Problem 42 - Prealgebra

Question

Add and subtract as indicated. $$(8.3-1.2)+3.4$$

Step-by-Step Solution

Answer

10.5

Step 1: Calculate the Difference

First, we need to subtract 1.2 from 8.3. Begin by aligning the decimal numbers vertically. Perform the subtraction: \[8.3 - 1.2 = 7.1\]So the result of the subtraction is 7.1.

Step 2: Add the Result to 3.4

Now, add the result from Step 1 to 3.4. Again, align the decimal numbers vertically and perform the addition: \[7.1 + 3.4 = 10.5\]The result of the addition is 10.5.

Key Concepts

Addition

Addition is one of the fundamental operations in mathematics. It helps us combine numbers to find the total. When adding numbers, it's important to ensure that the numbers are aligned correctly, especially if they involve decimal points. This is crucial because every digit should be in its correct place value.
For instance, when adding decimal numbers such as 7.1 and 3.4, align the decimals vertically:

• Place 7.1 and 3.4 one under the other, making sure the decimal points are aligned.
• Start adding from the rightmost digit, moving towards the left.
• If digits in a column add up to more than 9, carry the additional value over to the next column on the left.

When we add these, we get:\[\begin{array}{c} 7.1+ \ \underline{3.4} \ 10.5 \\end{array}\]This process gives us a final result of 10.5.

Subtraction

Subtraction is another primary arithmetic operation that allows us to find the difference between numbers. Just like addition, when dealing with decimal numbers, it's essential to align the numbers by their decimal points.
Consider the subtraction of 1.2 from 8.3:

• Align the decimals so that each digit is in the correct positional column.
• Subtract the numbers starting from the right, just like with addition.
• If the top digit is smaller than the bottom digit in any column, you may need to borrow from the next left column.

For our subtraction:\[\begin{array}{c} 8.3- \ \underline{1.2} \ 7.1 \\end{array}\]This results in a difference of 7.1.

Decimal Numbers

Decimal numbers are a way of representing numbers that include fractions of ten. They are used for precision and are commonly found in everyday situations, such as money or measurements.
Reading and interpreting decimal numbers can be straightforward once you understand their place value.

• The number 8.3 has '8' as the whole number and '.3' represents 3 tenths.
• Likewise, 1.2 has '1' as the whole number and '.2' as 2 tenths.
• They are written using the decimal point to separate the whole number part from the fractional part.

When working with these numbers, it's crucial to maintain the alignment of the decimal points for accuracy in calculations. This ensures that you are adding or subtracting numbers from the correct place values, whether they are whole numbers or fractional parts.