Calculate the Product: Solving 30 × 39 Step by Step

Q: Why break down 39 into (40-1) instead of just multiplying directly?

Breaking down 39 into (40-1) makes the math easier! It's much simpler to calculate 30×40=1,200 than to do long multiplication with 39. This technique works great with numbers close to round numbers.

Q: Can I break down 30 instead of 39?

Absolutely! You could write $ (3×10)×39 $ or even break down both numbers. The key is choosing the breakdown that makes the mental math easiest for you.

Q: How do I know when to add or subtract in the distributive property?

Look at the sign in your breakdown! Since we wrote 39 = (40-1), we subtract: 30×40 - 30×1. If we wrote 41 = (40+1), we'd add: 30×40 + 30×1.

Q: What if I get confused with the distributive property?

Remember the rule: multiply the outside number by everything inside the parentheses. So 30×(40-1) becomes (30×40) - (30×1). Keep the same operation that's inside!

Q: Is 1,170 really the right answer?

Yes! You can verify this by checking: 30×40 = 1,20030×1 = 301,200 - 30 = 1,170 Or use a calculator to confirm 30×39 = 1,170.

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:03 Let's use the distributive law

00:06 Let's break down 39 into 40 minus 1

00:12 Let's multiply each factor separately and subtract

00:26 Let's solve each multiplication and then subtract

00:35 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

1

Understand the problem

$30\times39=$

2

Step-by-step solution

To solving easier, we break down 39 into more convenient numbers, preferably round ones.

We obtain:

$30\times(40-1)=$

We multiply 30 by each of the terms in parentheses:

$(30\times40)-(30\times1)=$

We solve the exercises in parentheses and obtain:

$1,200-30=1,170$

3

Final Answer

1170

Key Points to Remember

Essential concepts to master this topic

Strategy: Break down complex numbers into easier parts to multiply
Technique: Rewrite 39 as (40-1) to get 30×(40-1)
Check: Verify 1,200 - 30 = 1,170 matches your final answer ✓

Common Mistakes

Avoid these frequent errors

Multiplying digits separately without proper place value
Don't multiply 3×3=9 and 0×9=0 to get 90! This ignores place values and gives completely wrong results. Always use the distributive property: 30×(40-1) = (30×40) - (30×1) = 1,200 - 30 = 1,170.

Practice Quiz

Test your knowledge with interactive questions

$$ 140-70= $$

FAQ

Everything you need to know about this question

Why break down 39 into (40-1) instead of just multiplying directly?

+

Breaking down 39 into (40-1) makes the math easier! It's much simpler to calculate 30×40=1,200 than to do long multiplication with 39. This technique works great with numbers close to round numbers.

Can I break down 30 instead of 39?

+

Absolutely! You could write $(3×10)×39$ or even break down both numbers. The key is choosing the breakdown that makes the mental math easiest for you.

How do I know when to add or subtract in the distributive property?

+

Look at the sign in your breakdown! Since we wrote 39 = (40-1), we subtract: 30×40 - 30×1. If we wrote 41 = (40+1), we'd add: 30×40 + 30×1.

What if I get confused with the distributive property?

+

Remember the rule: multiply the outside number by everything inside the parentheses. So 30×(40-1) becomes (30×40) - (30×1). Keep the same operation that's inside!

Is 1,170 really the right answer?

+

Yes! You can verify this by checking:

30×40 = 1,200
30×1 = 30
1,200 - 30 = 1,170

Or use a calculator to confirm 30×39 = 1,170.

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Calculate the Product: Solving 30 × 39 Step by Step

Multiplication using Distributive Property

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