Calculate the Product: 3 × 5 × 4 Step-by-Step

Q: Why can I change the order of multiplication but not addition problems?

The associative property works for multiplication because grouping doesn't change the result. $ 3 \times (5 \times 4) $ equals $ (3 \times 5) \times 4 $. This makes calculations easier!

Q: Should I always multiply from left to right?

Not necessarily! While left-to-right works, you can rearrange multiplication to make it easier. For example, $ 5 \times 4 = 20 $ is simpler than $ 3 \times 5 = 15 $.

Q: What's the difference between 3×5×4 and 3+5+4?

Multiplication (×) means repeated addition: $ 3 \times 5 \times 4 = 60 $. Addition (+) just combines: $ 3 + 5 + 4 = 12 $. Very different results!

Q: How do I know which numbers to group together?

Look for easier combinations! Numbers like 5×4=20, 2×5=10, or 3×4=12 are often simpler to calculate than other combinations. Practice will help you spot these quickly.

Q: Can I use a calculator for this?

While calculators help verify answers, practice mental math first! Understanding the associative property and grouping strategies will make you faster at all multiplication problems.

Multiplication Operations with Associative Property

$3\times5\times4=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:03 We'll use the commutative law and solve this multiplication first

00:09 We'll continue solving as usual

00:12 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

$3\times5\times4=$

Step-by-step solution

According to the order of operations, we must solve the exercise from left to right.

But, this can leave us with awkward or complicated numbers to calculate.

Since the entire exercise is a multiplication, you can use the associative property to reorganize the exercise:

3*5*4=

We will start by calculating the second exercise, so we will mark it with parentheses:

3*(5*4)=

3*(20)=

Now, we can easily solve the rest of the exercise:

3*20=60

Final Answer

Key Points to Remember

Essential concepts to master this topic

Order: Multiply from left to right or use associative property
Strategy: Group easier calculations like $5 \times 4 = 20$
Check: Verify by calculating left to right: $3 \times 5 = 15$ , then $15 \times 4 = 60$ ✓

Common Mistakes

Avoid these frequent errors

Adding instead of multiplying all terms
Don't calculate $3 + 5 + 4 = 12$ ! The × symbol means multiply, not add. Always multiply each number: $3 \times 5 \times 4 = 60$ .

Practice Quiz

Test your knowledge with interactive questions

$$ 94+12+6= $$

FAQ

Everything you need to know about this question

Why can I change the order of multiplication but not addition problems?

The associative property works for multiplication because grouping doesn't change the result. $3 \times (5 \times 4)$ equals $(3 \times 5) \times 4$ . This makes calculations easier!

Should I always multiply from left to right?

Not necessarily! While left-to-right works, you can rearrange multiplication to make it easier. For example, $5 \times 4 = 20$ is simpler than $3 \times 5 = 15$ .

What's the difference between 3×5×4 and 3+5+4?

Multiplication (×) means repeated addition: $3 \times 5 \times 4 = 60$ . Addition (+) just combines: $3 + 5 + 4 = 12$ . Very different results!

How do I know which numbers to group together?

Look for easier combinations! Numbers like 5×4=20, 2×5=10, or 3×4=12 are often simpler to calculate than other combinations. Practice will help you spot these quickly.

Can I use a calculator for this?

While calculators help verify answers, practice mental math first! Understanding the associative property and grouping strategies will make you faster at all multiplication problems.

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