Partial products method

Quick answer

The partial products method is a way to multiply big numbers by breaking them into smaller parts, multiplying those parts, and then adding the results together.

Learning outcome

By the end of this page, you will be able to use the partial products method to multiply two-digit numbers by breaking them into tens and ones, multiplying each part, and adding the results.

• You can split a two-digit number into tens and ones.
• You can multiply each part using the times tables you know.
• You can add the products together to get your final answer.
• You can use this method to solve bigger multiplication problems.

Why this matters

Learning the partial products method helps you understand how multiplication works. It's a useful strategy for multiplying larger numbers, like 23 × 15, without needing to memorise complicated steps. You can use it when you're solving puzzles, helping with shopping, or even in games and sports!

How it works

Here's how to use the partial products method:

1. Break one of the numbers into tens and ones.
2. Multiply each part of that number by the other number.
3. Add all the products together.

This method helps you think about multiplication step by step. It's like solving a puzzle where each piece is smaller and easier to manage.

Examples you can see

Let's try a simple example: 23 × 15.

1. Split 23 into tens and ones: 20 + 3.
2. Multiply each part by 15:
   • 20 × 15 = 300
   • 3 × 15 = 45
3. Add the products: 300 + 45 = 345.

So, 23 × 15 = 345.

Here's another example with larger numbers: 47 × 23.

1. Split 47 into tens and ones: 40 + 7.
2. Multiply each part by 23:
   • 40 × 23 = 920
   • 7 × 23 = 161
3. Add the products: 920 + 161 = 1081.

So, 47 × 23 = 1081.

Try it as a mini adventure

Adventure: The Garden Shop Challenge

You're helping your parent or teacher at a garden shop. They need to count how many flower pots are in 12 rows, with 15 pots in each row. You can use the partial products method to solve this!

1. Split 15 into tens and ones: 10 + 5.
2. Multiply each part by 12:
   • 10 × 12 = 120
   • 5 × 12 = 60
3. Add the products: 120 + 60 = 180.

There are 180 flower pots in total. Great job!

Common mistakes

• Mistake: Forgetting to split one number into tens and ones.
• Why it happens: Not understanding that you need to break the number apart first.
• Fix: Always split one number into tens and ones before multiplying.

• Mistake: Adding the wrong products together.
• Why it happens: Mixing up the multiplication results.
• Fix: Double-check your multiplication and make sure you're adding the right numbers.

• Mistake: Forgetting to include all the products in the final addition.
• Why it happens: Rushing through the steps.
• Fix: Write down each step clearly and check that you've added all the products.

Parent and carer guide

Help your child understand the partial products method by:

1. Using everyday examples like counting groups of items.
2. Letting them practice with simple numbers first, like 12 × 13.
3. Encouraging them to write out each step clearly.
4. Checking their work together to make sure they didn’t skip any steps.
5. Reinforcing that it’s okay to make mistakes – it’s part of learning!

Don’t worry if they get confused at first. The partial products method takes a bit of practice, but it helps build strong multiplication skills.

Practice questions

1. Use the partial products method to find 14 × 12.
2. Use the partial products method to find 21 × 16.
3. Use the partial products method to find 32 × 13.
4. Use the partial products method to find 25 × 14.
5. Use the partial products method to find 18 × 17.

Answers:

1. 14 × 12 = (10 × 12) + (4 × 12) = 120 + 48 = 168
2. 21 × 16 = (20 × 16) + (1 × 16) = 320 + 16 = 336
3. 32 × 13 = (30 × 13) + (2 × 13) = 390 + 26 = 416
4. 25 × 14 = (20 × 14) + (5 × 14) = 280 + 70 = 350
5. 18 × 17 = (10 × 17) + (8 × 17) = 170 + 136 = 306

FAQ

What is the partial products method?

The partial products method is a way to multiply larger numbers by breaking one number into tens and ones, multiplying each part, and then adding the results together.

Why do we use the partial products method?

We use it to make multiplication easier to understand and solve, especially for larger numbers. It helps you see how multiplication works step by step.

Can I use this method with any numbers?

Yes, you can use the partial products method with any two-digit numbers. It works for bigger numbers too, but it's most helpful for numbers up to 99.

Is this method the same as the standard way?

No, it’s different from the standard way. The partial products method shows you how the multiplication is broken down, while the standard method is a faster way to write it out.

How can I practice this at home?

You can practice by solving multiplication problems with 2-digit numbers, using the partial products method. Try with numbers you see in your daily life, like the number of items in a box or the number of rows in a garden.