# Multiplying 2-Digit Numbers by Multiples of 10

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## Multiplying 2-Digit Numbers by Multiples of 10 – Explanation

In this text, we will learn how to multiply 2-digit numbers by a multiple of 10. This skill will help us solve multiplication problems quickly and efficiently. We will explore different strategies and examples to understand this concept better.

When we multiply a number by a multiple of 10, the product will always have the same digits as the original number, but with one or more zeros written at the end. You might wonder why exactly this pattern occurs. This happens because multiplying by 10 means increasing the value of the number by ten times.

For example, if we multiply 25 by 10, the product will be 250. We can see that the digits 2 and 5 remain the same, but there is a zero at the end and the value of each digit has become 10 times more.

Let's look at another example. If we multiply 36 by 100, the product will be 3,600. Again, the digits 3 and 6 remain the same, but there are two zero at the end and the value of each digit has become 100 times more.

## Multiplying 2-Digit Numbers by Multiples of 10 – Strategies

There are a few strategies we can use to multiply 2-digit numbers by a multiple of 10:

• Using Mental Maths: If the multiple of 10 is a single-digit number, we can simply write the appropriate number of zeros at the end of the original number.

For example, to multiply 45 by 10, we write a zero at the end to get 450. This strategy is very helpful when multiplying by 10, 100, and 1000 but less helpful when multiplying by their multiples, such as 20, 300, 5000.

• Using Place Value: We can also use place value to multiply. We multiply the digit in the ones place of the original number by the multiple of 10. Then, we multiply the digit in the tens place by the multiple of 10 and write an additional zero. Finally, we add the two products together.

For example, to multiply 34 by 10, we multiply 4 by 10 to get 40, and multiply 30 by 10 to get 300. Then, we see that the values of each digit increased ten times, and we have a placeholder of 0 in the ones place

• Using the Distributive Property: Another strategy is to use the distributive property. We can break down the original number into its place value parts and multiply each part by the multiple of 10. Then, we add the products together.

For example, to multiply 27 by 50, we can break down 27 into 20 + 7. We multiply 20 by 50 to get 1,000, and multiply 7 by 50 to get 350. Finally, we add 1,000 and 350 to get 1,350.

## Multiplying 2-Digit Numbers by Multiples of 10 – Distributive Property Method

In exploring the concept of multiplication using the distributive property, an area model serves as an effective visual aid. In this approach, we decompose the factors into tens and ones, or their expanded form, and use these numbers to define the dimensions of a rectangle. The product of the multiplication is then represented by the total area of this rectangle.

Consider the example where we multiply fifteen (15) by seventy (70). First, we break down fifteen into its expanded form: ten (10) plus five (5). These values represent the sum of the lengths of the rectangle's sides. Next, we place seventy (70) as the width of the rectangle. Inside the rectangle, we apply multiplication for each part: 70 × 10. 70 × 10 gives us 700, and 70 × 5. 70 × 5 results in 350. By summing these areas – 700 and 350 – we find the total area, 1050, which is the product of our original equation.

## Multiplying 2-Digit Numbers by Multiples of 10 – Steps

In this example, we are going to show all the steps in detail of the multiplication process.

Let's explore the multiplication of 20 and 15 using distributive property and present it in an area model.

• First, we position the number twenty (20) along the left side of the area model, as this is our multiple of 10.

• Then, we decompose the number fifteen into its expanded form, which is ten plus five (10 + 5). This expanded form is placed along the top of the area model.

• In the area model, our first task is to multiply twenty by ten (20 × 10). In this step, we focus on the values of the numbers, disregarding the zeros temporarily. Multiplying two (from 20) by one (from 10) gives us two. Since the original numbers were ten times greater each, we need to increase the product (2) by 100. Thus, the product of twenty times ten is two hundred (20 × 10 = 200).

• Next, we move to multiplying twenty by five (20 × 5). Here, we multiply the natural numbers first: two times five, which equals ten. In this instance, one of the original numbers was 10 times greater, so we will need to make sure to increase the value of the product by 10 too. Therefore, the product of twenty times five is one hundred (20 × 5 = 100).

