Taking Away: Subtraction
Subtraction explores the fundamental operation of finding the difference between numbers, including whole numbers, decimals, and fractions. It examines how to handle borrowing, align digits properly, and work with different number types, empowering learners to solve everyday problems like calculating change, measuring differences, or tracking progress with confidence.
Components of Subtraction
This section breaks down the core aspects of performing subtraction across different number types:
- Whole Numbers: Subtracting integers without fractions or decimals, focusing on place value and borrowing.
- Decimals: Subtracting numbers with decimal points, ensuring proper alignment of digits.
- Fractions: Subtracting numbers with numerators and denominators, including finding common denominators.
- Applications of Subtraction: Practical uses of subtraction in real-life scenarios, such as determining differences or remaining amounts.
Examples of Subtraction
Whole Numbers Examples
- Subtracting 45 - 19: Borrow 1 from 4 (making it 3) so 15 - 9 equals 6, then 3 - 1 equals 2, resulting in 26.
- Finding the difference 103 - 78: Borrow across columns so 13 - 8 equals 5, 9 - 7 equals 2, giving 25.
- A student had 50 candies and gave away 23, subtracting 50 - 23 to find they have 27 candies left.
Decimals Examples
- Subtracting 5.73 - 2.19: Align the decimals, borrow so 13 - 9 equals 4, then 6 - 1 equals 5, and 5 - 2 equals 3, resulting in 3.54.
- Finding the difference 4.00 - 1.25: Borrow across, 10 - 5 equals 5, 9 - 2 equals 7, 3 - 1 equals 2, totaling 2.75.
- A shopper spends 10.50 from a budget of 15.00, subtracting 15.00 - 10.50 to find they have 4.50 remaining.
Fractions Examples
- Subtracting 3/4 - 1/4: Since the denominators are the same, subtract 3 - 1 to get 2, resulting in 2/4 or 1/2.
- Finding the difference 5/6 - 1/3: Use a common denominator (6), rewrite 1/3 as 2/6, then subtract 5/6 - 2/6 to get 3/6, simplified to 1/2.
- A recipe uses 2/3 cup of flour but only has 1/4 cup, subtracting with common denominator 12 gives 8/12 - 3/12 equals 5/12 cup needed.
Applications Examples
- A runner aims for 5.0 miles but only runs 3.25 miles, subtracting 5.0 - 3.25 to find they are 1.75 miles short.
- A child had 30 dollars and spent 12 dollars, subtracting 30 - 12 to calculate they have 18 dollars left.
- In a game, a player starts with 3/4 point and loses 1/2 point, subtracting 3/4 - 2/4 to get 1/4 point remaining.