Solve: 1.23 × 110 Decimal Multiplication Problem

Q: Why use the distributive property instead of regular multiplication?

The distributive property makes decimal multiplication easier by breaking it into simpler parts! Instead of calculating $ 1.23 \times 110 $ directly, you solve two easier problems: $ 1.23 \times 100 $ and $ 1.23 \times 10 $.

Q: What if I get different numbers when I split up the multiplication?

Make sure you're splitting correctly! $ 110 = 100 + 10 $, so you should get 123 + 12.3. If your numbers don't add up to 135.3, double-check your decimal point placement.

Q: Can I use this method for any multiplication problem?

Yes! The distributive property works for all multiplication. It's especially helpful when one number ends in zeros (like 110, 120, 300) because you can break it into easier parts.

Decimal Multiplication with Distributive Property

$1.23\times110=\text{ ?}$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:03 Multiply each digit by each digit, and place in the appropriate position

00:07 Any number multiplied by 0 always equals 0

00:11 Move on to multiply by the next digit, place in the appropriate position

00:17 Any number multiplied by 1 always equals itself

00:25 Connect between the results

00:28 Move on to multiply by the next digit, place in the appropriate position

00:31 Any number multiplied by 1 always equals itself

00:35 Connect between the results

00:41 Count the sum of digits after the decimal point

00:45 Based on this sum, position the decimal point

00:54 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$1.23\times110=\text{ ?}$

Step-by-step solution

We will use the distributive property to split 110 into two numbers—100 and 10.

Now we will multiply the original number (1.23) by these two numbers:

1.23*100=123

1.23*10=12.3

All that is left to do is to add the two products together to get our answer:

123 + 12.3 = 135.3

Final Answer

$135.3$

Key Points to Remember

Essential concepts to master this topic

Rule: Use distributive property to break down complex multiplication problems
Technique: Split 110 into 100 + 10, then calculate 1.23 × 100 = 123 and 1.23 × 10 = 12.3
Check: Add partial products: 123 + 12.3 = 135.3 ✓

Common Mistakes

Avoid these frequent errors

Misplacing decimal points in partial products
Don't forget to count decimal places when multiplying = wrong final answer! Students often calculate 1.23 × 10 = 1.23 instead of 12.3. Always move the decimal point correctly: multiplying by 10 moves it one place right, by 100 moves it two places right.

Practice Quiz

Test your knowledge with interactive questions

$\text{0}.07\times10=$

FAQ

Everything you need to know about this question

Why use the distributive property instead of regular multiplication?

The distributive property makes decimal multiplication easier by breaking it into simpler parts! Instead of calculating $1.23 \times 110$ directly, you solve two easier problems: $1.23 \times 100$ and $1.23 \times 10$ .

How do I multiply a decimal by 100 or 10?

It's simple! When multiplying by 10, move the decimal point one place right. When multiplying by 100, move it two places right. So 1.23 × 100 = 123.0 = 123.

What if I get different numbers when I split up the multiplication?

Make sure you're splitting correctly! $110 = 100 + 10$ , so you should get 123 + 12.3. If your numbers don't add up to 135.3, double-check your decimal point placement.

Can I use this method for any multiplication problem?

Yes! The distributive property works for all multiplication. It's especially helpful when one number ends in zeros (like 110, 120, 300) because you can break it into easier parts.

How do I know my final answer is correct?

You can verify by doing the multiplication the traditional way, or by checking that your partial products add correctly. Also, estimate: $1.23 \times 110$ should be close to $1 \times 100 = 100$ , and 135.3 makes sense!

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