Solve the Equation: Finding Missing Factors in 40-?×?=40

Q: Why does the product have to equal zero?

For the equation $ 40 - ? \times ? = 40 $ to be true, subtracting the product shouldn't change 40. This only happens when the product equals zero!

Q: Do both numbers have to be zero?

No! In multiplication, if any factor is zero, the entire product is zero. So 0 × 3 = 0, 0 × (-5) = 0, and even 0 × 1000 = 0.

Q: What if I picked a different pair like (4, -5)?

Let's check: $ 4 \times (-5) = -20 $, so $ 40 - (-20) = 40 + 20 = 60 $. This doesn't equal 40, so it's incorrect.

Q: Are there other correct answers besides (0, 3)?

Yes! Any pair where one number is zero works: (0, 5), (0, -2), (7, 0), etc. The key is having at least one zero in the pair.

Q: How do I remember the zero property of multiplication?

Think of it this way: zero groups of anything is still zero. Whether you have 0 × 100 or 0 × 3, you're taking zero groups, so the result is always zero!

Multiplication Properties with Zero Factors

Fill in the missing values (?):

$40-?\times?=40$

❤️ Continue Your Math Journey!

We have hundreds of course questions with personalized recommendations + Account 100% premium

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find the suitable unknowns

00:03 We'll substitute each option and calculate, we want to get a multiple of 0

00:14 Always solve multiplication and division before addition and subtraction

00:19 Let's calculate

00:27 These unknowns don't fit, let's continue to the next ones

00:35 Let's calculate

00:42 These unknowns don't fit, let's continue to the next ones

00:51 0 multiplied by any number always equals 0

00:57 These unknowns fit, let's continue to the next ones

01:08 Let's calculate

01:12 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

Fill in the missing values (?):

$40-?\times?=40$

Step-by-step solution

To solve this problem, we'll follow these steps:

Step 1: Recognize that for the equation $40 - ? \times ? = 40$ to remain true, the term $? \times ?$ must equal zero.
Step 2: Use the property of multiplication by zero to identify the values of $?$ .
Step 3: Check each pair from the given choices against this requirement.

Now, let's evaluate each choice:

Choice (1): $4, -5$ results in $4 \times -5 = -20$ , thus $40 - (-20) = 60$ . Does not satisfy the equation.
Choice (2): $6, 3$ results in $6 \times 3 = 18$ , thus $40 - 18 = 22$ . Does not satisfy the equation.
Choice (3): $0, 3$ results in $0 \times 3 = 0$ , thus $40 - 0 = 40$ . Satisfies the equation.
Choice (4): $1, 20$ results in $1 \times 20 = 20$ , thus $40 - 20 = 20$ . Does not satisfy the equation.

Hence, the correct choice is the pair $0, 3$ as it satisfies the condition required by the equation.

Therefore, the missing values are $0, 3$ .

Final Answer

$0,3$

Key Points to Remember

Essential concepts to master this topic

Zero Property: Any number multiplied by zero equals zero
Technique: For 40 - ? × ? = 40, the product must equal 0
Check: Substitute back: 40 - (0 × 3) = 40 - 0 = 40 ✓

Common Mistakes

Avoid these frequent errors

Testing pairs without considering the zero property
Don't just multiply random pairs like 6 × 3 = 18, giving 40 - 18 = 22! This ignores that we need the original value 40. Always recognize that for 40 - ? × ? = 40, the product ? × ? must equal zero.

Practice Quiz

Test your knowledge with interactive questions

$1\times1000=$

FAQ

Everything you need to know about this question

Why does the product have to equal zero?

For the equation $40 - ? \times ? = 40$ to be true, subtracting the product shouldn't change 40. This only happens when the product equals zero!

Do both numbers have to be zero?

No! In multiplication, if any factor is zero, the entire product is zero. So 0 × 3 = 0, 0 × (-5) = 0, and even 0 × 1000 = 0.

What if I picked a different pair like (4, -5)?

Let's check: $4 \times (-5) = -20$ , so $40 - (-20) = 40 + 20 = 60$ . This doesn't equal 40, so it's incorrect.

Are there other correct answers besides (0, 3)?

Yes! Any pair where one number is zero works: (0, 5), (0, -2), (7, 0), etc. The key is having at least one zero in the pair.

How do I remember the zero property of multiplication?

Think of it this way: zero groups of anything is still zero. Whether you have 0 × 100 or 0 × 3, you're taking zero groups, so the result is always zero!

🌟 Unlock Your Math Potential

Get unlimited access to all 18 Order of operations for beginners questions, detailed video solutions, and personalized progress tracking.

📹

Unlimited Video Solutions

Step-by-step explanations for every problem

📊

Progress Analytics

Track your mastery across all topics

🚫

Ad-Free Learning

Focus on math without distractions

No credit card required • Cancel anytime