Solve 0×(60×10): Applying the Zero Property in Multiplication

Q: Do I need to solve what's inside the parentheses first?

Not when zero is involved! The zero property tells us that $ 0 \times \text{anything} = 0 $. You can skip calculating $ 60 \times 10 $ entirely.

Q: What if the zero was inside the parentheses instead?

Same result! For example, $ 5 \times (0 \times 10) = 5 \times 0 = 0 $. Anywhere you see zero in multiplication, the entire expression equals zero.

Q: Why does multiplying by zero always give zero?

Think of multiplication as repeated addition. Zero groups of anything, or anything taken zero times, means you have nothing at all!

Q: Does order matter when multiplying with zero?

No! $ 0 \times 5 = 0 $ and $ 5 \times 0 = 0 $ both equal zero. This is called the commutative property of multiplication.

Q: What about zero divided by a number?

$ 0 ÷ 5 = 0 $, but $ 5 ÷ 0 $ is undefined! Division by zero is never allowed in mathematics.

Zero Property with Parenthetical Expressions

$0\times(60\times10)=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:03 Always solve parentheses first

00:06 Any number multiplied by 0 is always equal to 0

00:13 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

$0\times(60\times10)=$

Step-by-step solution

To solve this problem, we'll focus on the properties of zero in multiplication:

Step 1: Identify the expression inside the parentheses: $60 \times 10$ .
Step 2: Recognize the importance of zero: Any number multiplied by zero equals zero.
Step 3: Apply the property: Since zero is multiplying the result from the parentheses, the entire expression is equal to zero.

To expand further, even though $60 \times 10 = 600$ , the term $0 \times 600$ evaluates to 0 because multiplying by zero always results in zero.

Therefore, the solution to the problem is $0$ .

Final Answer

Key Points to Remember

Essential concepts to master this topic

Zero Property: Any number multiplied by zero always equals zero
Technique: Recognize zero factor first: $0 \times (60 \times 10) = 0 \times 600 = 0$
Check: Even if parentheses equal 600, zero times anything is zero ✓

Common Mistakes

Avoid these frequent errors

Computing the parentheses first and then multiplying
Don't calculate 60 × 10 = 600 first, then 0 × 600 = 0! While this gives the right answer, it wastes time and misses the key insight. Always recognize that zero multiplied by anything equals zero immediately.

Practice Quiz

Test your knowledge with interactive questions

$1\times1000=$

FAQ

Everything you need to know about this question

Do I need to solve what's inside the parentheses first?

Not when zero is involved! The zero property tells us that $0 \times \text{anything} = 0$ . You can skip calculating $60 \times 10$ entirely.

What if the zero was inside the parentheses instead?

Same result! For example, $5 \times (0 \times 10) = 5 \times 0 = 0$ . Anywhere you see zero in multiplication, the entire expression equals zero.

Why does multiplying by zero always give zero?

Think of multiplication as repeated addition. Zero groups of anything, or anything taken zero times, means you have nothing at all!

Does order matter when multiplying with zero?

No! $0 \times 5 = 0$ and $5 \times 0 = 0$ both equal zero. This is called the commutative property of multiplication.

What about zero divided by a number?

$0 ÷ 5 = 0$ , but $5 ÷ 0$ is undefined! Division by zero is never allowed in mathematics.

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