Problem 61 - Algebra 1: Concepts and Skills

Question

ESTIMATING AREA Estimate the area of a rectangle whose sides are given. First round each side length to the nearest whole number. Then multiply to find the area. $$ 17.3 \text { by } 2.8 $$

Step-by-Step Solution

Answer

The estimated area of the rectangle is 51 square units.

Step 1: Rounding The Numbers

The first step is to round the numbers to the nearest whole number. The rule of rounding is if the decimal is less than 0.5, the number is rounded down; if it's 0.5 or more, it's rounded up. Therefore, an approximation for the numbers is: \( 17.3 \) rounded to the nearest whole number becomes \( 17 \) and \( 2.8 \) becomes \( 3 \).

Step 2: Calculating The Area

After we have our approximations, we can calculate the area of the rectangle by multiplying the length and width. So, \( 17 \times 3 = 51 \) square units.

Key Concepts

Rounding Numbers

Rounding numbers is an essential skill in mathematics, especially when estimating values. It involves adjusting a number up or down to the nearest whole number or a specified place value, which makes calculations simpler and quicker. The basic rule for rounding is to look at the decimal point:

• If the digit is 5 or more, round up.
• If the digit is less than 5, round down.

For example, in estimating the area of a rectangle, you might round dimensions like 17.3 to 17 and 2.8 to 3. Rounding helps in making mental calculations more manageable and accurate enough for many practical purposes. It’s particularly useful when precise measurements are not crucial or when working with estimates.

Rectangle Area

The area of a rectangle is a fundamental concept in geometry. It measures how much surface the rectangle covers and is expressed in square units like square meters or square centimeters. To find the area, multiply the length by the width. For example, if you have a rectangular field with a length of 17 meters and a width of 3 meters, its area would be computed as:\[ Area = ext{Length} imes ext{Width} = 17 imes 3 = 51 \] square meters.This formula works because a rectangle has opposite sides that are equal in length. Knowing how to calculate the area of a rectangle is handy in various real-world situations, such as determining how much paint is needed for a wall or how much carpet to buy for a room.

Multiplication

Multiplication is a basic arithmetic operation that represents repeated addition. It is one of the four fundamental operations in math, along with addition, subtraction, and division. In the context of calculating the area of a rectangle, you multiply the length by the width.Multiplication can simplify complex problems and save time. Instead of adding a number to itself multiple times, multiplication does it in one step. For instance, calculating the area of a rectangle with sides that measure 17 units and 3 units is equivalent to adding 17, three times:\[ 17 + 17 + 17 = 51 \]This is the same as simply multiplying:\[ 17 imes 3 = 51 \]Being able to perform multiplication efficiently is crucial in math and science, as it forms the basis for more advanced concepts and calculations.