Lesson 5: Subtraction

For Grade 5 Students (Ages 10-11) - Let's master the art of taking away numbers!

What we will learn today:

In this lesson, you will learn to:

  • Subtract numbers up to 100,000 without regrouping.
  • Subtract numbers up to 100,000 with regrouping (borrowing).
  • Solve word problems involving subtraction.
  • Understand the relationship between addition and subtraction.

Introduction to Subtraction

Welcome back, young mathematicians! In our previous lessons, we learned about numbers and patterns. Today, we're going to learn about subtraction, which is all about taking away or finding the difference between two numbers.

Subtraction is a fundamental operation in mathematics. It helps us answer questions like "How many are left?" or "How much more/less?".

Let's dive in and see how subtraction works, even with large numbers!

Subtraction without Regrouping

When we subtract without regrouping, it means that in each place value column, the top digit is greater than or equal to the bottom digit. This makes subtraction straightforward!

Example 1: Subtract $5432$ from $8765$.

We align the numbers by place value and subtract column by column, starting from the Ones place.

    8765
-   5432
------
    3333

Here, $5-2=3$ (Ones), $6-3=3$ (Tens), $7-4=3$ (Hundreds), $8-5=3$ (Thousands).

Exercise 1: Subtract the following numbers without regrouping.

$9876 - 1234 = \underline{\hspace{2cm}}$

$7543 - 2101 = \underline{\hspace{2cm}}$

$6050 - 3020 = \underline{\hspace{2cm}}$

$4999 - 1888 = \underline{\hspace{2cm}}$

Subtraction with Regrouping (Borrowing)

Sometimes, the top digit in a column is smaller than the bottom digit. In such cases, we need to **regroup** or **borrow** from the next higher place value.

Example 2: Subtract $1234$ from $5000$.

Let's go step-by-step:

  1. Ones place: We cannot subtract $4$ from $0$. We need to borrow from the Tens place. But the Tens place is also $0$. So, we go to the Hundreds place, also $0$. We go to the Thousands place.
  2. Thousands place: Borrow $1$ from $5$ (Thousands), making it $4$. Give $10$ to the Hundreds place. Now Hundreds is $10$.
  3. Hundreds place: Borrow $1$ from $10$ (Hundreds), making it $9$. Give $10$ to the Tens place. Now Tens is $10$.
  4. Tens place: Borrow $1$ from $10$ (Tens), making it $9$. Give $10$ to the Ones place. Now Ones is $10$.
  5. Now subtract: 
        4 9 9 10  (after regrouping)
    5 0 0 0
-   1 2 3 4
----------
    3 7 6 6
    $10 - 4 = 6$ (Ones)
    $9 - 3 = 6$ (Tens)
    $9 - 2 = 7$ (Hundreds)
    $4 - 1 = 3$ (Thousands)

Exercise 2: Subtract the following numbers with regrouping.

$6321 - 1879 = \underline{\hspace{2cm}}$

$9000 - 4567 = \underline{\hspace{2cm}}$

$40000 - 12345 = \underline{\hspace{2cm}}$

$82005 - 37198 = \underline{\hspace{2cm}}$

Problem Solving with Subtraction

Subtraction is used in many real-life situations. Let's solve some word problems!

Exercise 3: Solve the following word problems.

  1. A library has $15,780$ books. If $8,525$ books are borrowed, how many books are left in the library?

  2. A farmer harvested $45,200$ kg of rice. He sold $28,950$ kg. How many kilograms of rice are remaining?

  3. The population of a town was $92,500$. If $17,800$ people moved out of the town, what is the current population?

Answers to Practice Time

Let's check your answers!

  1. Exercise 1: Subtraction without Regrouping

    • $9876 - 1234 = 8642$
    • $7543 - 2101 = 5442$
    • $6050 - 3020 = 3030$
    • $4999 - 1888 = 3111$

  2. Exercise 2: Subtraction with Regrouping

    • $6321 - 1879 = 4442$
    • $9000 - 4567 = 4433$
    • $40000 - 12345 = 27655$
    • $82005 - 37198 = 44807$

  3. Exercise 3: Problem Solving with Subtraction

    • $15,780 - 8,525 = 7,255$ books are left.
    • $45,200 - 28,950 = 16,250$ kg of rice are remaining.
    • $92,500 - 17,800 = 74,700$ is the current population.

You've completed Lesson 5!

Excellent work, Math Lanka students! You've successfully learned about subtraction, including regrouping and solving real-world problems. Keep practicing to become a subtraction master!

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