Grade 2
  1. Number Sense and Operations  1.1. Counting and Number Sequences  1.1.1. Counting up to 100  1.1.2. Counting by 2s, 5s, and 10s  1.1.3. Counting Backward from 20  1.1.4. Odd and even numbers in counting sequences  1.2. Place Value  1.2.1. Understanding ones and tens  1.2.2. Comparing Two-Digit Numbers  1.2.3. Identifying the Value of Each Digit in a Number  1.2.4. Building numbers using tens and ones  1.3. Addition and Subtraction  1.3.1. Basic addition up to 20  1.3.2. Basic subtraction up to 20  1.3.3. Addition with Regrouping  1.3.4. Subtraction with Borrowing  1.3.5. Solving word problems involving addition and subtraction  1.3.6. Addition and Subtraction with Multiples of 10  1.4. Odd and Even Numbers  1.4.1. Identifying Odd and Even Numbers  1.4.2. Understanding patterns in odd and even numbers  1.4.3. Simple operations with odd and even numbers
  2. Fractions and Decimals  2.1. Introduction to Fractions  2.1.1. Understanding halves and quarters  2.1.2. Representing fractions visually  2.1.3. Simple Fraction Comparisons  2.1.4. Writing Simple Fractions  2.1.5. Fractions as part of a whole  2.2. Fraction Equivalency  2.2.1. Understanding Equal Parts  2.2.2. Identifying Equivalent Fractions
  3. Measurement and Data  3.1. Length Measurement  3.1.1. Measuring objects using rulers  3.1.2. Comparing lengths  3.1.3. Estimating lengths  3.1.4. Understanding units of measurement (centimeters and inches)  3.1.5. Relating Length Measurements to Real-World Objects  3.2. Weight and Mass Measurement  3.2.1. Comparing Weights of Objects  3.2.2. Estimating weight in grams and kilograms  3.2.3. Using balance scales for comparison  3.3. Volume and Capacity Measurement  3.3.1. Understanding capacity with cups and liters  3.3.2. Comparing capacities of containers  3.3.3. Introduction to Milliliters  3.4. Time  3.4.1. Reading analog and digital clocks  3.4.2. Understanding hours and minutes  3.4.3. Calculating elapsed time in hours  3.4.4. Days of the week and months of the year  3.4.5. Understanding AM and PM  3.5. Money  3.5.1. Recognizing coins and bills  3.5.2. Counting money up to $1  3.5.3. Simple Addition and Subtraction with Money  3.5.4. Making Change for a Dollar
  4. Geometry and Spatial Reasoning  4.1. Shapes and Their Attributes  4.1.1. Identifying basic shapes (circle, triangle, square, rectangle)  4.1.2. Understanding sides and corners  4.1.3. Distinguishing between 2D and 3D shapes  4.1.4. Recognizing 3D Shapes (Cube, Sphere, Cone, Cylinder)  4.1.5. Composing and Decomposing Shapes  4.2. Symmetry  4.2.1. Understanding Lines of Symmetry  4.2.2. Drawing Symmetrical Shapes  4.2.3. Identifying Symmetrical Objects in the Environment  4.3. Patterns and Spatial Awareness  4.3.1. Recognizing and Creating Patterns  4.3.2. Extending Patterns  4.3.3. Understanding positions (left, right, above, below)  4.3.4. Using a grid to locate objects
  5. Data Handling and Probability  5.1. Collecting and Organizing Data  5.1.1. Using tally marks  5.1.2. Reading Bar Graphs  5.1.3. Simple Pictographs  5.1.4. Creating Bar Graphs from Given Data  5.2. Interpreting Data  5.2.1. Answering questions based on data  5.2.3. Identifying Most and Least in Data Sets  5.3. Introduction to Probability  5.3.1. Understanding likely and unlikely events

Grade 2 → Number Sense and Operations → Addition and Subtraction ↓


Subtraction with Borrowing


Subtraction with borrowing, often referred to as "rearrangement" or "trading," is an important arithmetic operation used in mathematics, when larger numbers are subtracted from smaller numbers. Let's learn how this process works, step by step, and with enough examples to build a strong understanding of the concept.

Understanding borrowing and subtracting

When we subtract two numbers, we subtract a smaller number (the subtractant) from a larger number (the minuend). There are times when the top number (the minuend) in one or more columns is smaller than the bottom number (the subtractant). When this happens, we need to borrow from the next column to the left to perform the subtraction.