• Finally, we add the sub-products 200 and 100 and arrive at the final product 300.

## Multiplying 2-Digit Numbers by Multiples of 10 – Summary

• Multiplying 2-digit numbers by a multiple of 10 is a useful skill that allows us to solve multiplication problems quickly.
• We can use strategies like mental maths, place value, and the distributive property to find the product.
• Remember, when we multiply by a multiple of 10, the digits of the original number remain the same, additional zeros appear at the end of them and the new digits have a value 10 or 100 times the original.
• When using the distributive property method, follow the steps:
Step # What to do
1 Set up an area model with a multiple of 10 on the left side.
2 Rewrite the two-digit number in expanded form – write the expression on the top of the area model.
3 Multiply the natural numbers first – natural numbers are all counting numbers starting with one.
4 Add the products – add the newly calculated products to find the overall product.

## Frequently Asked Questions about Multiplying 2-Digit Numbers by Multiples of 10

How do we multiply a single number by ten?
What is an area model?
What are natural numbers?
What is the expanded form in maths?
How do we write a number in expanded form?

## Multiplying 2-Digit Numbers by Multiples of 10 exercise

Would you like to apply the knowledge you’ve learnt? You can review and practice it with the tasks for the video Multiplying 2-Digit Numbers by Multiples of 10.
• ### How would you write the number 24 in expanded form?

Hints

The 2 is in the tens place, so how many zeros are there?

The 4 is in the ones place. Are there any zeros in the ones place?

Solution

24 = 20 + 4

• There is a 2 in the tens place which means there are 2 tens, which equals 20.
• There is a 4 in the ones place which means there are 4 ones, which equals 4.
• ### Which image represents the correct area model?

Hints

Remember to set up your model with the number that is a multiple of 10 on the left side.

Write the second number in expanded form.

Solution

Multiply 20 and 32:

• Put 20 on the left-hand side
• Write 32 in expanded form
• Multiply the numbers

• ### Calculate how much rope Mr. Squeaks will use.

Hints

Remember to put the number that is a multiple of 10 on the left-hand side of the area model.

Next, write 42 in expanded form and set up your equations.

Solution

Multiply 20 and 42:

• Put 20 on the left-hand side.
• Write 42 in expanded form.
• Multiply the numbers together.
• Then add the number of zeros in the equation.
• Finally, add the partial products.
20 x 42 = 840

• ### How much cable wire does Mr. Squeaks need?

Hints

Create an area model with the 50 on the left-hand side.

Write 36 in expanded form.

Set up equations in the table by multiplying 50 with the expanded form of 36.

Solution

1,800 cm of cable wire is needed.

Multiply 50 and 36:

• Put 50 on the left-hand side.
• Write 36 in expanded form.
• Multiply the numbers together.
• Then add the number of zeros in the equation.
• Finally, add the partial products.

• ### What is your first step to setting up the area model?

Hints

What number do you put on the left-hand side?

After drawing a rectangle, this shows the first step.

Solution
• Once you have your equation of 30 x 45, put 30 on the left-hand side of the area model.*
• We would then write 45 in expanded form: 40 + 5.
• Multiply 30 x 40 to get 1,200.
• Multiply 30 x 5 to get 150.
• Add 1,200 + 150 = 1,350.
• Mr. Squeaks needs 1,350 pieces of wood.
• ### How much material is needed for the jackets?

Hints

You will set up two area models, one for small jackets and one for large jackets.

For the small jackets, multiply 30 x 22 like this.

Solution

For small jackets:

• Multiply 30 and 22:
• Put 30 on the left-hand side.
• Write 22 in expanded form.
• Multiply the numbers together.
• Then add the number of zeros in the equation.
• Finally, add the partial products to get 660 cm.
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For large jackets:

• Multiply 40 and 45:
• Put 40 on the left-hand side.
• Write 45 in expanded form.
• Multiply the numbers together.
• Then add the number of zeros in the equation.
• Finally, add the partial products to get 1,800 cm.