is \(31,000\).

Step-by-step solution

Round each number to the nearest thousands

First, we will round each number in the "Tickets Sold" column to the nearest thousand. This will make addition easier without a calculator. - Ghastly Girls: 4,721 ≈ 5,000 - Directions: 5,301 ≈ 5,000 - lor Speedy: 8,783 ≈ 9,000 - oon 6: 270 ≈ 0 (This number is less than 500, so we'll round it down to 0.) - Subdominants: 11,802 ≈ 12,000

Add these rounded numbers

Now, add up the rounded numbers to get an estimate for the total tickets sold: 5,000 + 5,000 + 9,000 + 0 + 12,000 = 31,000

Choose the correct answer

With our estimate of 31,000 total tickets sold, we can choose the closest answer among the options given: (A) 27,000 (B) 29,000 (C) 31,000 (D) 31,877 Our estimate matches option (C), so the correct answer is (C) 31,000 tickets sold.

Key concepts

Rounding Numbers

Rounding numbers is a fundamental skill in arithmetic, particularly useful when exact figures are not required or when simplicity is needed for quick calculations. The concept of rounding involves adjusting a number to the nearest digit of significance. When estimating, we often round to the nearest ten, hundred, or thousand, depending on the context. For instance, in the GED Math practice exercise involving concert ticket sales, each number was rounded to the nearest thousand.

To round a number, look at the digit to the immediate right of the target place value. If this digit is five or more, increase the target digit by one; if it's less than five, leave the target digit unchanged and change all digits to the right of it to zero. Following this, rounding 4,721 to the nearest thousand results in 5,000 because the digit in the hundreds place (7) is greater than five. This simplification through rounding is particularly effective when performing arithmetic without a calculator.

Estimation

Estimation is a process of finding an approximate value that is sensibly close to an exact amount. The skill of estimation is particularly useful for making quick decisions or checking the reasonableness of a calculated result. To estimate, one often uses rounding as a tool. In the exercise above, estimation is used to quickly determine the approximate total number of tickets sold.

When estimating a sum, as with the concert ticket problem, we first rounded each individual number to the nearest thousand and then added these rounded numbers together. This gives a reasonable approximation without the use of a calculator, saving time on complex calculations. In GED Math practice, becoming proficient in estimation means being comfortable with rounding numbers and using these estimated figures to quickly arrive at an approximate answer.

Arithmetic Without a Calculator

In many testing environments, such as the GED exam, calculators may not be permitted for certain sections. This necessitates proficiency in manual arithmetic, including addition, subtraction, multiplication, and division. By rounding and estimating as shown in the exercise, one can perform these operations more simply.

Without a calculator, adding large numbers together might be daunting, but when those numbers are rounded, it becomes much more manageable. As seen with the concert ticket sales, by rounding each figure to the nearest thousand, we avoid dealing with hundreds, tens, and ones. It simplifies mental math, and while it may not give an exact value, it provides a close estimate that is valuable in multiple-choice scenarios where options are given. Regular practice with such problems enhances arithmetic skills and builds confidence in tackling calculations without technology.