Problem 54 - Fundamentals of Mathematics

Question

For the following problems, perform the subtractions. You may chedk each difference with a calculator. $$ \begin{array}{r} 59 \\ -26 \\ \hline \end{array} $$

Step-by-Step Solution

Answer

The result is 33.

Step 1: Set Up the Problem

Write the numbers in a vertical format so that their digits are aligned according to place value (units under units, tens under tens). For our problem:\[\begin{array}{r}59 \-26 \\hline\end{array}\]

Step 2: Subtract the Units Column

Subtract the number in the units column on the bottom from the one on the top. So, we subtract 6 from 9. Since 9 is greater than 6, simply subtract:\[9 - 6 = 3\]Write 3 below the line in the units position.

Step 3: Subtract the Tens Column

Move to the tens column and subtract the bottom number from the top number. Subtract 2 from 5:\[5 - 2 = 3\]Write 3 below the line in the tens position.

Step 4: Write Down the Result

After completing the subtractions, the result is:\[33\]

Key Concepts

Place Value

Understanding place value is essential when working with subtraction. Place value refers to the value of each digit in a number, based on its position. For instance, in the number 59, the '5' represents fifty because it is in the tens place, while the '9' represents nine because it is in the units place.

When setting up a subtraction problem, ensure the numbers are aligned according to their place value. Let's look at 59 - 26. Align these numbers in a column with '9' over '6' for units, and '5' over '2' for tens. Do this by placing these numbers in a vertical format:

• Place each digit directly over the corresponding digit in the other number based on their position
• Ensure units (ones) line up vertically, and tens line up on their own

Aligning numbers by place value makes subtraction straightforward, allowing us to subtract each place individually.

Units and Tens

To subtract, begin with the units column, which holds the numbers without any tens—just singular units.
Consider our example subtraction 59 - 26. We focus first on units: 9 - 6. This is straightforward because 9 is larger than 6. Subtract 6 from 9 to get 3. Write it in the units place below the line. This step verifies you've subtracted correctly among units.

Next, move to the tens column. Here, you subtract tens as we did with units. From 59 - 26, subtract tens: position '5' minus '2'. Same as before, 5 is larger than 2, so directly subtract: 5 - 2 = 3. Place the result, 3, below the line in the tens column.

• Subtract units first, then tens
• Always write the result below the corresponding column
• Ensure each step checks out before moving on to the next

This method ensures accuracy and helps in understanding how place values work as individual components during subtraction.

Check with a Calculator

After completing subtraction, it can be beneficial to double-check your work using a calculator. This tool offers a quick way to ensure accuracy.

Start by inputting the numbers you subtracted on the calculator. In our case, type 59, press the minus sign, then type 26, and press equals. The calculator should display 33, confirming your manual calculations were correct.

• Input the first number
• Use the minus (–) function
• Enter the second number
• Press equals (=) to find the result

Performing this check gives confidence in your answer. It is a helpful habit, especially when dealing with more complex problems, ensuring each part of the subtraction was done right.