Subtraction of Decimals

Definition

Subtraction of decimals is the process of subtracting two decimal numbers to find the difference between them. It involves aligning the decimal points and subtracting the digits in the corresponding places, just like subtracting whole numbers.

5 Must Know Facts For Your Next Test

1. When subtracting decimals, it is important to align the decimal points of the two numbers before subtracting.
2. If the subtrahend has more decimal places than the minuend, add zeros as placeholders to the minuend to match the decimal places.
3. Regrouping may be necessary when the digit in the subtrahend is larger than the digit in the minuend in the same place value.
4. The result of subtracting decimals will always have the same number of decimal places as the number with the most decimal places.
5. Subtraction of decimals follows the same rules and procedures as subtraction of whole numbers, with the additional step of aligning the decimal points.

Review Questions

• Explain the process of subtracting decimals, including the importance of aligning the decimal points.
  • To subtract decimals, first align the decimal points of the two numbers. This ensures that the digits in the same place value are being subtracted correctly. If the subtrahend has more decimal places than the minuend, add zeros as placeholders to the minuend to match the decimal places. Then, subtract the digits in the corresponding place values, just like subtracting whole numbers. The result will have the same number of decimal places as the number with the most decimal places.
• Describe the concept of regrouping when subtracting decimals and explain why it is necessary.
  • Regrouping is the process of borrowing from the next place value when the digit in the subtrahend is larger than the digit in the minuend. This is necessary to maintain the correct place value and ensure the subtraction is performed accurately. For example, if subtracting 4.72 - 2.89, the 9 in the subtrahend is larger than the 2 in the minuend, so we need to regroup by borrowing 1 from the 7 in the tens place, making it 6.72. This allows us to subtract 9 from 12 and arrive at the correct difference of 1.83.
• Analyze the importance of understanding decimal place value in the context of subtracting decimals.
  • Understanding decimal place value is crucial when subtracting decimals because it ensures that the digits are being subtracted in the correct places. If the decimal places are not properly aligned, the subtraction will not be accurate. Additionally, knowledge of place value helps in determining when regrouping is necessary, as well as understanding the relationship between the minuend, subtrahend, and the resulting difference. Mastering decimal place value allows students to confidently and correctly perform decimal subtraction, which is a fundamental skill in mathematics.

Related terms

Decimal Place Value: The value of a digit in a decimal number based on its position relative to the decimal point.

Place Holder: A zero used as a placeholder to maintain the correct place value when subtracting decimals.

Regrouping: The process of borrowing from the next place value when the digit in the subtrahend is larger than the digit in the minuend.