Solve (400+20)×(4+1): Finding Equivalent Expressions

Q: Why can't I just distribute the multiplication first?

The parentheses tell us to add first! When you see $ (400+20)\times(4+1) $, the parentheses group the additions together. You must complete these additions before multiplying.

Q: What if I get confused about which operation to do first?

Remember PEMDAS! Parentheses always come first. Solve everything inside parentheses, then move to the next operation (multiplication in this case).

Q: What's the final numerical answer to check my work?

$ 420\times5 = 2100 $. You can verify this matches your original expression by calculating $ (400+20)\times(4+1) = 420\times5 = 2100 $ ✓

Order of Operations with Parenthetical Expressions

Which equation is the same as the following?

$(400+20)\times(4+1)$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:08 Let's find the expression that correctly breaks down the exercise. Ready? Let's go!

00:14 First, solve inside the parentheses to find the expression. Take it step by step.

00:20 Great job! And that's the solution to our question.

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Which equation is the same as the following?

$(400+20)\times(4+1)$

Step-by-step solution

Let's consider that each set of parentheses represent a number.

That is, if we solve the exercises within parentheses we will obtain a multiplication exercise of two numbers.

We solve each of the exercises within parentheses to reveal what the numbers are:

$400+20=420$

$4+1=5$

That is, the exercise we obtained is the multiplication between two numbers:

$420\times5$

Final Answer

$420\times5$

Key Points to Remember

Essential concepts to master this topic

Rule: Always solve parentheses first before multiplying the results
Technique: Calculate $400+20=420$ and $4+1=5$ separately
Check: Final expression $420\times5$ equals 2100 ✓

Common Mistakes

Avoid these frequent errors

Multiplying before solving parentheses
Don't multiply 400×4 and 20×1 separately = wrong order! This ignores the parentheses grouping and gives incorrect results. Always solve what's inside parentheses first, then multiply the complete results.

Practice Quiz

Test your knowledge with interactive questions

$$ 140-70= $$

FAQ

Everything you need to know about this question

Why can't I just distribute the multiplication first?

The parentheses tell us to add first! When you see $(400+20)\times(4+1)$ , the parentheses group the additions together. You must complete these additions before multiplying.

What if I get confused about which operation to do first?

Remember PEMDAS! Parentheses always come first. Solve everything inside parentheses, then move to the next operation (multiplication in this case).

How do I know which answer choice matches my result?

After solving the parentheses, you get two simple numbers to multiply: 420 and 5. Look for the answer choice that shows exactly $420\times5$ .

Can I use the distributive property instead?

Not directly! The distributive property works for expressions like $a(b+c)$ , but here you have $(a+b)\times(c+d)$ . You need to simplify each parentheses first.

What's the final numerical answer to check my work?

$420\times5 = 2100$ . You can verify this matches your original expression by calculating $(400+20)\times(4+1) = 420\times5 = 2100$ ✓

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