Calculate the Product: Solving 3×56 Step by Step

Q: Why break 56 into 50 + 6 instead of just multiplying directly?

Breaking numbers into friendly parts makes mental math much easier! Multiplying by 50 (or any multiple of 10) is simpler than multiplying by 56 directly.

Q: Can I break 56 into different parts, like 40 + 16?

Absolutely! You could use $ 3×(40+16) = 3×40 + 3×16 = 120 + 48 = 168 $. The key is choosing parts that are easy for you to multiply.

Q: How can I check if 168 is the right answer?

You can verify by working backwards: $ 168 ÷ 3 = 56 $, which matches our original problem! Or use a different method like repeated addition.

Q: Is there a faster way to multiply 3×56?

With practice, you might memorize that $ 3×56 = 168 $, but using the distributive property helps you understand why it works and builds stronger math skills!

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

00:07 Let's break down 56 into 50 plus 6

00:12 Multiply the outer factor by each term in parentheses

00:22 Solve each multiplication separately and then add

00:33 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

$3\times56=$

2

Step-by-step solution

In order to facilitate the resolution process, we break down 56 into an exercise with smaller, preferably round, numbers.

$3\times(50+6)=$

We use the distributive property and multiply each of the terms in parentheses by 3:

$(3\times50)+(3\times6)=$

We then solve each of the exercises inside of the parentheses and obtain the following result:

$150+18=168$

3

Final Answer

168

Key Points to Remember

Essential concepts to master this topic

Distributive Property: Break larger numbers into smaller, easier parts to multiply
Technique: Split 56 into 50 + 6, then calculate 3×50 + 3×6
Check: Verify 150 + 18 = 168 matches your final answer ✓

Common Mistakes

Avoid these frequent errors

Multiplying only part of the decomposed number
Don't multiply 3×50 and forget the 3×6 = incomplete calculation! This gives you only 150 instead of the correct 168. Always multiply by every part of the decomposed number and add all results together.

Practice Quiz

Test your knowledge with interactive questions

$$ 140-70= $$

FAQ

Everything you need to know about this question

Why break 56 into 50 + 6 instead of just multiplying directly?

+

Breaking numbers into friendly parts makes mental math much easier! Multiplying by 50 (or any multiple of 10) is simpler than multiplying by 56 directly.

Can I break 56 into different parts, like 40 + 16?

+

Absolutely! You could use $3×(40+16) = 3×40 + 3×16 = 120 + 48 = 168$ . The key is choosing parts that are easy for you to multiply.

What if I forget to add the two products together?

+

This is a common mistake! Always remember the distributive property has two steps: multiply each part, then add the results. Write it out: $150 + 18 = 168$

How can I check if 168 is the right answer?

+

You can verify by working backwards: $168 ÷ 3 = 56$ , which matches our original problem! Or use a different method like repeated addition.

Is there a faster way to multiply 3×56?

+

With practice, you might memorize that $3×56 = 168$ , but using the distributive property helps you understand why it works and builds stronger math skills!

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Calculate the Product: Solving 3×56 Step by Step

Multiplication with Distributive Property

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