Compare Expressions: Is 3+3+3+3 Equal to 3×4?

Q: Why does 3×4 equal 3+3+3+3?

Multiplication is just a shortcut for repeated addition! When you see $ 3 \times 4 $, it means "add 3 exactly 4 times" which gives you $ 3+3+3+3 $.

Q: How do I count how many times a number is being added?

Count each occurrence of the number being added. In $ 3+3+3+3 $, you have four 3's, so this equals $ 3 \times 4 $.

Q: Is 4×3 the same as 3×4?

Yes! Due to the commutative property, $ 4 \times 3 = 3 \times 4 = 12 $. You can think of it as either "4 added 3 times" or "3 added 4 times".

Q: Can I use this idea with other numbers?

Absolutely! For example, $ 5+5+5 = 5 \times 3 = 15 $ or $ 2+2+2+2+2+2 = 2 \times 6 = 12 $. Any repeated addition can be written as multiplication!

Multiplication as Repeated Addition

Are the expressions the same or not?

$3+3+3+3$

$3\times4$

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Step-by-step video solution

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00:00 Are the expressions equal?

00:02 Let's calculate both expressions

00:05 And this is the solution to the question

Step-by-step written solution

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Understand the problem

Are the expressions the same or not?

$3+3+3+3$

$3\times4$

Step-by-step solution

To solve this problem, we'll analyze the expressions $3+3+3+3$ and $3 \times 4$ to determine if they are equivalent.

First, evaluate the expression $3+3+3+3$ :

Add the numbers: $3 + 3 = 6$
Add again: $6 + 3 = 9$
Add the last $3$ : $9 + 3 = 12$

The result of $3+3+3+3$ is $12$ .

Next, evaluate the expression $3 \times 4$ :

Perform the multiplication: $3 \times 4 = 12$

The result of $3 \times 4$ is also $12$ .

Since both expressions result in the same number, we conclude that

The expressions are the same.

Therefore, the correct answer is Yes.

Final Answer

Yes

Key Points to Remember

Essential concepts to master this topic

Connection: Multiplication represents adding the same number multiple times
Technique: Count how many 3's are added: 3+3+3+3 has four 3's
Check: Both expressions equal 12, confirming they are equivalent ✓

Common Mistakes

Avoid these frequent errors

Thinking multiplication and repeated addition are different operations
Don't assume $3+3+3+3$ and $3\times4$ must be different = missing the fundamental connection! Multiplication IS repeated addition of the same number. Always recognize that $a \times b$ means adding 'a' exactly 'b' times.

Practice Quiz

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$3x+4x+7+2=\text{?}$

FAQ

Everything you need to know about this question

Why does 3×4 equal 3+3+3+3?

Multiplication is just a shortcut for repeated addition! When you see $3 \times 4$ , it means "add 3 exactly 4 times" which gives you $3+3+3+3$ .

How do I count how many times a number is being added?

Count each occurrence of the number being added. In $3+3+3+3$ , you have four 3's, so this equals $3 \times 4$ .

Is 4×3 the same as 3×4?

Yes! Due to the commutative property, $4 \times 3 = 3 \times 4 = 12$ . You can think of it as either "4 added 3 times" or "3 added 4 times".

What if I get different answers when I calculate each expression?

Double-check your addition! Make sure you're adding each 3 correctly: $3+3=6$ , then $6+3=9$ , then $9+3=12$ .

Can I use this idea with other numbers?

Absolutely! For example, $5+5+5 = 5 \times 3 = 15$ or $2+2+2+2+2+2 = 2 \times 6 = 12$ . Any repeated addition can be written as multiplication!

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