This grade 4 multiplication lesson explains multi-digit multiplication in one printable page, with definitions, a method and a worked example.
Multi-digit multiplication finds a product by splitting factors into place-value parts, multiplying each part, and adding the partial products. An area model shows each partial product as a smaller rectangle. For example, 24 × 36 = 600 + 120 + 120 + 24 = 864. Estimate first to check that an answer is reasonable.
Grade 4 Multiplication Lesson: key facts
- Split each factor by place value: 24 = 20 + 4.
- Multiply every part by every part to get partial products.
- Add all partial products to find the total.
- An area model shows each partial product as a rectangle.
- Estimate with rounded factors to check the answer.
What does multi-digit multiplication mean?
Multiplying finds the total in equal groups or the area of a rectangle. A rectangular array shows this clearly: 4 rows with 12 dots in each row is \(4 \times 12 = 48\).
A partial product is the product of one part of a factor and another. Because of the distributive property, we can split a number by place value, multiply each part, and add the results.
How do you multiply by a one-digit number?
Split the larger factor into hundreds, tens, and ones. Multiply each part by the one-digit factor, then add. For \(6 \times 345\), think \(345 = 300 + 40 + 5\).
Add the partial products: \(1{,}800 + 240 + 30 = 2{,}070\). So 6 × 345 = 2,070.
How do you multiply two two-digit numbers?
Split both factors by place value. This gives four partial products: tens times tens, tens times ones, ones times tens, and ones times ones.
- Write each factor as tens plus ones: \(24 = 20 + 4\) and \(36 = 30 + 6\).
- Multiply every part by every part: 600, 120, 120, 24.
- Add: \(600 + 120 + 120 + 24 = 864\).
Which properties make multiplying easier?
The commutative property lets you swap factors, and the associative property lets you regroup them. For example, \(5 \times 138\) can be seen as five equal parts of 138.
Why does splitting work? A number such as 345 is really 300 + 40 + 5, so multiplying each piece and adding keeps the total the same. This is the distributive property, and it works for any size of factor. Each partial product tells you how much of the rectangle each piece covers, which helps you notice a missing piece right away.
Always estimate first. Since 24 × 36 is close to \(20 \times 40 = 800\), the answer 864 is reasonable.
Multi-Digit Multiplication: frequently asked questions
What is a partial product?
It is the product of one place-value part of a number and another number or part. Adding all partial products gives the full product.
How does an area model help with multiplication?
It draws a rectangle whose sides are the place-value parts of the factors. Each smaller rectangle is one partial product, and the total area is the answer.
How many partial products are there for 2-digit by 2-digit numbers?
Usually four: tens times tens, tens times ones, ones times tens, and ones times ones. Zeros in a number reduce the count.
How can I check a multiplication answer?
Estimate by rounding each factor, or redo the problem by swapping the factors. If the answer is far from the estimate, look for a missing partial product.
Why does multiplying by 10 add a zero?
Each digit moves one place to the left and becomes worth ten times as much, so a zero is needed in the ones place to hold the places.
How to use this grade 4 multiplication lesson
Use this grade 4 multiplication lesson before the worksheet, then check what you learned with the quiz.
See every chapter on the Grade 4 math page.
