Solve the Equation: ? × ? + 67 = 67 Missing Numbers Challenge

Q: Why does the equation simplify to multiply by zero?

When you subtract 67 from both sides of $ ? \times ? + 67 = 67 $, you get $ ? \times ? = 0 $. This is the key step that shows the product must equal zero!

Q: Do both missing numbers have to be zero?

No! The zero-product property says at least one factor must be zero. So you could have 0 and any other number, like $ 0 \times 3 = 0 $ or $ 0 \times 100 = 0 $.

Q: How do I remember the zero-product property?

Think of it this way: "If a product is zero, something had to be zero." You can't multiply two non-zero numbers and get zero as the result!

Zero-Product Property with Missing Factors

Fill in the missing values (?):

$?\times?+67=67$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Identify the correct variables

00:03 Try each operation and check whether the result is a multiple of 0

00:08 Always solve multiplication and division before addition and subtraction

00:15 These variables are not compatible, let's continue to the next ones

00:21 Let's calculate

00:31 These variables are not compatible, let's continue to the next ones

00:38 0 multiplied by any number always equals 0

00:47 These variables are compatible, let's continue to the next ones

00:54 Let's calculate

01:00 Let's calculate, these variables are not compatible, let's continue to the next ones

01:05 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 (?):

$?\times?+67=67$

Step-by-step solution

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

Step 1: Recognize that the equation $? \times ? + 67 = 67$ simplifies to $? \times ? = 0$ .
Step 2: Apply the zero-product property, which implies that at least one of the terms multiplying equals zero.
Step 3: Check each answer choice to determine which contains zero as one of its elements.

Now, let's work through each step:
Step 1: The problem gives us the equation $? \times ? + 67 = 67$ , which simplifies to $? \times ? = 0$ since 67 plus zero equals 67.
Step 2: We apply the zero-product property: If $a \times b = 0$ , then $a = 0$ or $b = 0$ .
Step 3: Among the choices given, $0,3$ surely results in $0 \times 3 = 0$ . This fulfills the condition of the problem.

Therefore, the values to fill the missing digits in the equation are $0,3$ .

Final Answer

$0,3$

Key Points to Remember

Essential concepts to master this topic

Zero Product Rule: When product equals zero, at least one factor is zero
Simplification Technique: $? \times ? + 67 = 67$ becomes $? \times ? = 0$
Verification Check: Substitute back: $0 \times 3 + 67 = 0 + 67 = 67$ ✓

Common Mistakes

Avoid these frequent errors

Trying to find factors that multiply to 67
Don't look for numbers that multiply to give 67 = wrong equation! Students often forget to subtract 67 from both sides first. Always simplify the equation to $? \times ? = 0$ before applying the zero-product property.

Practice Quiz

Test your knowledge with interactive questions

$1\times1000=$

FAQ

Everything you need to know about this question

Why does the equation simplify to multiply by zero?

When you subtract 67 from both sides of $? \times ? + 67 = 67$ , you get $? \times ? = 0$ . This is the key step that shows the product must equal zero!

Do both missing numbers have to be zero?

No! The zero-product property says at least one factor must be zero. So you could have 0 and any other number, like $0 \times 3 = 0$ or $0 \times 100 = 0$ .

What if I chose a different pair with zero?

Any pair with zero works mathematically! However, you must choose from the given answer choices. Among the options, only $0, 3$ contains zero.

Can negative numbers work in this problem?

Negative numbers can multiply to give zero only if one of them is zero. For example, $-5 \times 0 = 0$ , but $-5 \times 2 = -10 \neq 0$ .

How do I remember the zero-product property?

Think of it this way: "If a product is zero, something had to be zero." You can't multiply two non-zero numbers and get zero as the result!

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