Borrowing is like temporarily taking a value from the next higher place value to make subtraction possible. Let's look at a visual example to understand this better:

31 - 17 Step 1: Check the unit location 1 (ones) - 7 (ones) = not possible Step 2: Borrow from the tens place Cross out 3, it becomes 2 (ten) Add 10 to the unit: 11 (unit)

Step-by-step example

Let us understand the example of 31 minus 17 on the basis of borrowing.

  1. Identify the column that needs borrowing: In 31, 7 cannot be subtracted from the number 1 in the units place because 1 is smaller than 7.
  2. Borrow from the tens place: Borrow 1 tens from the 3 in the tens place. 3 becomes 2.
  3. Add it to the ones place: Add the borrowed ten to the ones place. Since we are borrowing a "ten," we add 10 to the ones place, turning 1 into 11.
  4. Subtract as usual: Now subtract 7 from 11. This will equal 4.
  5. Go to the next column: go to the tens place. Subtract 1 (the tens place of 17) from 2 (now borrowed from the borrowed tens place of 31), which is 1.
  6. Result: The difference is 14.
2 1 (originally 31) - 1 7 ------ 1 4

Why is borrowing important?

Borrowing is essential for fluency in arithmetic calculations involving subtraction. It helps in dealing with larger numbers, making it easier to handle complex calculations. Learning to borrow at an early age prepares students for advanced mathematical concepts.

Text example without borrowing

Consider trying to subtract 7 from 1 without borrowing:

3 1 - 1 7 ------

As you can see, it is impossible to cut costs in the current situation without going below zero, so we resort to borrowing.

See more examples

Example 2: 52 - 28

52 - 28 Step 1: Check the unit location 2 (ones) - 8 (ones) = not possible Step 2: Borrow from the tens place Cross out 5, it becomes 4 (ten) Add 10 to the unit: 12 (unit) 
4 12 (originally 52) - 2 8 ------ 2 4

Its analysis:

  1. Check the units place: You can't subtract 8 from 2 directly, so borrowing is necessary.
  2. Borrow from tens: Give 5 from 10 (which will be 4) Give 2 from 12.
  3. Subtract the units digit: 12 - 8 = 4.
  4. Subtract the tens place: 4 - 2 = 2.
  5. The result is 24.

Practice makes perfect

Let's practice more problems to master subtraction by borrowing:

Problem 1

714 - 436
  1. Units place: 4 < 6, borrow from tens.
  2. Tens place: 1 borrows from 7 and turns it into 6 (and has 14 in the ones place).
  3. New equation: 14 (at units) - 6 = 8.
  4. New tens place: 0 - 3 borrow from hundreds.
  5. Subtract and shuffle. The thousands place handles remainders.
6 14 - 4 36 ------ 2 78

Problem 2

103 - 68
  1. Single Position: Can't do 3 - 8, need to borrow.
  2. Tens place: Can't borrow from 0, borrow from hundreds.
  3. This is rewritten as: 9 in the tens place, and 13 in the units place.
  4. Now basic subtraction works as:
0 9 13 (adjust numbers) - 6 8 ------ 3 5

These examples help explain the borrowing process in a more visual way. Once we understand the visualization, the process becomes easier with practice and patience.

Tips to reduce borrowing

Here are some tips to make borrowing more accessible:

  • Think in terms of place value: always consider the ones, tens, hundreds, etc.
  • Be careful with columns: align numbers correctly to avoid errors.
  • Practice mental math: Familiarity and speed increase over time.
  • Go slowly in the beginning: Going slowly can help strengthen understanding.
  • Check your work yourself: Revisit the problem solution to verify that you borrowed correctly.

Subtracting by borrowing is a core math skill that applies from elementary school to more complex problem-solving in higher math. Building a solid foundation for borrowing can help build confidence in solving a variety of arithmetic problems.

Conclusion

In conclusion, mastering subtraction by borrowing is a step towards being life-long comfortable with numbers. We understand borrowing as taking a higher value to aid in simpler subtraction operations that lead to the correct results.

The ability to mentally represent place values and borrow builds confidence and develops the mathematical proficiency students need to progress in their education. Learning to borrow can be exciting with visualization and frequent practice that contributes to the enjoyment of numerical mastery.


Grade 2 → 1.3.4


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Addition with Regrouping
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Solving word problems involving addition and subtraction

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Subtraction with Borrowing

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