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Chapter 2: Problem 13

Add or subtract. $$36.47-15.21$$

Short Answer

Expert verified
The result of the operation \(36.47 - 15.21\) is \(21.26\).

Step by step solution

01

Align the decimal points

Ensure the decimal places of the two numbers align. Write them one below the other for easier comparison.\n\n 36.47\n - 15.21
02

Subtraction from right to left

Start subtracting from the rightmost digit. Move toward the left, subtracting each corresponding digit from the top number with the bottom one.\n\n 36.47\n - 15.21\n ________\n 21.26
03

Check the correctness

After executing the subtraction, you can run a quick check by adding the result with the subtracted number (15.21). It should equate to the original total (36.47). So, 21.26 + 15.21 = 36.47. If the addition doesn't yield the original total, this means some error has occurred in the subtraction operation.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Aligning Decimal Points
When you start to subtract decimals, the first and foremost step is aligning the decimal points.
This step is crucial to ensure you are subtracting the correct place values. Place the numbers vertically, one above the other, so their decimal points line up. For instance, when you have to subtract \(36.47 - 15.21\), write it out like this:
  • Top number: 36.47
  • Bottom number: 15.21
Align the numbers directly underneath each other according to the decimal point, not the edges of the number. Each digit will then be in its place value column: ones on ones, tenths on tenths, etc.
This way, you can visually and accurately see which numbers to subtract from each grouping of digits.
Subtracting Decimals
Once your decimal points are aligned, it's time to subtract 鈥� just like you would with whole numbers.
Start with the digits in the rightmost column, the hundredths place here, and work your way left.
  • Subtract each column separately: Begin with the far right digits. Here, it鈥檚 \(7 - 1 = 6\). Next is \(4 - 2 = 2\), moving left to the tenths. Then, \(6 - 5 = 1\) for the ones, and finally \(3 - 1 = 2\) for the tens.
  • Borrow if necessary: If the bottom digit in a column is greater than the top digit, borrowing from the next column to the left is necessary, just as in whole number subtraction.
After each subtraction, write down the result directly beneath the column you're working on. Keep your decimals aligned so the final result, \(21.26\) in this example, maintains its correct decimal place.
Checking Subtraction Result
Checking your work helps confirm accuracy. With subtraction, you can easily confirm the result by performing a quick addition. This is done by adding the answer you got to the number you subtracted from to see if it matches the first number.
  • Use the example: In the case of \(36.47 - 15.21\), after getting \(21.26\) as a result, you should add this result back to \(15.21\).
  • Confirmation: Calculate \(21.26 + 15.21\) and check if it equals \(36.47\). If it does, your initial subtraction was likely correct.
If the sum is not the same as the original number, re-evaluate your subtraction steps to locate any errors, ensuring an accurate computation.

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