Solve the Equation: 25+?:?=25 with Missing Values

Q: Why can't the first missing value be anything other than 0?

Because we need $ 25 + ? = 25 $ to be true. Only when we add zero does a number stay the same. Any other number would change the result!

Q: Does it matter what the second missing value is?

As long as it's not zero, any number works! Since $ 0 ÷ \text{anything} = 0 $, we get the same result whether we use 4, 5, 10, or any other nonzero number.

Q: What if I put 5,5 like in choice B?

Let's check: $ 25 + 5 : 5 = 25 + 1 = 26 $. This doesn't equal 25, so it's wrong! The equation becomes unbalanced.

Q: How do I remember the order of operations?

Use PEMDAS: Parentheses, Exponents, Multiplication/Division (left to right), Addition/Subtraction (left to right). Division comes before addition!

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Identify the correct unknown values

00:03 Test each sign until the result comes out as 0

00:07 Always solve multiplication and division before addition and subtraction

00:12 0 divided by any number always equals 0

00:18 These unknowns are compatible, let's continue to the next ones

00:29 Any number divided by itself always equals 1

00:39 These unknowns are not compatible, let's continue to the next ones

00:52 Let's calculate, these unknowns are not compatible, let's continue to the next ones

01:10 Division by 0 is not allowed, therefore it's not possible

01:18 This is the solution

Step-by-step written solution

Follow each step carefully to understand the complete solution

1

Understand the problem

Fill in the missing values (?):

$25+?:?=25$

2

Step-by-step solution

To solve this problem, we need to find the missing values that satisfy the equation $25 + ? : ? = 25$ . Let's analyze each operation involved in this expression:

Addition: The sum of any number and 0 is the original number, i.e., $a + 0 = a$ .
Division: A number divided by 1 remains unchanged, i.e., $a : 1 = a$ .

Let’s apply these properties step by step.

Step 1: Assume the first missing value is 0. This transforms the equation to $25 + 0 : ? = 25$ .
Step 2: Simplifying, we are left with $25 + (0 : ?) = 25$ .
Step 3: The term $0 : ?$ results in 0 for any nonzero divisor. Therefore, we effectively have $25 + 0 = 25$ , which is true for any value of the second placeholder as 1 (since $0 : 4 = 0$ also holds).

After analyzing, let's verify the given choices. The choice $0,4$ fits the criteria:

The first value, 0, ensures the sum does not change $(25 + 0 = 25)$ .
The second value, 4, ensures division results in zero which corresponds with $0$ .

Thus, the missing values are indeed correctly filled by $0,4$ .

Therefore, the solution to the problem is:

$0,4$

3

Final Answer

$0,4$

Key Points to Remember

Essential concepts to master this topic

Identity Rule: Adding zero keeps the original number unchanged
Technique: Zero divided by any nonzero number equals zero
Check: Substitute values: $25 + 0 : 4 = 25 + 0 = 25$ ✓

Common Mistakes

Avoid these frequent errors

Ignoring order of operations when solving
Don't solve left to right without following PEMDAS = wrong equation structure! Division must be performed before addition according to order of operations. Always evaluate the division $0 : 4$ first, then add to 25.

Practice Quiz

Test your knowledge with interactive questions

$1\times1000=$

FAQ

Everything you need to know about this question

Why can't the first missing value be anything other than 0?

+

Because we need $25 + ? = 25$ to be true. Only when we add zero does a number stay the same. Any other number would change the result!

Does it matter what the second missing value is?

+

As long as it's not zero, any number works! Since $0 ÷ \text{anything} = 0$ , we get the same result whether we use 4, 5, 10, or any other nonzero number.

What if I put 5,5 like in choice B?

+

Let's check: $25 + 5 : 5 = 25 + 1 = 26$ . This doesn't equal 25, so it's wrong! The equation becomes unbalanced.

How do I remember the order of operations?

+

Use PEMDAS: Parentheses, Exponents, Multiplication/Division (left to right), Addition/Subtraction (left to right). Division comes before addition!

Can I work backwards from the answer?

+

Yes! Since we want the final result to be 25, and we start with 25, whatever we add must equal zero. This means our division $? : ?$ must equal 0.

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Solve the Equation: 25+?:?=25 with Missing Values

Order of Operations with Missing Values

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