Multi-Digit Multiplication

Big multiplication problems are just lots of small ones, done in the right order. Break the numbers apart, then let the Step Coach walk you through every step. No paper needed.

Start by breaking numbers apart below. Ready to go? Jump to the Step Coach or practice.

Break It Apart

First, a shortcut you'll use in every step: to multiply numbers that end in zeros, multiply the front digits, then tack on all the zeros.

4 × 3 = 12a basic fact

40 × 3 = 120one zero

40 × 30 = 1200two zeros

A big number is just its place-value parts added together: 47 = 40 + 7 and 26 = 20 + 6. So 47 × 26 is a rectangle cut into smaller pieces. Find each piece, then add them up.

Area Model Explorer

Tap each box to find its piece of the answer.

Notice the rows. The blue pieces are everything times the ones digit. The purple pieces are everything times the tens. The standard algorithm finds each of those rows, then adds them, just faster.

The Step Coach

The standard algorithm works one digit at a time, right to left. Choose Watch it to see every step explained, or Your turn to type each digit yourself. The coach checks every step as you go.

Estimate first so you know about how big the answer should be.

Multiply by the ones digit. Go right to left. When a product is 10 or more, write the ones and carry the tens.

Multiply by the tens digit. Start this row with a 0 in the ones place, because you're multiplying by tens.

Add the rows. Then check your answer against your estimate.

row 1: × onesrow 2: × tensadding the rows

Or try your own: ×

Spot the Mistake

Calc-U-Bot is learning to multiply, and it makes the same mistakes people do. Check its work. Which part went wrong, or did it get everything right?

Round 1 of 6Score: 0

I solved it! Did I get it right?

Let's Practice

Two activities. Aim for 80% or better on each to show you've mastered multi-digit multiplication.

Partial Products Pick

Zeros, carrying, estimating, and breaking numbers apart. Choose the best answer.

Question 1 of 10Score: 0

Solve It Yourself

No coaching this time. Tap a box, type digits with the keypad or your keyboard, and press Check. Carry boxes are there if you want them.

Problem 1 of 8Score: 0

Nice work! Multiplying multi-digit numbers is a skill you'll use for the rest of math. Head back to Whole Number Operations to keep going.