How to Use Partial Products to Multiply Two-Digit Numbers By Two-digit Numbers

A Step-by-step Guide to Using Partial Products to Multiply Two-Digit Numbers By Two-digit Numbers

Here’s a step-by-step guide to using the Partial Products method to multiply two-digit numbers. We’ll use the problem (24×35) as an example.

Step 1: Break down the numbers into tens and ones

The first step is to break down both numbers into their tens and ones:

• 24 is broken down into (20+4)
• 35 is broken down into (30+5)

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Step 2: Multiply each part of the first number with each part of the second number

Now, you multiply each part of the first number with each part of the second number:

• 20 (from 24) (times30) (from 35) = 600
• 20 (from 24) (times5) (from 35) = 100
• 4 (from 24) (times30) (from 35) = 120
• 4 (from 24) (times5) (from 35) = 20

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Step 3: Add up all the products

Finally, add up all these products to get the final answer:
(600+100+120+20=840)
So, (24times35=840)

This method is called the Partial Products method because you are finding the product of parts of the numbers (the “partial products”) and then adding them together. This method helps students understand the concept of multiplication and the importance of place value. It can be a great stepping stone before learning more traditional multiplication algorithms.

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Partial Products With an Area Model

An area model is a box that keeps the four partial products organized. Let’s find 47 × 36.

Split 47 into 40 + 7 and 36 into 30 + 6. Put one number across the top and the other down the side, then multiply to fill each box.

Add the four boxes: 1,200 + 240 + 210 + 42 = 1,692. So 47 × 36 = 1,692.

The model works because of the distributive property: (40 + 7) × (30 + 6) means every part of one number gets multiplied by every part of the other. Each box is a small rectangle, and the whole box is the area of a 47 by 36 rectangle.

Common mistakes: forgetting the zero when you multiply tens (writing 40 × 30 = 120 instead of 1,200), skipping one of the four boxes, and adding the products before every box is filled in.

Partial Products Practice: 2-Digit by 2-Digit Answers

1. 13 × 22 = 200 + 20 + 60 + 6 = 286
2. 38 × 45 = 1,200 + 150 + 320 + 40 = 1,710
3. 56 × 27 = 1,000 + 350 + 120 + 42 = 1,512
4. 64 × 19 = 600 + 540 + 40 + 36 = 1,216

Try each one yourself before you look at the partial products. Then check your answer by estimating: 64 × 19 is close to 60 × 20 = 1,200, so 1,216 makes sense.

Frequently Asked Questions

How do you do partial products multiplication?

Break each factor into place-value parts, multiply every part of one factor by every part of the other, then add all the results. For 24 × 35, split into (20 + 4) × (30 + 5) and find 600, 100, 120 and 20. Their sum, 840, is the answer. Each smaller product is called a partial product.

How do you do partial products with 2 digits by 2 digits?

A 2-digit by 2-digit problem always has four partial products: tens × tens, tens × ones, ones × tens and ones × ones. For 42 × 28, find 40 × 20 = 800, 40 × 8 = 320, 2 × 20 = 40 and 2 × 8 = 16. Add them: 800 + 320 + 40 + 16 = 1,176.

How do you use partial products to multiply 48 by 71?

Split 48 into 40 + 8 and 71 into 70 + 1. Multiply each pair: 40 × 70 = 2,800, 40 × 1 = 40, 8 × 70 = 560 and 8 × 1 = 8. Add the four partial products: 2,800 + 40 + 560 + 8 = 3,408. So 48 × 71 = 3,408.

How do you use an area model and partial products to multiply two-digit numbers?

Draw a 2-by-2 box. Write the tens and ones of one number across the top and the other number down the side, then fill each box with the product of its row and column. For 47 × 36, the boxes hold 1,200, 240, 210 and 42. Adding them gives 1,692.

How do you use partial products to multiply 35 by 12?

Write 35 as 30 + 5 and 12 as 10 + 2. The four partial products are 30 × 10 = 300, 30 × 2 = 60, 5 × 10 = 50 and 5 × 2 = 10. Add them to get 420. A quick check: 35 × 12 is the same as 35 × 10 + 35 × 2 = 350 + 70 = 420.