Problem 49 - Prealgebra

Question

Add and subtract as indicated. Subtract 5 from the sum of 8.2 and 0.072.

Step-by-Step Solution

Answer

The result of subtracting 5 from the sum of 8.2 and 0.072 is 3.272.

Step 1: Understand the Problem

We need to find the result of the operation where we first add 8.2 and 0.072, and then subtract 5 from this result.

Step 2: Add the Numbers

Calculate the sum of 8.2 and 0.072. To do this, ensure both numbers have the same number of decimal places. Thus, rewrite 8.2 as 8.200 and then add:\[ 8.200 + 0.072 = 8.272 \]

Step 3: Subtract from the Sum

Take the result from Step 2, which is 8.272, and subtract 5:\[ 8.272 - 5 = 3.272 \]

Step 4: Solution Review

Review the calculations to ensure the accuracy of the addition and the subtraction steps. Once verified, the final answer is 3.272.

Key Concepts

Understanding Addition

Addition in prealgebra is all about combining quantities. It is one of the most fundamental operations. When we add numbers, we align them by place value. This means we match up units, tens, hundreds, and so on.

When dealing with decimal numbers, things follow the same rule. It's crucial to ensure that the decimal points are lined up with each other. In situations where numbers have differing decimal places, adding zeros to the end of a shorter decimal can help.

• For example, when adding 8.2 and 0.072, rewriting 8.2 as 8.200 makes the calculation straightforward.
• This way, both numbers have three decimal places, and you can easily add them up to get 8.272.

Understanding and applying this method can make complex additions much simpler.

The Process of Subtraction

Subtraction is the process of taking one number away from another. In prealgebra problems, it's important to consider the placement of decimal points as well.

When you subtract a smaller number from a larger one, align the decimal points to ensure the accuracy of your calculation. This was crucial in our exercise when subtracting 5 from 8.272. When needed, add zeros to the whole number to match the decimal length.

• In the example given in our problem, 5 becomes 5.000 which aligns perfectly with 8.272 for easy subtraction.
• After aligning, subtract to obtain the answer, in this case, 3.272.

Subtraction is not just about removing numbers but ensuring careful alignment for precision in results.

Mastering Decimal Places

Decimal places play a critical role in both addition and subtraction. They allow us to express values that are not whole numbers and require care when performing arithmetic operations.

In both addition and subtraction, aligning decimal places ensures that each digit corresponds correctly with its value.

• Decimals are fractions expressed in a base of ten, so each move to the right represents a division by ten (e.g., tenths, hundredths, thousandths).
• This concept was particularly significant in our problem when rewriting 8.2 to 8.200 to match the decimal places of 0.072.

Understanding how to manage decimal places will allow you to handle a wide range of arithmetic problems with ease and accuracy.