Multi-Digit Multiplication

✖️ Multi-Digit Multiplication

When numbers get bigger, you cannot always solve them in your head. Instead, you use a step-by-step method called the standard algorithm. It breaks one big problem into a few small, easy multiplication facts.

The Big Idea

Multiplication is just a fast way of adding equal groups.

• $4 \times 23$ means "4 groups of 23."
• Instead of adding $23 + 23 + 23 + 23$, you multiply.

The secret to large numbers is to multiply one digit at a time, always working from right to left, and to carry when a product is 10 or more.

Place Value Is Your Friend

Every digit lives in a column: ones, tens, hundreds. Keeping digits lined up in their columns is what makes the algorithm work.

Hundreds	Tens	Ones
	2	3

The $2$ is really 2 tens (20) and the $3$ is 3 ones. We multiply each part and put it back together.

Multiplying by One Digit

Let's multiply $23 \times 4$.

Step 1 — Multiply the ones. $3 \times 4 = 12$. That is too big for one column, so write the 2 and carry the 1 to the tens.

Step 2 — Multiply the tens. $2 \times 4 = 8$, then : . Write the 9.

Multiplying by Two Digits

When the bottom number has two digits, you multiply twice and then add.

Example: $34 \times 26$

1. Multiply by the ones digit (6): $34 \times 6 = 204$
2. Multiply by the tens digit (2): $34 \times 2 = 68$. Because the 2 means , you , so it becomes .

Concept Check 🎯

Make sure the core idea makes sense before we practice.

📝 Worked Examples

Let's slow down and watch every step.

Example 1: $46 \times 3$ (one digit)

Step 1 — Ones: $6 \times 3 = 18$. Write 8, carry 1.

Step 2 — Tens: $4 \times 3 = 12$, plus the carried . Since there are no more digits, write in front.

🧭 Guided Practice

Work through each problem carefully. Use the standard algorithm and check with estimation.

Build the Algorithm 🔍

Choose the correct words to complete the rules of multi-digit multiplication.

🌍 Real-World Multiplication

Multiplication shows up everywhere in daily life. The trick is spotting the equal groups.

Shopping

If one toy costs $24 and you buy $15$ toys, the total is $24 \times 15 = 360$, i.e. $360.

Area

A garden is $18$ feet long and $12$ feet wide. Its area is square feet.

🏆 Review & Challenge

You now have all the tools for multi-digit multiplication. Here is the whole method in one place.

The Standard Algorithm, Step by Step

Step	What to Do	Why
1	Start at the ones place on the right	Carrying flows left
2	Carry when a product is 10 or more	Keeps each column under 10
3	Shift left for the tens digit (write a 0)	The tens digit means tens
4	Add all partial products	Combines the equal groups
5	Estimate to check	Catches mistakes

Remember

• Line up your columns carefully — ones under ones, tens under tens.
• Shift one place left when you multiply by the tens digit.
• Estimate first so a wrong answer stands out.

You've got this! 🌟

Mixed Challenge 📋

Pull together everything you've learned.