Borrowing

Definition

Borrowing is a mathematical operation used to facilitate subtraction when the minuend (the number being subtracted from) does not have a sufficient digit in a particular place value to subtract the corresponding digit in the subtrahend (the number being subtracted). It involves temporarily 'borrowing' from the next higher place value to make the subtraction possible.

5 Must Know Facts For Your Next Test

1. Borrowing is necessary when the digit in the minuend is smaller than the corresponding digit in the subtrahend.
2. When borrowing, the value of the minuend's digit is increased by 10, and 1 is subtracted from the next higher place value.
3. Borrowing is a key concept in subtraction of whole numbers, as well as in the addition and subtraction of mixed numbers and decimal operations.
4. Proper understanding of borrowing is crucial for accurately performing multi-digit subtraction problems.
5. Borrowing can be extended to decimal subtraction, where the process involves 'borrowing' from the next higher place value, such as the ones place or the tenths place.

Review Questions

• Explain the purpose of borrowing in the context of subtracting whole numbers.
  • The purpose of borrowing in whole number subtraction is to facilitate the subtraction process when the minuend (the number being subtracted from) does not have a sufficient digit in a particular place value to subtract the corresponding digit in the subtrahend (the number being subtracted). Borrowing involves temporarily 'borrowing' from the next higher place value to make the subtraction possible, increasing the value of the minuend's digit by 10 and subtracting 1 from the next higher place value.
• Describe how the concept of borrowing is applied when adding and subtracting mixed numbers.
  • When adding and subtracting mixed numbers, the concept of borrowing is used in a similar manner to whole number subtraction. If the fractional part of the minuend is smaller than the fractional part of the subtrahend, the whole number part of the minuend is decreased by 1, and 1 whole is 'borrowed' and converted to the appropriate fraction (e.g., 1 whole = 4/4) to be added to the fractional part of the minuend. This allows the subtraction of the fractional parts to be performed, and the whole number part is then adjusted accordingly.
• Analyze the role of borrowing in decimal operations, such as subtraction.
  • In decimal operations, the concept of borrowing is extended to the decimal places. When subtracting decimal numbers, if the digit in the minuend's place value is smaller than the corresponding digit in the subtrahend, the minuend's digit is increased by 10 (by 'borrowing' 1 from the next higher place value, such as the ones place or the tenths place) to allow the subtraction to be performed. This process is repeated for each place value as necessary, ensuring accurate decimal subtraction.

Related terms

Minuend: The number from which another number is to be subtracted.

Subtrahend: The number that is to be subtracted from the minuend.

Place Value: The value of a digit based on its position in a number.