Problem 15 - Algebra A Combined Function

Question

Add or subtract as indicated. $$ 18-2.78 $$

Step-by-Step Solution

Answer

18 - 2.78 = 15.22.

Step 1: Understand the Problem

We need to subtract the number 2.78 from 18. This operation is a basic subtraction involving a whole number and a decimal.

Step 2: Align the Numbers

Write the number 18 as a decimal with two decimal places for easier alignment with 2.78. Thus, 18 becomes 18.00.

Step 3: Perform the Subtraction

Subtract 2.78 from 18.00 by aligning the decimal points: \[\begin{array}{r} 18.00 \- 2.78 \\hline\end{array}\]Borrow if necessary from the integer part of 18 to complete the subtraction.

Step 4: Calculate the Result

Subtract each column starting from the rightmost digit. After borrowing: \[\begin{array}{r} 17.10 \- 2.78 \\hline 15.22 \end{array}\]Therefore, the result of the subtraction is 15.22.

Key Concepts

Whole Numbers and Decimals

In mathematics, understanding the difference between whole numbers and decimals is essential. Whole numbers are exactly what they sound like - numbers without fractions or decimals. Examples include 0, 1, 2, 3, and so on. On the other hand, decimal numbers include a fractional part separated from the whole number by a decimal point, like 2.78 or 0.56.
When performing arithmetic operations, such as subtraction, involving both whole numbers and decimals, it's important to handle each part correctly. You must convert the whole number to a decimal format if necessary.
For instance, when subtracting 2.78 from 18, as shown in the exercise, it helps to represent 18 as 18.00. This conversion ensures that both numbers align correctly according to their decimal places, simplifying the arithmetic process.

Borrowing in Subtraction

Borrowing is a crucial step in subtraction, especially when the digit being subtracted is larger than the corresponding digit in the minuend (the number from which another number is subtracted).
Consider the subtraction operation of 2.78 from 18.00. Once the numbers are aligned, the process starts from the rightmost digits moving leftwards.
In our example:

• You cannot subtract 8 from 0, so you need to borrow from the next digit to the left, which is the tenths place (0 in 18.00).
• This borrowing involves reducing the nearest left number by 1, turning the 0 into a 10 for subtraction.
• If necessary, continue borrowing from leftward digits until you can complete the subtraction.

Laying out this borrowing process thoughtfully is key to successfully ending up with the correct result, here being 15.22.

Aligning Decimal Points

Aligning the decimal points is a fundamental aspect of performing operations with decimal numbers. It ensures each digit has the same place value during calculations, which is particularly useful in addition and subtraction.
Consider the subtraction of 2.78 from 18. When you write 18 as 18.00, both numbers share two decimal places, allowing easy alignment.
This involves:

• Writing both numbers vertically, ensuring the decimal points of both numbers are directly above each other.
• Filling in additional zeros if necessary, to the right of the whole number, ensuring it matches the decimal length.

This technique simplifies the calculation by making sure digits with similar place values, such as tenths and hundredths, are aligned correctly, preventing any errors during subtraction.