Matemáticas - Resta y Propiedades

Definition and Concept

• Restas are a fundamental arithmetic operation.
• It represents the difference between two numbers.
• Subtracting one number from another is a key mathematical operation.
• The operation is depicted using the subtraction symbol (-).

Basic Subtraction

• The minuend is the larger number.
• The subtrahend is the smaller number.
• The difference is the result of the subtraction.
• Example: 10 - 5 = 5.

Properties of Subtraction

• The order matters: a - b ≠ b - a, unless a = b. (Non-commutative)
• Subtraction is not associative: (a - b) - c ≠ a - (b - c), in general.
• Subtraction of zero from a number results in the number itself: a - 0 = a
• Subtracting a number from itself results in zero: a - a = 0
• Subtracting a number from a smaller number results in a negative number: 5 - 8 = -3

Borrowing (or Carrying)

• Used when the digit in the subtrahend is larger than the digit in the minuend.
• Involves regrouping from the next higher place value.
• Example: 25 - 8 = ? 25 can be regrouped as 1 tens + 15 ones 1 ten + 15 ones = 15 - 8 = 7 ones, 1 ten = 10 Thus 2 ten + 5 one - 8 one =1 ten + 7 one

Mental Subtraction Strategies

• Counting back: Subtract the subtrahend by counting backward from the minuend.
• Using number lines: Visualize the numbers on a number line and find the difference.
• Breaking down numbers: Break the subtrahend into smaller parts for easier subtraction.

Subtraction with Larger Numbers

• Similar to basic subtraction, but with more digits.
• Follow the same borrowing/carrying rules for each place value.
• Example: 234 - 128 = ? Hundreds: 2 - 1 = 1 hundred Tens: 3 - 2 = 1 ten Ones: 4 - 8 (Requires borrowing).

Word Problems

• Subtraction is frequently used to solve word problems.
• Determine the known and unknown quantities in the problem.
• Determine which operation (addition or subtraction) will solve the problem
• Perform the calculations and find the solution.
• Example: If a store has 50 apples and sells 25, how many are left? (50 - 25 = 27)

Subtraction in Different Bases

• Subtraction can be performed in different number systems (e.g., binary, base 8).
• The borrowing/carrying rules will change, however the concept is same.

Real-World Applications

• Budgeting: Calculate the difference between income and expenses.
• Measuring: Find the difference in length or weights of two objects
• Comparisons: Decide which product has lower price.

Negative Numbers in Subtraction

• When subtracting a larger number from a smaller number, a negative result should be expected.
• Understanding the rules involving negative values for subtraction.
• Performing subtraction of negative numbers involve the following principles; for example, if (-5) - (-7), it will be equivalent to (-5) + (-7).