Mastering the Four Big Operations!

Hello, Super Mathematician! Get ready to power up your brain because in this chapter, we're going to become experts at the four arithmetic operations: addition, subtraction, multiplication, and division, even with larger numbers!

Why is this important? Well, these skills are like superpowers you use every day! You use them when you're counting your savings, sharing sweets with friends, figuring out scores in a game, or solving multi-step word problems. Let's get started!


1. Multiplication with Multi-Digit Numbers

Multiplication is a fast way of doing repeated addition. In Primary 4, we multiply numbers up to 4 digits by a 1-digit number, and up to 3 digits by a 2-digit number.

Part A: Multiplying by a 1-Digit Number

We use the column method to keep our place values neat and tidy.

Step-by-Step: Multiplying 345 by 3

Let's calculate \(345 \times 3\).

  1. Set it up: Line up the digits in their place value columns (ones, tens, hundreds).

      345
    x    3
    -----

  2. Multiply the Ones: Multiply the ones digit: \(3 \times 5 = 15\). Write 5 in the ones place and regroup (carry over) 1 ten to the tens column.

      1
      345
    x    3
    -----
         5

  3. Multiply the Tens: Multiply the tens digit: \(3 \times 4 = 12\). Add the regrouped 1 ten: \(12 + 1 = 13\). Write 3 in the tens place and regroup 1 hundred.

     11
      345
    x    3
    -----
        35

  4. Multiply the Hundreds: Multiply the hundreds digit: \(3 \times 3 = 9\). Add the regrouped 1 hundred: \(9 + 1 = 10\). Write 10 in front.

     11
      345
    x    3
    -----
     1035

So, \(345 \times 3 = 1035\). The same method works for 4-digit numbers!

Part B: Multiplying by a 2-Digit Number

When multiplying by a 2-digit number, we break it into two smaller multiplication steps and add the results.

Step-by-Step: Multiplying 134 by 12

Let's calculate \(134 \times 12\).

  1. Multiply by the Ones Digit: First multiply \(134 \times 2 = 268\).

      134
    x  12
    -----
      268  (This is 134 x 2)

  2. Multiply by the Tens Digit: Next multiply 134 by 1 ten (10). Put a placeholder zero in the ones place first, then calculate \(134 \times 1 = 134\).

      134
    x  12
    -----
      268
     1340  (This is 134 x 10)

  3. Add Them Up: Add the two partial products together: \(268 + 1340 = 1608\).

      134
    x  12
    -----
      268
    + 1340
    -----
     1608

Common Mistake to Avoid: Always remember the placeholder zero when multiplying by the tens digit!


2. Long Division by a 1-Digit Number

Division means sharing equally or finding how many groups can be made. In Primary 4, we divide numbers up to 4 digits by a 1-digit number.

Remember the Steps:

Use the handy phrase Does McDonald's Sell Burgers?

  • Divide

  • Multiply

  • Subtract

  • Bring down

Step-by-Step: Dividing 924 by 4

Let's calculate \(924 \div 4\).

  1. Divide Hundreds: \(9 \div 4 = 2\) with a remainder of 1. Write 2 on top in the hundreds place.

  2. Multiply & Subtract: \(2 \times 4 = 8\). Subtract: \(9 - 8 = 1\).

  3. Bring Down: Bring down the tens digit 2 to make 12.

  4. Divide Tens: \(12 \div 4 = 3\). Write 3 on top. \(3 \times 4 = 12\). Subtract: \(12 - 12 = 0\).

  5. Bring Down & Divide Ones: Bring down the 4. \(4 \div 4 = 1\). Write 1 on top. Subtract: \(4 - 4 = 0\).

So, \(924 \div 4 = 231\).

What About Leftovers? (Remainders)

When a number does not divide evenly, the leftover part is the remainder.

Example: \(925 \div 4 = 231\text{ R }1\). Here, the quotient is 231 and the remainder is 1.


3. Solving Multi-Step Word Problems

Word problems often require combining addition, subtraction, multiplication, or division in up to 3 steps.

Tips for Solving:

  • Read the problem carefully and identify what is given and what you need to find.

  • Draw a model (bar model) to visualise the relationships between quantities.

  • Write clear mathematical equations and include units in your final answer.


4. Estimation: Your Secret Weapon!

Estimation means finding a value that is close to the exact answer. It helps you check if your final calculated answer is reasonable.

We estimate by rounding numbers to the nearest 10 or 100 before calculating.

Example: Estimating an Addition

Problem: \(489 + 312\)
Round each number to the nearest hundred: 489 rounds to 500, and 312 rounds to 300.
Estimated answer: \(500 + 300 = 800\)
(The exact answer is 801, showing our calculation makes sense!)

Example: Estimating a Multiplication

Problem: \(48 \times 19\)
Round each number to the nearest ten: 48 rounds to 50, and 19 rounds to 20.
Estimated answer: \(50 \times 20 = 1000\)
(The exact answer is 912.)

Key Takeaway: Estimation helps you catch careless mistakes quickly. If your exact answer is far away from your estimate, check your calculation steps again!