Solve for Missing Values: ?:9×?+26=26 Equation Challenge

Algebraic Equations with Zero Products

Fill in the missing values (?):

?:9×?+26=26 ?:9\times?+26=26

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:08 Let's find the unknowns that match. Ready?
00:11 Try each option and calculate the result. Easy steps.
00:22 Remember! Always do multiplication and division first, before adding or subtracting.
00:28 Did you know? Any number divided by itself equals 1. Think about that!
00:43 These don't match, so let's move on to the next ones. Keep going!
01:03 Here's a tip. Zero multiplied by any number is always zero.
01:12 Great! These match. Let's look at the next ones.
01:46 Time to calculate. You've got this!
01:56 These don't match. Let's try the next set.
02:02 Let's calculate and see what we find.
02:16 They don't match, but keep going. Almost there!
02:23 And there's your solution! Well done, you did it!

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Fill in the missing values (?):

?:9×?+26=26 ?:9\times?+26=26

2

Step-by-step solution

To solve this problem, let's carefully follow these steps:

First, examine the equation ?:9×?+26=26 ?:9 \times ? + 26 = 26 . To maintain equality at 26 on both sides, the multiplication component should give a product of zero since adding zero to 26 keeps it unchanged.

Let's break this down:

  • The structure of the equation implies ?:9×?=0 ?:9 \times ? = 0 . This tells us that the multiplication must result in zero for the equality to hold without changing the addition outcome.
  • To achieve 9×?=09 \times ? = 0, the second '?' must be 0 because 9×0=09 \times 0 = 0.
  • This means the first '?' is 9 itself, as this does not influence the multiplication involving zero.

By selecting these values, substituting back simplifies to:

  • 9:9×0+26=269:9 \times 0 + 26 = 26
  • This results in 0+26=260 + 26 = 26, confirming the equation holds true.

Thus, the correct values to fill in are 9 and 0, making the equation valid.

Therefore, the solution to the problem is 9,09, 0.

3

Final Answer

9, 0

Key Points to Remember

Essential concepts to master this topic
  • Zero Property: Any number multiplied by zero equals zero
  • Technique: Set multiplication part to zero: 9×0=0 9 \times 0 = 0
  • Check: Substitute values back: 9:9×0+26=0+26=26 9:9 \times 0 + 26 = 0 + 26 = 26

Common Mistakes

Avoid these frequent errors
  • Trying to make both question marks the same value
    Don't assume both ? must be identical = wrong answer like 9,1 or 9,2! The equation structure allows different values for each position. Always analyze what each ? position needs independently to satisfy the equation.

Practice Quiz

Test your knowledge with interactive questions

\( 2+0= \)

FAQ

Everything you need to know about this question

Why can't both question marks be the same number?

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The equation doesn't require both ? to be identical! Each ? serves a different purpose - one is part of a ratio, the other creates the zero product needed for the equation to balance.

How do I know which number goes where?

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Work backwards from the equation! Since we need ?×?+26=26 ? \times ? + 26 = 26 , the multiplication must equal zero. Only 9×0=0 9 \times 0 = 0 works.

What does the colon (:) mean in this equation?

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The colon represents a ratio or division. So 9:9 9:9 means "9 to 9" or "9 divided by 9", but it doesn't affect our main calculation here.

Could there be other correct answers?

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No - this equation has only one solution! Since we need the multiplication to equal zero, and we can't change the 9, the second ? must be 0.

Why is getting zero so important here?

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Because 0+26=26 0 + 26 = 26 ! If the multiplication gave any other number, adding 26 would make the left side not equal to 26 on the right side.

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