Find Equivalent Expressions: Solving 36×4 Multiplication

Q: How do I know which expression is equivalent?

Calculate the value of each option and compare! The original expression $ 36\times4 = 144 $, so find which choice also equals 144.

Q: Why does the distributive property work here?

Because 36 can be broken down into $ 30+6 $. Then $ 4\times(30+6) $ means multiply 4 by each part: $ 4\times30 + 4\times6 $.

Q: What's wrong with option d?

Option d forgets parentheses! $ 4\times30+6 $ means multiply first, then add: $ 120+6=126 $. But we need $ 4\times(30+6) $ with parentheses.

Q: Can I use other ways to break down 36?

Absolutely! You could write $ 36\times4 $ as $ 4\times(20+16) $ or $ 4\times(40-4) $. Any way that breaks 36 into two numbers works!

Q: How do I remember order of operations?

Use PEMDAS: Parentheses first, then Multiplication/Division left to right, then Addition/Subtraction left to right. Always do what's in parentheses before anything else!

Distributive Property with Multiplication Equivalence

Which equation is the same as the following?

$36\times4$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find the expression that represents the correct factorization of the exercise

00:03 Let's use the distributive law

00:06 Let's break down 36 into 30 plus 6

00:13 Let's use the commutative law and arrange the expression

00:16 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

Which equation is the same as the following?

$36\times4$

Step-by-step solution

We solve each of the options and keep in mind the order of operations: calculation of the operation within parentheses, multiplication and division (from left to right), addition and subtraction (from left to right).

$36+4=40$

$4\times(30+6)=4\times36$

$40-4+4=36+4=40$

$4\times30+6=120+6=126$

Therefore, the answer is option B.

Final Answer

$4\times(30+6)$

Key Points to Remember

Essential concepts to master this topic

Distributive Property: Multiplication over addition breaks down complex expressions
Technique: $4\times(30+6) = 4\times30 + 4\times6 = 120+24$
Check: Calculate both expressions to verify they equal 144 ✓

Common Mistakes

Avoid these frequent errors

Confusing addition with multiplication
Don't think 36+4 equals 36×4 = wrong operation entirely! Addition gives 40 while multiplication gives 144. Always identify whether you need to add values together or multiply them.

Practice Quiz

Test your knowledge with interactive questions

$$ 140-70= $$

FAQ

Everything you need to know about this question

How do I know which expression is equivalent?

Calculate the value of each option and compare! The original expression $36\times4 = 144$ , so find which choice also equals 144.

Why does the distributive property work here?

Because 36 can be broken down into $30+6$ . Then $4\times(30+6)$ means multiply 4 by each part: $4\times30 + 4\times6$ .

What's wrong with option d?

Option d forgets parentheses! $4\times30+6$ means multiply first, then add: $120+6=126$ . But we need $4\times(30+6)$ with parentheses.

Can I use other ways to break down 36?

Absolutely! You could write $36\times4$ as $4\times(20+16)$ or $4\times(40-4)$ . Any way that breaks 36 into two numbers works!

How do I remember order of operations?

Use PEMDAS: Parentheses first, then Multiplication/Division left to right, then Addition/Subtraction left to right. Always do what's in parentheses before anything else!

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